(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 233907, 5150] NotebookOptionsPosition[ 211899, 4693] NotebookOutlinePosition[ 229314, 5013] CellTagsIndexPosition[ 229234, 5008] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[TextData[{ StyleBox[" ", FontSize->14], "\[LineSeparator]Jak povzbudit z\[AAcute]jem student\:016f \[LineSeparator]o \ matematiku?" }], "Title", CellChangeTimes->{{3.440000808*^9, 3.440000821890625*^9}, 3.440179672703125*^9, 3.44022051090625*^9, 3.440220549484375*^9, 3.440220760140625*^9, 3.44022082925*^9, {3.44480429778125*^9, 3.44480431740625*^9}, {3.444922591203125*^9, 3.44492261878125*^9}, { 3.444922685203125*^9, 3.44492268709375*^9}, {3.448948847546875*^9, 3.448948847921875*^9}, {3.448956659859375*^9, 3.448956684890625*^9}, { 3.449154028578125*^9, 3.449154051734375*^9}, 3.44915408328125*^9}, TextAlignment->Center], Cell[TextData[{ "\nAnton\[IAcute]n Slav\[IAcute]k\nMatematicko-fyzik\[AAcute]ln\[IAcute] \ fakulta UK\n", StyleBox["slavik@karlin.mff.cuni.cz", FontFamily->"Courier New"] }], "Subtitle", CellChangeTimes->{{3.440179682015625*^9, 3.440179688375*^9}, { 3.44022083796875*^9, 3.44022084571875*^9}, 3.444922632921875*^9, { 3.449036806265625*^9, 3.449036839140625*^9}}, TextAlignment->Center, FontColor->GrayLevel[0]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Fibonacciova \[CHacek]\[IAcute]sla", "Section", CellChangeTimes->{{3.43988196128125*^9, 3.43988197603125*^9}, { 3.439884632796875*^9, 3.439884632921875*^9}, {3.439988280046875*^9, 3.4399882845625*^9}, {3.444804443515625*^9, 3.444804450765625*^9}, { 3.44894891940625*^9, 3.448948925609375*^9}}], Cell[CellGroupData[{ Cell["\[CapitalUAcute]loha o kr\[AAcute]l\[IAcute]c\[IAcute]ch", "Subsection", CellChangeTimes->{{3.4449120814375*^9, 3.444912092078125*^9}, { 3.444922216109375*^9, 3.444922220046875*^9}, {3.448948950765625*^9, 3.4489489559375*^9}}], Cell[TextData[{ "Leonardo Pis\[AAcute]nsk\[YAcute] (Fibonacci, 1202):\nM\[AAcute]me jeden p\ \[AAcute]r mlad\[YAcute]ch kr\[AAcute]l\[IAcute]k\:016f. Ka\:017ed\[YAcute] \ kr\[AAcute]l\[IAcute]k dosp\[IAcute]v\[AAcute] za jeden m\:011bs\[IAcute]c, \ dosp\:011bl\[EAcute]mu p\[AAcute]ru se ka\:017ed\[YAcute] m\:011bs\[IAcute]c \ narod\[IAcute] dal\[SHacek]\[IAcute] p\[AAcute]r \ kr\[AAcute]l\[IAcute]k\:016f. Kolik p\[AAcute]r\:016f budeme m\[IAcute]t po ", Cell[BoxData[ FormBox["n", TraditionalForm]]], " m\:011bs\[IAcute]c\[IAcute]ch?" }], "Text", CellChangeTimes->{{3.44894910921875*^9, 3.448949221140625*^9}, { 3.449151801625*^9, 3.4491518561875*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"grf", "=", GraphicsBox[RasterBox[CompressedData[" 1:eJy1lmlQU1cUx53px37qp37pMq0zbXXcKm6ASNhCQvaFhISwJEDYEgKJBJJI wr6IQhQUqURAQdwiotJREbVg3Ypa7YhWZRCwEtZGoYRs7/W8h1IFsa2d3ryb d++bd3/nf88999z3hUTBlnywaNGiz6F+BhVro/9bcS9QXHiZ7cKbCAL/CNyg zLyw0NhZBl4RlxvFX3W63YgbAG4UuwEKdQNq2mYbfvZkuL/bOtzzwjricroQ GIE4cAI2FowjuNkZ6GwD2IgbY7tQ1wwOOpOTNovFcv/+vc7OjtMtx0vytMbC jKry/M72NsvAoMPufDUdZGb6OM01S8bNQbW7pyes4xbL0EBPz8Pr16+dOtFS VVmZnaVTqxSFuboG0y6DKiVFIjIW5HR1/nCn68bg09/cmAr0uXXsWufF61cu DQ0POJw2bMowC8xZONk1bentbqyuUCZKuRQymeAXK+DLogXRobT4CHapQWUy FkVyaPEiYW3FjuMHTfl65dnTzQ67wzY9ffxw4/49xo72EyNjfU7XHzgZYyK4 Y6EM9fXka9PIvutWLP6UTyUa83Tb9SqNLFKTFFmkS0uNF5MIXsRNXsrEWHPD Xn267Hyr2TFpbaytMZYWPbh32+W0IYhz1hu4WvvMErhsE82NNZGcEB4tIFst ryo1VBRqi3UKXYo4MyWOTSWuXfENXFxacO3ucnPjvktnTrQeazJVGs2HGsbH R7A1f7PgZGCjTtvEnrLCcBYpJU6Um5lalqvN1yoMm5PlkjBxGEvEZaxfuXTN 8q/DGORqY0n7KXPLwfrayvJDdaZzrSenpyYwdW8jw0q8GB/OVqfIY4Q5GSmq xOjEKJ40gisOo3MpfuEcCj3Yb/2qpX5eazRpSWUF+sN11Vfav+88e7rVfPhq xwWHfep1P7wMj5cBjzjs0/WmPdnq1MxkqTiMLRZwQGo4m8qlBPEZ5E3rv/Ve syKUToqJ4GWpFeWF2ccbajvOnLpyqa377m379FvIf4lH0WtXOvI0m5WxYhGH HsaiCllUZnAAPYhAJxJ8N6wO9FlPC/INZZC1KnmxQVu3a0frkcazJ4/dvHbZ bptE5nnjdfJA3+NivUadECdgUniMED6NzAz2p/j7ABCwBE+PoE0bwrn0LekK IJflGapKC/fu3Np8aP/o4ACKk9+65YE8PDhQmrMFNPPpZDYliEcNZhL9ZsjU IF8gBxO8RDymIkGiSU3OlCdqZNJMeWzD3sq7P/04NfEcsDabbT4cyNax0Z1b i9WyxGgem88I4QKZFEAN3ARkkp83YFnkAHC1NEoQyWMKWFRtalKSRJgQLagq LzE31d/pumqbfIFlCfcbEYjtdIf96MEGWaxEGiHgUIhUIkEUymCFBIJgoq8n NCCY4QmNSNi4diWYELCpfGaI5+plwX7eYUwShM3Q0z48f86LbRSxPHuarctQ JMSGscDVmE8g3rC1IxKgAShoeK1eDoagCxaFHBqD5O/lsTzAy4NDCey62oli 2WwuGVYAHreda9Wp0+KjhSAPUGIhNzaCDwS4OFQiWAHBwAcs2X8jmAYyOIpE 8KT4e3debFuIjKDuqanJutqaDKVcJYuLjxLI4qL0GWn5WRm5uvTNMimgQLDP ulUQ4R7Lvlry5ScQkAyyP59G0iqSnzz6FSPPB79aytHR0fp9NTk6tS49VSmL l8dLCrN1u42lZcV5cqk4IpQBfHDvqiWLP/7oQ1CeKBGlSiVl+bmT1nFkYTKE DZZ1fx9rbTFvK84vyMnSqlWa9LTtxQVHmw4cMFVH8Vkw/YCN68APIBjckpGa lK3dXG+qdjlsr50mCyiHs8rlGBkafND9y62uGz/f6urv7RkbGZq0jm3Ny4Ig lISHxoh4ybGRaUkx2wsMu3Zue/i4GxLbu7Ez2vEFRd48kLFuxfYCsq93BJeZ qUwEqSV5hsa6mqf9vSiKvCN7/M1EUHR8dCQmnMEj+wd5b9BrUkoLDPWm76zj o+/4DPiH5MsXL/Ip3skiJjeElKdXk/x8inL0eNZ/T7Wz5LaTJ2PYBFUMM12W dPP6ZRY5UBwhHB8bnnek/HvNF87HhwYqo+lHDtRBtzBnCzMkuPvuLfS90Mir 7yJA9T56kBDO1CSI+nofYYY62hlBAaeaj83x89/G3hwylrWcdkOmcndZERz6 QIM8wySTzEea3o88Z0hfX59lcBDPDy673d5Yv7+/v9/932LDje1QzCkgFxrw c+IbFrat3TV3j/wJ+6Y4uw== "], {{0, 0}, {54., 55.800000000000004`}}, {0, 255}, ColorFunction->RGBColor], ImageSize->{54., 54.}, PlotRange->{{0, 54.}, {0, 55.800000000000004`}}]}], ";"}], "\n", RowBox[{ RowBox[{"grm", "=", GraphicsBox[RasterBox[CompressedData[" 1:eJy1VmlTU1cYdqZ/oB/6sdMZ+0WndS9MkCUhCSGE7DcrMYGQxCSELZAFhECU BioIArURAyrFDcEVCsUFxYrjVi2LgYhiFaWugEDIfnPTk6DWguMynb659865 uec+73Oe9zn3nKWSbEjy2ZIlS756dQbbgf8t/O8LGIQf/Lwen9vhcdndLsfC x6DD67sFLyMI8qaBICBRAPaDa+hPxAcO55xz/MHo0M0Lf1zuunH1wqOHYxOT E3b7tNvtgn0ga8CPzPcP5vjnXT/8BhmGvW63Y/rl5NTEC4/HNc/CPjP358jd i91nqkuLijVKo17derDpaEtzR0fbpUu9Q1bb+Pjjiakpu33W4Zr1eOb8Po/f 73szolAWxAs7nz4f6+3p6jzZYhvs83g8gJLt1kDniZbeM511leUZYqEmTdK0 q8ZUpEmTCTPkks2b8morKy1mc2vzgfNnO4f6rzlfPgv4PSFSgRDn4BBg2G13 TN0bGTjT3rrXYrYODnhdzo4TLQUaxZEmS9X3Rj6NAiXgKoz6imJNtpSrSoby 0yWZqSJCJAq9dpUIotZVlT55cDsAzyMjbxcECBYIIH+Nj/3csNNSu/3ecP9v p9rMlabDjXUSASsmfDUmYp04iWXUpRdkiLdoFLWmvJ+2FqUl82LDVrBJWMv2 sunJp6FiIQjsXVjQAOKYmznd2d7cWH+oYWfXieau4831tRVcGjFs5fKwlcvY NGKmdIM2TVRakFVVoq8tM2zOy5KLINkG6GRzI+J1htgi88z/ZSQ/7HE7Ll04 d/LQvmMH9p5pa+08ctBcWSpP5kd+twK15hseI1HIoqRwKWqFSKtKNeQqC9XK /EyZTACBKjtnp/0hJy9G9geRnX2/X+35tf1yd9f5juN7zFVlRXpthpyEi4lY 8208JlIAkVmJ2GQ2RZLElAlZYAjFmoy8LNmOStPczEvkFfJCNYLILqdtsP9S z6lzvxw7tLtuW0mRQZctYNPY1HhMxFo0ag2LTIAS8FwaKZnDEPHoKVymTiEr Nei7OtoQZBHe6wgg8NzMVG/PKSBFc0OdZXvFVmNBoTaLxyATY6Pw0ShcVDgl DkPBoxnxWB6NBMQRQXStXLptS9Ht4VvvnNRBA4Nwu+7fGTrcVF+xOe8Hg26L PrckX5unVol4DMAYcE7ARlEJGDIuhk7E8WgJHDpRwKTolbLqspJnTx4uRgaQ TufcxLMntlt9p9uPVpcV5yjEetVGZbIgXSpSpgr5TDIAjItBJeLRVEIsGYem E7EcCpFFIQpZdJ1Kbq7cOvni6SJkoDoyM/lin2VHnlopT0mKx6wXsWkqqYhN JZJw0QI2lQ9RIDKBGh9LjF1PicfQE7A8BolBwvPpJLmQr8lQHWjc45yzIwuF BsiBEeugQsyn4mOiw1fHoVFAWMCKSSagI9ZhUGs51ARAm0GKS8THAEFAA9yC pxw6KV0mLtTlDvbfBPQWeTiIfKX3ApOEw0eFgSEzE+PYFMA2hkLA0OJjI8NW AapcOolFIXCAtlQin5kIGgKIIhVxC3U54Lvh9bgWG2Me2WYdyFFIgKOAjPgY VNS6lYA8AY3CRobhIsNBCoVYAEoJDmAVlSxZKuSky1J06vSd5trHjx+FBF74 iYYRMG8C0y+e15SZlCkbUgVsIjbyyy8+X71s6fp1K0HJuAySVMQrM26qLjeV lxTnpm9Up0m1WUpjfs6Omkqr1fqeFQQo73U5murrjHm5uZlyalzsmuVfA+bA ZkCNZB6zpqJ0f2PDj1XlhnytNifTWKA3bTbs3WUeHbF9aGEC4L7r1y/XVm0t LzEoJRuAgGI+JICA1yIKNJn379hs1sGLPd0nj7a0HT/Sfaqz78a1menJxVV7 F7QPRjyD/TcaLebSLQaDJluTIZUIOGRsdF1t+VsrJxgfDK6h5vwa9RHYSLD/ 2IN7+3dbqitMxoIsIjqaGRebpRA63uHVT40gn507apIgWlG+mkbAKZJoXHL0 jatXPqjn+wMMcHb6ZbZKQSZgzp/uyJbLNFJmKgNztr3tvyIHkNHbQ0kcqFCr Dvh9TZa6XDFNwcGD5ftTkReoB17v7urgUBI7246B9t3bVv1GniKJOjI8OI8c 2pZ8lOCLkY+1NjNICXdHhoNQsLfKVKTLVIQmL/JJyAsTAW+MPdhb32CfnYVD icYfPRwdvfNRvn1vBLcvcBDQF9rSBc9AcK8Af5xv346/AVxi8SE= "], {{0, 0}, {54., 54.}}, {0, 255}, ColorFunction->RGBColor], ImageSize->{54., 54.}, PlotRange->{{0, 54.}, {0, 54.}}]}], ";"}], "\n", RowBox[{ RowBox[{"gr", "=", RowBox[{"GraphicsRow", "[", RowBox[{"{", RowBox[{"grf", ",", "grm"}], "}"}], "]"}]}], ";"}], "\n", RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"pos", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.`", ",", "0.`"}], "}"}], ",", RowBox[{"{", RowBox[{"0.`", ",", "1.`"}], "}"}], ",", RowBox[{"{", RowBox[{"0.9258200997725514`", ",", "1.8516401995451028`"}], "}"}], ",", RowBox[{"{", RowBox[{"1.7741310502909748`", ",", "2.6611965754364624`"}], "}"}], ",", RowBox[{"{", RowBox[{"3.3528371517369977`", ",", "3.3528371517369977`"}], "}"}], ",", RowBox[{"{", RowBox[{"5.3285658939847975`", ",", "3.806118495703427`"}], "}"}], ",", RowBox[{"{", RowBox[{"8.182608119098033`", ",", "4.091304059549016`"}], "}"}], ",", RowBox[{"{", RowBox[{"11.759742747173759`", ",", "4.115909961510815`"}], "}"}]}], "}"}], "[", RowBox[{"[", "generations", "]"}], "]"}]}], "}"}], ",", RowBox[{"Column", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"MapAt", "[", RowBox[{ RowBox[{ RowBox[{"Prepend", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\\"", ",", "16"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}], "+", RowBox[{".5", RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}], "/", RowBox[{"(", RowBox[{"generations", "-", "1"}], ")"}]}]}]}]}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\\"", ",", "16"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "1", "]"}], "]"}], "+", "2"}], ",", RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}], "+", RowBox[{".5", RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}], "/", RowBox[{"(", RowBox[{"generations", "-", "1"}], ")"}]}]}]}]}], "}"}]}], "]"}], ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"First", "@", "#2"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "#"}], "}"}]}], "]"}], "&"}], ",", RowBox[{"Range", "[", RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}]}], "/", RowBox[{"(", RowBox[{"generations", "-", "1"}], ")"}]}]}], "]"}]}], "]"}], ",", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"Fibonacci", "[", RowBox[{"First", "@", "#2"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "1", "]"}], "]"}], "+", "2"}], ",", "#"}], "}"}]}], "]"}], "&"}], ",", RowBox[{"Range", "[", RowBox[{ RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "0", ",", RowBox[{ RowBox[{"-", RowBox[{"pos", "[", RowBox[{"[", "2", "]"}], "]"}]}], "/", RowBox[{"(", RowBox[{"generations", "-", "1"}], ")"}]}]}], "]"}]}], "]"}]}], "}"}], ",", "#"}], "]"}], "&"}], ",", RowBox[{"ToExpression", "@", RowBox[{"ToBoxes", "@", RowBox[{"TreeForm", "[", RowBox[{ RowBox[{ RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"n", "[", RowBox[{"m", "@@", RowBox[{"Nest", "[", RowBox[{ RowBox[{ RowBox[{"m", "[", RowBox[{"#", ",", RowBox[{"n", "[", "#", "]"}]}], "]"}], "&"}], ",", RowBox[{"n", "[", "m", "]"}], ",", "12"}], "]"}]}], "]"}], ",", RowBox[{ RowBox[{"(", RowBox[{"n", "|", "m"}], ")"}], "[", "__", "]"}], ",", RowBox[{"{", "generations", "}"}]}], "]"}], "/.", RowBox[{ RowBox[{"m_", "[", "]"}], "\[Rule]", "m"}]}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"500", ",", "375"}], "}"}]}], ",", RowBox[{"VertexRenderingFunction", "\[Rule]", " ", RowBox[{"If", "[", RowBox[{ RowBox[{"show", "==", "\"\\""}], ",", "Automatic", ",", " ", RowBox[{"(", RowBox[{ RowBox[{"Inset", "[", RowBox[{"gr", ",", "#1", ",", "Automatic", ",", RowBox[{"{", RowBox[{"1.", ",", ".3"}], "}"}]}], "]"}], "&"}], ")"}]}], "]"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"Thickness", "[", ".01", "]"}]}], ",", RowBox[{"EdgeRenderingFunction", "\[Rule]", RowBox[{"Function", "[", RowBox[{ RowBox[{"{", RowBox[{"p", ",", "vl", ",", "el"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Which", "[", RowBox[{ RowBox[{ RowBox[{"vl", "[", RowBox[{"[", "1", "]"}], "]"}], "===", "n"}], ",", "Orange", ",", RowBox[{ RowBox[{"ReleaseHold", "@", "vl"}], "===", RowBox[{"{", RowBox[{"m", ",", "n"}], "}"}]}], ",", "Blue", ",", RowBox[{ RowBox[{"ReleaseHold", "@", "vl"}], "===", RowBox[{"{", RowBox[{"m", ",", "m"}], "}"}]}], ",", "Brown"}], "]"}], ",", RowBox[{"Arrowheads", "[", "Medium", "]"}], ",", RowBox[{"Arrow", "[", RowBox[{"p", ",", ".15"}], "]"}]}], "}"}]}], "]"}]}]}], "]"}]}]}], ",", "1"}], "]"}], ",", RowBox[{"Text", "@", RowBox[{"Style", "[", RowBox[{ RowBox[{"Row", "[", RowBox[{ RowBox[{"Riffle", "[", RowBox[{ RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\<\!\(\*\n\ StyleBox[\\\"born\\\",\\nFontColor->RGBColor[0, 0, 1]]\)\>\"", ",", "\"\<\!\(\*\n\ StyleBox[\\\"mature\\\",\\nFontColor->RGBColor[1, 0.5, 0]]\)\>\"", ",", "\"\<\!\(\*\n\ StyleBox[\\\"survive\\\",\\nFontColor->RGBColor[0.6, 0.4, 0.2]]\)\>\""}], "}"}], ",", RowBox[{"{", RowBox[{"\"\<\>\"", ",", "\"\<|\>\"", ",", "\"\<|\>\""}], "}"}]}], "]"}], ",", "\"\< \>\""}], "]"}], ",", "18"}], "]"}]}]}], "}"}], ",", RowBox[{"Alignment", "\[Rule]", "Center"}]}], "]"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"generations", ",", "2", ",", "\"\\""}], "}"}], ",", "2", ",", "8", ",", "1", ",", " ", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"show", ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], "}"}], ",", RowBox[{"SaveDefinitions", "\[Rule]", "True"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{ 3.35696210375764*^9, {3.3966485931390038`*^9, 3.3966486095930843`*^9}, { 3.3966486881023407`*^9, 3.396648771057144*^9}, {3.396650808931676*^9, 3.396650808931727*^9}, {3.396651178252659*^9, 3.396651240399289*^9}, { 3.3966513137701283`*^9, 3.3966513137701807`*^9}, {3.396782917557918*^9, 3.396782917557969*^9}, 3.396805426809012*^9, {3.396809553165823*^9, 3.396809602449284*^9}, {3.39681473061665*^9, 3.396814766919941*^9}, { 3.396887292007166*^9, 3.396887294037224*^9}, {3.399145261947691*^9, 3.399145273920473*^9}, 3.448949058546875*^9, {3.449146290234375*^9, 3.4491462955*^9}, {3.44914632584375*^9, 3.44914640253125*^9}, { 3.449146474734375*^9, 3.449146483421875*^9}, {3.44915167971875*^9, 3.449151680234375*^9}, {3.44915171559375*^9, 3.449151747125*^9}}, FontSize->18, CellID->876584969], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`generations$$ = 2, $CellContext`show$$ = "labels", Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`generations$$], 2, "generations"}, 2, 8, 1}, {{ Hold[$CellContext`show$$], "labels"}, {"labels", "rabbits"}}}, Typeset`size$$ = {500., {197., 206.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`generations$130886$$ = 0, $CellContext`show$130887$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`generations$$ = 2, $CellContext`show$$ = "labels"}, "ControllerVariables" :> { Hold[$CellContext`generations$$, $CellContext`generations$130886$$, 0], Hold[$CellContext`show$$, $CellContext`show$130887$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> With[{$CellContext`pos$ = Part[{{0., 0.}, {0., 1.}, {0.9258200997725514, 1.8516401995451028`}, {1.7741310502909748`, 2.6611965754364624`}, { 3.3528371517369977`, 3.3528371517369977`}, {5.3285658939847975`, 3.806118495703427}, {8.182608119098033, 4.091304059549016}, { 11.759742747173759`, 4.115909961510815}}, $CellContext`generations$$]}, Column[{ MapAt[Prepend[{ Text[ Style[ "generations", 16], {-2, Part[$CellContext`pos$, 2] + 0.5 (Part[$CellContext`pos$, 2]/($CellContext`generations$$ - 1))}], Text[ Style["number of pairs", 16], { Part[$CellContext`pos$, 1] + 2, Part[$CellContext`pos$, 2] + 0.5 (Part[$CellContext`pos$, 2]/($CellContext`generations$$ - 1))}], MapIndexed[Text[ First[#2], {-2, #}]& , Range[ Part[$CellContext`pos$, 2], 0, (-Part[$CellContext`pos$, 2])/($CellContext`generations$$ - 1)]], MapIndexed[Text[ Fibonacci[ First[#2]], {Part[$CellContext`pos$, 1] + 2, #}]& , Range[ Part[$CellContext`pos$, 2], 0, (-Part[$CellContext`pos$, 2])/($CellContext`generations$$ - 1)]]}, #]& , ToExpression[ ToBoxes[ TreeForm[ ReplaceAll[ DeleteCases[ $CellContext`n[ Apply[$CellContext`m, Nest[$CellContext`m[#, $CellContext`n[#]]& , $CellContext`n[$CellContext`m], 12]]], Alternatives[$CellContext`n, $CellContext`m][ BlankSequence[]], {$CellContext`generations$$}], Pattern[$CellContext`m, Blank[]][] -> $CellContext`m], ImageSize -> {500, 375}, VertexRenderingFunction -> If[$CellContext`show$$ == "labels", Automatic, Inset[$CellContext`gr, #, Automatic, {1., 0.3}]& ], PlotStyle -> Thickness[0.01], EdgeRenderingFunction -> Function[{$CellContext`p, $CellContext`vl, $CellContext`el}, { Which[ Part[$CellContext`vl, 1] === $CellContext`n, Orange, ReleaseHold[$CellContext`vl] === {$CellContext`m, \ $CellContext`n}, Blue, ReleaseHold[$CellContext`vl] === {$CellContext`m, \ $CellContext`m}, Brown], Arrowheads[Medium], Arrow[$CellContext`p, 0.15]}]]]], 1], Text[ Style[ Row[ Riffle[{"a pair of rabbits:", "\!\(\*\nStyleBox[\"born\",\nFontColor->RGBColor[0, 0, 1]]\)", "\!\(\*\nStyleBox[\"mature\",\nFontColor->RGBColor[1, 0.5, 0]]\ \)", "\!\(\*\nStyleBox[\"survive\",\nFontColor->RGBColor[0.6, 0.4, 0.2]]\)"}, \ {"", "|", "|"}], " "], 18]]}, Alignment -> Center]], "Specifications" :> {{{$CellContext`generations$$, 2, "generations"}, 2, 8, 1, Appearance -> "Labeled"}, {{$CellContext`show$$, "labels"}, { "labels", "rabbits"}}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{553., {262., 271.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`gr = Graphics[{{}, {{ Inset[ Graphics[ Raster[CompressedData[" 1:eJy1lmlQU1cUx53px37qp37pMq0zbXXcKm6ASNhCQvaFhISwJEDYEgKJBJJI wr6IQhQUqURAQdwiotJREbVg3Ypa7YhWZRCwEtZGoYRs7/W8h1IFsa2d3ryb d++bd3/nf88999z3hUTBlnywaNGiz6F+BhVro/9bcS9QXHiZ7cKbCAL/CNyg zLyw0NhZBl4RlxvFX3W63YgbAG4UuwEKdQNq2mYbfvZkuL/bOtzzwjricroQ GIE4cAI2FowjuNkZ6GwD2IgbY7tQ1wwOOpOTNovFcv/+vc7OjtMtx0vytMbC jKry/M72NsvAoMPufDUdZGb6OM01S8bNQbW7pyes4xbL0EBPz8Pr16+dOtFS VVmZnaVTqxSFuboG0y6DKiVFIjIW5HR1/nCn68bg09/cmAr0uXXsWufF61cu DQ0POJw2bMowC8xZONk1bentbqyuUCZKuRQymeAXK+DLogXRobT4CHapQWUy FkVyaPEiYW3FjuMHTfl65dnTzQ67wzY9ffxw4/49xo72EyNjfU7XHzgZYyK4 Y6EM9fXka9PIvutWLP6UTyUa83Tb9SqNLFKTFFmkS0uNF5MIXsRNXsrEWHPD Xn267Hyr2TFpbaytMZYWPbh32+W0IYhz1hu4WvvMErhsE82NNZGcEB4tIFst ryo1VBRqi3UKXYo4MyWOTSWuXfENXFxacO3ucnPjvktnTrQeazJVGs2HGsbH R7A1f7PgZGCjTtvEnrLCcBYpJU6Um5lalqvN1yoMm5PlkjBxGEvEZaxfuXTN 8q/DGORqY0n7KXPLwfrayvJDdaZzrSenpyYwdW8jw0q8GB/OVqfIY4Q5GSmq xOjEKJ40gisOo3MpfuEcCj3Yb/2qpX5eazRpSWUF+sN11Vfav+88e7rVfPhq xwWHfep1P7wMj5cBjzjs0/WmPdnq1MxkqTiMLRZwQGo4m8qlBPEZ5E3rv/Ve syKUToqJ4GWpFeWF2ccbajvOnLpyqa377m379FvIf4lH0WtXOvI0m5WxYhGH HsaiCllUZnAAPYhAJxJ8N6wO9FlPC/INZZC1KnmxQVu3a0frkcazJ4/dvHbZ bptE5nnjdfJA3+NivUadECdgUniMED6NzAz2p/j7ABCwBE+PoE0bwrn0LekK IJflGapKC/fu3Np8aP/o4ACKk9+65YE8PDhQmrMFNPPpZDYliEcNZhL9ZsjU IF8gBxO8RDymIkGiSU3OlCdqZNJMeWzD3sq7P/04NfEcsDabbT4cyNax0Z1b i9WyxGgem88I4QKZFEAN3ARkkp83YFnkAHC1NEoQyWMKWFRtalKSRJgQLagq LzE31d/pumqbfIFlCfcbEYjtdIf96MEGWaxEGiHgUIhUIkEUymCFBIJgoq8n NCCY4QmNSNi4diWYELCpfGaI5+plwX7eYUwShM3Q0z48f86LbRSxPHuarctQ JMSGscDVmE8g3rC1IxKgAShoeK1eDoagCxaFHBqD5O/lsTzAy4NDCey62oli 2WwuGVYAHreda9Wp0+KjhSAPUGIhNzaCDwS4OFQiWAHBwAcs2X8jmAYyOIpE 8KT4e3debFuIjKDuqanJutqaDKVcJYuLjxLI4qL0GWn5WRm5uvTNMimgQLDP ulUQ4R7Lvlry5ScQkAyyP59G0iqSnzz6FSPPB79aytHR0fp9NTk6tS49VSmL l8dLCrN1u42lZcV5cqk4IpQBfHDvqiWLP/7oQ1CeKBGlSiVl+bmT1nFkYTKE DZZ1fx9rbTFvK84vyMnSqlWa9LTtxQVHmw4cMFVH8Vkw/YCN68APIBjckpGa lK3dXG+qdjlsr50mCyiHs8rlGBkafND9y62uGz/f6urv7RkbGZq0jm3Ny4Ig lISHxoh4ybGRaUkx2wsMu3Zue/i4GxLbu7Ez2vEFRd48kLFuxfYCsq93BJeZ qUwEqSV5hsa6mqf9vSiKvCN7/M1EUHR8dCQmnMEj+wd5b9BrUkoLDPWm76zj o+/4DPiH5MsXL/Ip3skiJjeElKdXk/x8inL0eNZ/T7Wz5LaTJ2PYBFUMM12W dPP6ZRY5UBwhHB8bnnek/HvNF87HhwYqo+lHDtRBtzBnCzMkuPvuLfS90Mir 7yJA9T56kBDO1CSI+nofYYY62hlBAaeaj83x89/G3hwylrWcdkOmcndZERz6 QIM8wySTzEea3o88Z0hfX59lcBDPDy673d5Yv7+/v9/932LDje1QzCkgFxrw c+IbFrat3TV3j/wJ+6Y4uw== "], {{0, 0}, {54., 55.800000000000004`}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {54., 54.}, PlotRange -> {{0, 54.}, {0, 55.800000000000004`}}], { 28.8, -28.35}, ImageScaled[{0.5, 0.5}], {54., 54.}], Inset[ Graphics[ Raster[CompressedData[" 1:eJy1VmlTU1cYdqZ/oB/6sdMZ+0WndS9MkCUhCSGE7DcrMYGQxCSELZAFhECU BioIArURAyrFDcEVCsUFxYrjVi2LgYhiFaWugEDIfnPTk6DWguMynb659865 uec+73Oe9zn3nKWSbEjy2ZIlS756dQbbgf8t/O8LGIQf/Lwen9vhcdndLsfC x6DD67sFLyMI8qaBICBRAPaDa+hPxAcO55xz/MHo0M0Lf1zuunH1wqOHYxOT E3b7tNvtgn0ga8CPzPcP5vjnXT/8BhmGvW63Y/rl5NTEC4/HNc/CPjP358jd i91nqkuLijVKo17derDpaEtzR0fbpUu9Q1bb+Pjjiakpu33W4Zr1eOb8Po/f 73szolAWxAs7nz4f6+3p6jzZYhvs83g8gJLt1kDniZbeM511leUZYqEmTdK0 q8ZUpEmTCTPkks2b8morKy1mc2vzgfNnO4f6rzlfPgv4PSFSgRDn4BBg2G13 TN0bGTjT3rrXYrYODnhdzo4TLQUaxZEmS9X3Rj6NAiXgKoz6imJNtpSrSoby 0yWZqSJCJAq9dpUIotZVlT55cDsAzyMjbxcECBYIIH+Nj/3csNNSu/3ecP9v p9rMlabDjXUSASsmfDUmYp04iWXUpRdkiLdoFLWmvJ+2FqUl82LDVrBJWMv2 sunJp6FiIQjsXVjQAOKYmznd2d7cWH+oYWfXieau4831tRVcGjFs5fKwlcvY NGKmdIM2TVRakFVVoq8tM2zOy5KLINkG6GRzI+J1htgi88z/ZSQ/7HE7Ll04 d/LQvmMH9p5pa+08ctBcWSpP5kd+twK15hseI1HIoqRwKWqFSKtKNeQqC9XK /EyZTACBKjtnp/0hJy9G9geRnX2/X+35tf1yd9f5juN7zFVlRXpthpyEi4lY 8208JlIAkVmJ2GQ2RZLElAlZYAjFmoy8LNmOStPczEvkFfJCNYLILqdtsP9S z6lzvxw7tLtuW0mRQZctYNPY1HhMxFo0ag2LTIAS8FwaKZnDEPHoKVymTiEr Nei7OtoQZBHe6wgg8NzMVG/PKSBFc0OdZXvFVmNBoTaLxyATY6Pw0ShcVDgl DkPBoxnxWB6NBMQRQXStXLptS9Ht4VvvnNRBA4Nwu+7fGTrcVF+xOe8Hg26L PrckX5unVol4DMAYcE7ARlEJGDIuhk7E8WgJHDpRwKTolbLqspJnTx4uRgaQ TufcxLMntlt9p9uPVpcV5yjEetVGZbIgXSpSpgr5TDIAjItBJeLRVEIsGYem E7EcCpFFIQpZdJ1Kbq7cOvni6SJkoDoyM/lin2VHnlopT0mKx6wXsWkqqYhN JZJw0QI2lQ9RIDKBGh9LjF1PicfQE7A8BolBwvPpJLmQr8lQHWjc45yzIwuF BsiBEeugQsyn4mOiw1fHoVFAWMCKSSagI9ZhUGs51ARAm0GKS8THAEFAA9yC pxw6KV0mLtTlDvbfBPQWeTiIfKX3ApOEw0eFgSEzE+PYFMA2hkLA0OJjI8NW AapcOolFIXCAtlQin5kIGgKIIhVxC3U54Lvh9bgWG2Me2WYdyFFIgKOAjPgY VNS6lYA8AY3CRobhIsNBCoVYAEoJDmAVlSxZKuSky1J06vSd5trHjx+FBF74 iYYRMG8C0y+e15SZlCkbUgVsIjbyyy8+X71s6fp1K0HJuAySVMQrM26qLjeV lxTnpm9Up0m1WUpjfs6Omkqr1fqeFQQo73U5murrjHm5uZlyalzsmuVfA+bA ZkCNZB6zpqJ0f2PDj1XlhnytNifTWKA3bTbs3WUeHbF9aGEC4L7r1y/XVm0t LzEoJRuAgGI+JICA1yIKNJn379hs1sGLPd0nj7a0HT/Sfaqz78a1menJxVV7 F7QPRjyD/TcaLebSLQaDJluTIZUIOGRsdF1t+VsrJxgfDK6h5vwa9RHYSLD/ 2IN7+3dbqitMxoIsIjqaGRebpRA63uHVT40gn507apIgWlG+mkbAKZJoXHL0 jatXPqjn+wMMcHb6ZbZKQSZgzp/uyJbLNFJmKgNztr3tvyIHkNHbQ0kcqFCr Dvh9TZa6XDFNwcGD5ftTkReoB17v7urgUBI7246B9t3bVv1GniKJOjI8OI8c 2pZ8lOCLkY+1NjNICXdHhoNQsLfKVKTLVIQmL/JJyAsTAW+MPdhb32CfnYVD icYfPRwdvfNRvn1vBLcvcBDQF9rSBc9AcK8Af5xv346/AVxi8SE= "], {{0, 0}, {54., 54.}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {54., 54.}, PlotRange -> {{0, 54.}, {0, 54.}}], { 86.4, -28.35}, ImageScaled[{0.5, 0.5}], {54., 54.}]}}, {}}, ImageSize -> {127.2, 68.7}, PlotRangePadding -> {6, 5}, ContentSelectable -> True], Attributes[PlotRange] = {ReadProtected}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.449146336671875*^9, 3.4491464040625*^9}, { 3.44914647553125*^9, 3.449146484140625*^9}, 3.449151681234375*^9, { 3.449151726203125*^9, 3.449151747828125*^9}}] }, {2}]], Cell[TextData[{ StyleBox[ButtonBox["Fibonacci Rabbits", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FibonacciRabbits/"], FontSize->14], StyleBox[" ze str\[AAcute]nek ", FontSize->14], StyleBox[ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontSize->14], StyleBox["\[ParagraphSeparator]", FontSize->14], StyleBox[ButtonBox["http://demonstrations.wolfram.com/FibonacciRabbits/\n", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FibonacciRabbits/"], FontSize->14], StyleBox["Autor: ", FontSize->14], StyleBox[ButtonBox["Enrique Zeleny", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Enrique+Zeleny"]\ , None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Enrique+Zeleny"], FontSize->14] }], "Text", CellChangeTimes->{ 3.448955826234375*^9, {3.448955858875*^9, 3.448955869140625*^9}, { 3.449146540984375*^9, 3.449146557265625*^9}, 3.44915499846875*^9}], Cell[TextData[{ "Je-li ", Cell[BoxData[ FormBox[ SubscriptBox["F", "n"], TraditionalForm]]], " po\[CHacek]et kr\[AAcute]l\[IAcute]k\:016f po ", Cell[BoxData[ FormBox["n", TraditionalForm]]], " m\:011bs\[IAcute]c\[IAcute]ch, pak ", Cell[BoxData[ FormBox[ SubscriptBox["F", "0"], TraditionalForm]]], "=", Cell[BoxData[ FormBox[ SubscriptBox["F", "1"], TraditionalForm]]], "=1 a ", Cell[BoxData[ FormBox[ SubscriptBox["F", "n"], TraditionalForm]]], "=", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["F", RowBox[{"n", "-", "1"}]], "+"}], TraditionalForm]]], Cell[BoxData[ FormBox[ SubscriptBox["F", RowBox[{"n", "-", "2"}]], TraditionalForm]]], " pro ka\:017ed\[EAcute] ", Cell[BoxData[ FormBox["n", TraditionalForm]]], "\[GreaterEqual]2." }], "Text", CellChangeTimes->{{3.44894953315625*^9, 3.448949774890625*^9}, { 3.448949860234375*^9, 3.448949861078125*^9}, 3.448953455953125*^9}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"fib", "[", "0", "]"}], ":=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fib", "[", "1", "]"}], ":=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fib", "[", "n_", "]"}], ":=", RowBox[{ RowBox[{"fib", "[", RowBox[{"n", "-", "1"}], "]"}], "+", RowBox[{"fib", "[", RowBox[{"n", "-", "2"}], "]"}]}]}]}], "Input", CellChangeTimes->{{3.44894979571875*^9, 3.448949839828125*^9}}], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"fib", "[", "n", "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.448949776375*^9, 3.448949786625*^9}, { 3.448949853234375*^9, 3.44894985340625*^9}}], Cell[TextData[{ "Ob\[CHacek]as se jako ", Cell[BoxData[ FormBox[ SubscriptBox["F", "n"], TraditionalForm]]], " ozna\[CHacek]uj\[IAcute] i posunut\[EAcute] posloupnosti." }], "Text", CellChangeTimes->{{3.44894988565625*^9, 3.44894994175*^9}}], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Fibonacci", "[", "n", "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.448949944203125*^9, 3.4489499579375*^9}}], Cell[BoxData[ RowBox[{"fib20", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"fib", "[", "n", "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.44895009275*^9, 3.4489501086875*^9}, { 3.4489501565625*^9, 3.448950178359375*^9}, {3.448950375359375*^9, 3.4489503808125*^9}}], Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{"fib20", ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}]}], "]"}]], "Input", CellChangeTimes->{{3.44895004734375*^9, 3.448950075109375*^9}, { 3.448950186796875*^9, 3.448950249328125*^9}, {3.44895032840625*^9, 3.448950391765625*^9}, {3.448955670203125*^9, 3.448955677859375*^9}}], Cell[BoxData[ RowBox[{"ListLogPlot", "[", RowBox[{"fib20", ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}]}], "]"}]], "Input", CellChangeTimes->{{3.44895004734375*^9, 3.448950075109375*^9}, { 3.448950186796875*^9, 3.448950249328125*^9}, {3.44895032840625*^9, 3.448950391765625*^9}, {3.448950431046875*^9, 3.448950431375*^9}, 3.4489556950625*^9}] }, Closed]], Cell[CellGroupData[{ Cell["\[CapitalUAcute]loha o dla\:017edic\[IAcute]ch", "Subsection", CellChangeTimes->{{3.44895055475*^9, 3.44895056153125*^9}}], Cell[TextData[{ "Kolika zp\:016fsoby lze vydl\[AAcute]\:017edit obd\[EAcute]ln\[IAcute]k o \ rozm\:011brech 2\[Times]", Cell[BoxData[ FormBox["n", TraditionalForm]], FormatType->"TraditionalForm"], ", m\[AAcute]me-li k dispozici dla\:017edice o rozm\:011brech 2", "\[Times]", "1?" }], "Text", CellChangeTimes->{{3.448950571375*^9, 3.4489506751875*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"start", "[", "l_", "]"}], ":=", RowBox[{ RowBox[{"{", "0", "}"}], "~", "Join", "~", RowBox[{"Delete", "[", RowBox[{ RowBox[{"Accumulate", "[", "l", "]"}], ",", RowBox[{"Length", "[", "l", "]"}]}], "]"}]}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"tiling", "[", "l_", "]"}], ":=", RowBox[{"MapThread", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"#1", " ", "/.", " ", RowBox[{"{", RowBox[{ RowBox[{"1", "\[Rule]", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"#2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"#2", "+", "1"}], ",", "2"}], "}"}]}], "]"}]}], ",", RowBox[{"2", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"#2", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"#2", "+", "2"}], ",", "1"}], "}"}]}], "]"}], ",", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"#2", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"#2", "+", "2"}], ",", "2"}], "}"}]}], "]"}]}], "}"}]}]}], "}"}]}], ")"}], "&"}], ",", RowBox[{"{", RowBox[{"l", ",", RowBox[{"start", "[", "l", "]"}]}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"showTiling", "[", "l_", "]"}], ":=", RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"EdgeForm", "[", "Black", "]"}], ",", "Yellow"}], "}"}], "~", "Join", "~", RowBox[{"tiling", "[", "l", "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"allTilings", "[", "1", "]"}], ":=", RowBox[{"{", RowBox[{"{", "1", "}"}], "}"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"allTilings", "[", "2", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", "2", "}"}]}], "}"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"allTilings", "[", "n_", "]"}], ":=", RowBox[{ RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "1", "}"}], "~", "Join", "~", "#"}], "&"}], ",", RowBox[{"allTilings", "[", RowBox[{"n", "-", "1"}], "]"}]}], "]"}], "~", "Join", "~", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"{", "2", "}"}], "~", "Join", "~", "#"}], "&"}], ",", RowBox[{"allTilings", "[", RowBox[{"n", "-", "2"}], "]"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"showAllTilings", "[", "n_", "]"}], ":=", RowBox[{"Map", "[", RowBox[{"showTiling", ",", RowBox[{"allTilings", "[", "n", "]"}]}], "]"}]}]}], "Input", CellChangeTimes->{{3.417693237609375*^9, 3.417693289421875*^9}, { 3.438262813421875*^9, 3.4382628815625*^9}, {3.438328320359375*^9, 3.4383283314375*^9}, {3.438338922578125*^9, 3.438338930328125*^9}, { 3.44895085028125*^9, 3.4489508615625*^9}, {3.448951207140625*^9, 3.448951209859375*^9}, {3.448953127078125*^9, 3.4489531480625*^9}, { 3.448953325125*^9, 3.448953360921875*^9}, {3.4491520801875*^9, 3.449152112421875*^9}, {3.449152215328125*^9, 3.449152227328125*^9}, { 3.449152260515625*^9, 3.449152299171875*^9}, {3.44915241759375*^9, 3.4491524349375*^9}}], Cell[BoxData[ RowBox[{"showAllTilings", "[", "2", "]"}]], "Input", CellChangeTimes->{{3.44895286646875*^9, 3.448952868546875*^9}, { 3.448952967625*^9, 3.448952971328125*^9}, {3.44895302675*^9, 3.448953064828125*^9}, 3.448953102234375*^9, {3.448953152296875*^9, 3.448953157609375*^9}}], Cell[BoxData[ RowBox[{"showAllTilings", "[", "3", "]"}]], "Input", CellChangeTimes->{{3.44895286646875*^9, 3.448952868546875*^9}, { 3.448952967625*^9, 3.448952971328125*^9}, {3.44895302675*^9, 3.448953064828125*^9}, 3.448953102234375*^9, {3.448953152296875*^9, 3.44895316734375*^9}}], Cell[BoxData[ RowBox[{"showAllTilings", "[", "4", "]"}]], "Input", CellChangeTimes->{{3.44895286646875*^9, 3.448952868546875*^9}, { 3.448952967625*^9, 3.448952971328125*^9}, {3.44895302675*^9, 3.448953064828125*^9}, 3.448953102234375*^9, {3.448953152296875*^9, 3.44895316928125*^9}, 3.44895355365625*^9}], Cell[BoxData[ RowBox[{"showAllTilings", "[", "5", "]"}]], "Input", CellChangeTimes->{{3.44895286646875*^9, 3.448952868546875*^9}, { 3.448952967625*^9, 3.448952971328125*^9}, {3.44895302675*^9, 3.448953064828125*^9}, 3.448953102234375*^9, {3.448953152296875*^9, 3.4489531934375*^9}, {3.448953235515625*^9, 3.448953235671875*^9}, 3.44895328225*^9}], Cell[BoxData[ RowBox[{"showAllTilings", "[", "6", "]"}]], "Input", CellChangeTimes->{{3.44895286646875*^9, 3.448952868546875*^9}, { 3.448952967625*^9, 3.448952971328125*^9}, {3.44895302675*^9, 3.448953064828125*^9}, 3.448953102234375*^9, {3.448953152296875*^9, 3.448953157609375*^9}, 3.448953297125*^9}], Cell[TextData[{ "Je-li ", Cell[BoxData[ FormBox[ SubscriptBox["a", "n"], TraditionalForm]]], " po\[CHacek]et dl\[AAcute]\:017ed\:011bn\[IAcute] obd\[EAcute]ln\[IAcute]ka \ 2\[Times]", Cell[BoxData[ FormBox["n", TraditionalForm]]], ", pak ", Cell[BoxData[ FormBox[ SubscriptBox["a", "0"], TraditionalForm]]], "=", Cell[BoxData[ FormBox[ SubscriptBox["a", "1"], TraditionalForm]]], "=1 a ", Cell[BoxData[ FormBox[ SubscriptBox["a", "n"], TraditionalForm]]], "=", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["a", RowBox[{"n", "-", "1"}]], "+"}], TraditionalForm]]], Cell[BoxData[ FormBox[ SubscriptBox["a", RowBox[{"n", "-", "2"}]], TraditionalForm]]], " pro ka\:017ed\[EAcute] ", Cell[BoxData[ FormBox["n", TraditionalForm]]], "\[GreaterEqual]2.\nPlat\[IAcute] tedy ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["a", "n"], "=", SubscriptBox["F", "n"]}], TraditionalForm]]], " pro ka\:017ed\[EAcute] ", Cell[BoxData[ FormBox["n", TraditionalForm]]], "." }], "Text", CellChangeTimes->{{3.44894953315625*^9, 3.448949774890625*^9}, { 3.448949860234375*^9, 3.448949861078125*^9}, 3.448953455953125*^9, { 3.448953556390625*^9, 3.44895365090625*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Periodicita zbytk\:016f", "Subsection", CellChangeTimes->{{3.448953817234375*^9, 3.4489538243125*^9}}], Cell[TextData[{ "Zbytky ", Cell[BoxData[ FormBox[ SubscriptBox["F", "n"], TraditionalForm]], FormatType->"TraditionalForm"], " p\:0159i d\:011blen\[IAcute] dv\:011bma (perioda 3):" }], "Text", CellChangeTimes->{{3.44895386821875*^9, 3.448953896890625*^9}, { 3.448954110296875*^9, 3.4489541165*^9}}], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Mod", "[", RowBox[{ RowBox[{"fib", "[", "n", "]"}], ",", "2"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.448953833078125*^9, 3.448953850140625*^9}}], Cell[TextData[{ "Zbytky ", Cell[BoxData[ FormBox[ SubscriptBox["F", "n"], TraditionalForm]], FormatType->"TraditionalForm"], " p\:0159i d\:011blen\[IAcute] t\:0159emi (perioda 8):" }], "Text", CellChangeTimes->{{3.44895386821875*^9, 3.44895391609375*^9}, { 3.448954119828125*^9, 3.448954135609375*^9}}], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Mod", "[", RowBox[{ RowBox[{"fib", "[", "n", "]"}], ",", "3"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.448953833078125*^9, 3.448953850140625*^9}, 3.448953918671875*^9}], Cell[TextData[{ "Zbytky ", Cell[BoxData[ FormBox[ SubscriptBox["F", "n"], TraditionalForm]]], " p\:0159i d\:011blen\[IAcute] \[CHacek]ty\:0159mi (perioda 6):" }], "Text", CellChangeTimes->{{3.44895386821875*^9, 3.448953946859375*^9}, { 3.44895416478125*^9, 3.448954168671875*^9}}], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Mod", "[", RowBox[{ RowBox[{"fib", "[", "n", "]"}], ",", "4"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.448953833078125*^9, 3.448953850140625*^9}, { 3.448953918671875*^9, 3.448953939296875*^9}}], Cell[TextData[{ StyleBox["V\:011bta:", FontWeight->"Bold"], " Zbytky ", Cell[BoxData[ FormBox[ SubscriptBox["F", "n"], TraditionalForm]]], " p\:0159i d\:011blen\[IAcute] libovoln\[YAcute]m \[CHacek]\[IAcute]slem tvo\ \:0159\[IAcute] periodickou posloupnost.\n(D. D. Wall, ", StyleBox["Fibonacci Series Modulo", FontSlant->"Italic"], " ", Cell[BoxData[ FormBox["m", TraditionalForm]], FormatType->"TraditionalForm"], ", American ", "Mathematical", " Monthly 67, 525-532, 1960.)" }], "Text", CellChangeTimes->{{3.4489542298125*^9, 3.44895426534375*^9}, { 3.449154278421875*^9, 3.4491543249375*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{ RowBox[{"m", "=", RowBox[{"Min", "[", RowBox[{"{", RowBox[{"m", ",", "w"}], "}"}], "]"}]}], ";", RowBox[{"ArrayPlot", "[", RowBox[{ RowBox[{"Partition", "[", RowBox[{ RowBox[{ RowBox[{"Mod", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fibonacci", "[", "#", "]"}], "&"}], "/@", RowBox[{"Range", "[", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"w", " ", "^", "2"}]}]}], " ", "]"}]}], ",", "m"}], "]"}], "/", RowBox[{"If", "[", RowBox[{ RowBox[{"h", "===", "Hue"}], ",", "m", ",", RowBox[{"m", "-", "1"}]}], "]"}]}], ",", "w"}], "]"}], ",", RowBox[{"ImageSize", "\[Rule]", "350"}], ",", RowBox[{"ColorFunction", "\[Rule]", "h"}], ",", " ", RowBox[{"ColorFunctionScaling", "\[Rule]", "False"}], ",", RowBox[{"AspectRatio", "\[Rule]", "1"}], ",", RowBox[{"Mesh", "\[Rule]", "True"}], ",", RowBox[{"Frame", "\[Rule]", "False"}]}], "]"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"w", ",", "8", ",", "\"\\""}], "}"}], ",", "2", ",", "64", ",", "1", ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m", ",", "3", ",", " ", "\"\\""}], "}"}], ",", "2", ",", "w", ",", "1", ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"h", ",", "\"\\"", ",", "\"\<\>\""}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"\"\\"", "\[Rule]", "\"\\""}], ",", RowBox[{"GrayLevel", "\[Rule]", "\"\\""}]}], "}"}], ",", RowBox[{"ControlType", "\[Rule]", "SetterBar"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{ 3.35757176568782*^9, {3.36923182557301*^9, 3.36923183298958*^9}, 3.36937940170145*^9, 3.36938067565753*^9, {3.3709048062174873`*^9, 3.37090486206066*^9}, {3.370904911439968*^9, 3.3709049527896214`*^9}, { 3.370905050520063*^9, 3.370905064109676*^9}, {3.370905139117625*^9, 3.3709051851882877`*^9}, {3.3709052571019697`*^9, 3.370905340097289*^9}, { 3.370905400266094*^9, 3.3709054191982927`*^9}, {3.370906693272941*^9, 3.370906697473196*^9}, 3.3709068103867493`*^9, {3.3710695573150883`*^9, 3.371069583248221*^9}, 3.371077599945698*^9, 3.371592579615781*^9, { 3.371592631662272*^9, 3.371592637166875*^9}, {3.371983942422117*^9, 3.371983967630344*^9}, {3.372116851379757*^9, 3.3721168579192963`*^9}, { 3.372907841771763*^9, 3.372907843684291*^9}, 3.372967399259552*^9, { 3.373862712980719*^9, 3.3738627653028793`*^9}, {3.373862802213633*^9, 3.373862827318376*^9}, 3.3751823324955807`*^9, 3.375182536775049*^9, { 3.375182583174333*^9, 3.375182605231394*^9}, {3.385754399663869*^9, 3.3857544222563553`*^9}, {3.3857544548832703`*^9, 3.3857544551136017`*^9}, {3.385919853657155*^9, 3.3859199187507553`*^9}, { 3.3859199769644623`*^9, 3.385920057630454*^9}, {3.3859201454367137`*^9, 3.3859202187220926`*^9}, {3.389721104554471*^9, 3.389721107882681*^9}, { 3.390160088227022*^9, 3.390160098477022*^9}, 3.3901601345551476`*^9, { 3.449152727625*^9, 3.449152752359375*^9}, {3.449152843734375*^9, 3.449152845171875*^9}, {3.44915288253125*^9, 3.44915291825*^9}, { 3.4491529784375*^9, 3.44915298365625*^9}, {3.449153047671875*^9, 3.44915304840625*^9}, {3.44915459015625*^9, 3.44915463490625*^9}}, FontSize->18, CellID->1496021318], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`h$$ = "LightTemperatureMap", $CellContext`m$$ = 3, $CellContext`w$$ = 8, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`w$$], 8, "size n"}, 2, 64, 1}, {{ Hold[$CellContext`m$$], 3, "modulus m"}, 2, Dynamic[$CellContext`w$$], 1}, {{ Hold[$CellContext`h$$], "LightTemperatureMap", ""}, { "LightTemperatureMap" -> "color", GrayLevel -> "gray-level"}}}, Typeset`size$$ = {350., {173., 177.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`w$37907$$ = 0, $CellContext`m$37908$$ = 0, $CellContext`h$37909$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`h$$ = "LightTemperatureMap", $CellContext`m$$ = 3, $CellContext`w$$ = 8}, "ControllerVariables" :> { Hold[$CellContext`w$$, $CellContext`w$37907$$, 0], Hold[$CellContext`m$$, $CellContext`m$37908$$, 0], Hold[$CellContext`h$$, $CellContext`h$37909$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`m$$ = Min[{$CellContext`m$$, $CellContext`w$$}]; ArrayPlot[ Partition[Mod[ Map[Fibonacci[#]& , Range[0, -1 + $CellContext`w$$^2]], $CellContext`m$$]/ If[$CellContext`h$$ === Hue, $CellContext`m$$, $CellContext`m$$ - 1], $CellContext`w$$], ImageSize -> 350, ColorFunction -> $CellContext`h$$, ColorFunctionScaling -> False, AspectRatio -> 1, Mesh -> True, Frame -> False]), "Specifications" :> {{{$CellContext`w$$, 8, "size n"}, 2, 64, 1, Appearance -> "Labeled"}, {{$CellContext`m$$, 3, "modulus m"}, 2, Dynamic[$CellContext`w$$], 1, Appearance -> "Labeled"}, {{$CellContext`h$$, "LightTemperatureMap", ""}, { "LightTemperatureMap" -> "color", GrayLevel -> "gray-level"}, ControlType -> SetterBar}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{403., {249., 258.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.44915273684375*^9, 3.449152753515625*^9}, 3.44915284590625*^9, {3.449152886828125*^9, 3.449152918890625*^9}, 3.4491529845*^9, 3.4491530491875*^9, {3.4491545821875*^9, 3.4491546356875*^9}, 3.44915471609375*^9, 3.449154756453125*^9}] }, {2}]], Cell[TextData[{ StyleBox[ButtonBox["Fibonacci Residues are Periodic ", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciResiduesArePeriodic/"], None}, ButtonNote-> "http://demonstrations.wolfram.com/FibonacciResiduesArePeriodic/"], FontSize->14], StyleBox["ze str\[AAcute]nek ", FontSize->14], StyleBox[ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontSize->14], StyleBox["\[ParagraphSeparator]", FontSize->14], StyleBox[ButtonBox["http://demonstrations.wolfram.com/\ FibonacciResiduesArePeriodic/", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciResiduesArePeriodic/"], None}, ButtonNote-> "http://demonstrations.wolfram.com/FibonacciResiduesArePeriodic/"], FontSize->14], StyleBox[ButtonBox["\n", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FibonacciRabbits/"], FontSize->14], StyleBox["Autor: ", FontSize->14], StyleBox[ButtonBox["Michael Schreiber", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Michael+\ Schreiber"], None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Michael+Schreiber"], FontSize->14] }], "Text", CellChangeTimes->{ 3.448955826234375*^9, {3.448955858875*^9, 3.448955869140625*^9}, { 3.44895591803125*^9, 3.448955939828125*^9}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Fibonacciova prvo\[CHacek]\[IAcute]sla", "Subsection", CellChangeTimes->{{3.44895492459375*^9, 3.448954927828125*^9}, { 3.448955168109375*^9, 3.44895517153125*^9}}], Cell["\<\ V t\[EAcute]to \[CHacek]\[AAcute]sti pracujeme s posunutou Fibonacciovou \ posloupnost\[IAcute] (0,1,1,2,3,...).\ \>", "Text", CellChangeTimes->{{3.448955180625*^9, 3.448955216484375*^9}}], Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Fibonacci", "[", "n", "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.448949944203125*^9, 3.4489499579375*^9}}], Cell[TextData[{ "Kdy je ", Cell[BoxData[ FormBox[ SubscriptBox["F", "k"], TraditionalForm]]], " prvo\[CHacek]\[IAcute]slo?" }], "Text", CellChangeTimes->{{3.448955300078125*^9, 3.448955351828125*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"fibprimes", "[", "n_", "]"}], ":=", RowBox[{"Cases", "[", RowBox[{ RowBox[{"Range", "[", "n", "]"}], ",", RowBox[{"k_", "/;", RowBox[{"PrimeQ", "[", RowBox[{"Fibonacci", "[", "k", "]"}], "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.437050878234375*^9, 3.437050934921875*^9}, { 3.437051854265625*^9, 3.43705187946875*^9}, {3.4370523219375*^9, 3.4370523261875*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"fibprimes", "[", "5000", "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.437051884453125*^9, 3.43705190178125*^9}, { 3.4370523304375*^9, 3.43705234890625*^9}, {3.437052384625*^9, 3.43705243784375*^9}, {3.448955371390625*^9, 3.448955373046875*^9}, { 3.44915312415625*^9, 3.449153157390625*^9}, {3.4491532676875*^9, 3.449153270671875*^9}, {3.4491535028125*^9, 3.449153502921875*^9}}], Cell[BoxData[ RowBox[{"IntegerLength", "[", RowBox[{"Fibonacci", "[", "5000", "]"}], "]"}]], "Input", CellChangeTimes->{{3.44915355553125*^9, 3.44915356425*^9}}], Cell[TextData[{ "Pro ", Cell[BoxData[ FormBox["k", TraditionalForm]]], "\[GreaterEqual]5 plat\[IAcute]: Je-li ", Cell[BoxData[ FormBox[ SubscriptBox["F", "k"], TraditionalForm]]], " prvo\[CHacek]\[IAcute]slo, pak ", Cell[BoxData[ FormBox["k", TraditionalForm]]], " je prvo\[CHacek]\[IAcute]slo." }], "Text", CellChangeTimes->{{3.448955427828125*^9, 3.4489554763125*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"fibprimes2", "[", "n_", "]"}], ":=", RowBox[{"Cases", "[", RowBox[{ RowBox[{"Range", "[", "n", "]"}], ",", RowBox[{"k_", "/;", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"k", "\[Equal]", "4"}], "||", RowBox[{"PrimeQ", "[", "k", "]"}]}], ")"}], "&&", RowBox[{"PrimeQ", "[", RowBox[{"Fibonacci", "[", "k", "]"}], "]"}]}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.437050878234375*^9, 3.437050934921875*^9}, { 3.437051854265625*^9, 3.43705187946875*^9}, {3.4370523219375*^9, 3.4370523261875*^9}, {3.449153203875*^9, 3.449153215625*^9}, { 3.44915330325*^9, 3.44915331115625*^9}, {3.449153815125*^9, 3.44915382340625*^9}, {3.4491538789375*^9, 3.449153895*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"fibprimes2", "[", "5000", "]"}], "//", "Timing"}]], "Input", CellChangeTimes->{{3.44915334221875*^9, 3.449153342640625*^9}, { 3.449153465546875*^9, 3.449153465921875*^9}}], Cell[TextData[{ "Otev\:0159en\[YAcute] probl\[EAcute]m: Obsahuje Fibonacciova posloupnost \ nekone\[CHacek]n\:011b mnoho prvo\[CHacek]\[IAcute]sel?\nPravd\:011bpodobn\ \:011b nejv\:011bt\[SHacek]\[IAcute] zn\[AAcute]m\[EAcute] Fibonacciovo prvo\ \[CHacek]\[IAcute]slo je ", Cell[BoxData[ FormBox[ SubscriptBox["F", "604711"], TraditionalForm]]], " (126 377 cifer - Lifschitz, 2005)." }], "Text", CellChangeTimes->{{3.448955532703125*^9, 3.448955562484375*^9}, { 3.448956485375*^9, 3.44895656728125*^9}, {3.4489565973125*^9, 3.448956603875*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Zobecn\:011bn\[AAcute] \[UAcute]loha o \ kr\[AAcute]l\[IAcute]c\[IAcute]ch", "Subsection", CellChangeTimes->{{3.44895560190625*^9, 3.44895560925*^9}}], Cell[TextData[{ "Viz nap\:0159. \[CHacek]l\[AAcute]nek A. M. Oller, ", StyleBox["The Dying Rabbit Problem Revisited", FontSlant->"Italic"], "." }], "Text", CellChangeTimes->{{3.44915450184375*^9, 3.44915454865625*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MortalRabbitsEvolution", "[", RowBox[{ "LifeSpan_", ",", "FertilityAge_", ",", "InitialNumber_", ",", " ", "ObservationTime_"}], "]"}], ":=", "\[IndentingNewLine]", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{"\[ScriptCapitalC]", ",", "\[CapitalChi]"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[ScriptCapitalC]", "[", RowBox[{"h_", ",", RowBox[{"n_Integer", "?", "NonNegative"}]}], "]"}], "/;", RowBox[{"n", "<", "h"}]}], "=", "InitialNumber"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[ScriptCapitalC]", "[", RowBox[{"h_", ",", RowBox[{"n_Integer", "?", "NonNegative"}]}], "]"}], "/;", RowBox[{"n", "\[GreaterEqual]", "h"}]}], ":=", RowBox[{"(", RowBox[{ RowBox[{"\[ScriptCapitalC]", "[", RowBox[{"h", ",", "n"}], "]"}], "=", RowBox[{ RowBox[{"\[ScriptCapitalC]", "[", RowBox[{"h", ",", RowBox[{"n", "-", "1"}]}], "]"}], "+", RowBox[{"\[ScriptCapitalC]", "[", RowBox[{"h", ",", RowBox[{"n", "-", "h"}]}], "]"}]}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[CapitalChi]", "[", RowBox[{ RowBox[{"{", RowBox[{"k_", ",", "h_"}], "}"}], ",", RowBox[{"n_Integer", "?", "NonNegative"}]}], "]"}], "/;", RowBox[{"n", "<", RowBox[{"k", "-", "1"}]}]}], ":=", RowBox[{"\[ScriptCapitalC]", "[", RowBox[{"h", ",", "n"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[CapitalChi]", "[", RowBox[{ RowBox[{"{", RowBox[{"k_", ",", "h_"}], "}"}], ",", RowBox[{"n_Integer", "?", "NonNegative"}]}], "]"}], "/;", RowBox[{"n", ">", RowBox[{"k", "-", "2"}]}]}], ":=", RowBox[{ RowBox[{"\[CapitalChi]", "[", RowBox[{ RowBox[{"{", RowBox[{"k", ",", "h"}], "}"}], ",", "n"}], "]"}], "=", RowBox[{"Array", "[", RowBox[{ RowBox[{ RowBox[{"\[CapitalChi]", "[", RowBox[{ RowBox[{"{", RowBox[{"k", ",", "h"}], "}"}], ",", RowBox[{"n", "-", "#1"}]}], "]"}], "&"}], ",", RowBox[{"k", "-", "h"}], ",", "h", ",", "Plus"}], "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"\[CapitalChi]", "[", RowBox[{ RowBox[{"{", RowBox[{"LifeSpan", ",", "FertilityAge"}], "}"}], ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "ObservationTime"}], "}"}]}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "seq", "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"ls", "<", "fa"}], ",", RowBox[{"ls", "=", "fa"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"seq", "=", RowBox[{"MortalRabbitsEvolution", "[", RowBox[{"ls", ",", "fa", ",", "in", ",", "30"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"FreeQ", "[", RowBox[{"seq", ",", "0"}], "]"}], ",", "ListLogPlot", ",", "ListPlot"}], "]"}], "[", RowBox[{"seq", ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"500", ",", "350"}], "}"}]}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"ls", ",", "10", ",", "\"\\""}], "}"}], ",", "1", ",", "20", ",", "1", ",", RowBox[{"ControlType", "\[Rule]", "SetterBar"}], ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"fa", ",", "1", ",", "\"\\""}], "}"}], ",", "1", ",", "10", ",", "1", ",", RowBox[{"ControlType", "\[Rule]", "SetterBar"}], ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"in", ",", "1", ",", "\"\\""}], "}"}], ",", "1", ",", "5", ",", "1", ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Bookmarks", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", "\[RuleDelayed]", RowBox[{"{", RowBox[{ RowBox[{"ls", "=", "4"}], ",", RowBox[{"fa", "=", "2"}], ",", RowBox[{"in", "=", "1"}]}], "}"}]}], "}"}]}], ",", RowBox[{"SaveDefinitions", "\[Rule]", "True"}], ",", RowBox[{"AutorunSequencing", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.401152040722498*^9, 3.4011521348336797`*^9}, 3.401152617485893*^9, {3.4011528394940653`*^9, 3.4011528451814194`*^9}, { 3.4011545399274626`*^9, 3.401154690041641*^9}, {3.4011550805029817`*^9, 3.401155087534322*^9}, {3.4011555847594357`*^9, 3.4011555912126436`*^9}, { 3.401156650960583*^9, 3.401156654054373*^9}, {3.44915097425*^9, 3.449150978625*^9}}, FontSize->18, CellID->14096020], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`fa$$ = 1, $CellContext`in$$ = 1, $CellContext`ls$$ = 10, Typeset`show$$ = True, Typeset`bookmarkList$$ = { "\"Perrin sequence\"" :> {$CellContext`ls$$ = 4, $CellContext`fa$$ = 2, $CellContext`in$$ = 1}}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`ls$$], 10, "life span"}, 1, 20, 1}, {{ Hold[$CellContext`fa$$], 1, "fertility age"}, 1, 10, 1}, {{ Hold[$CellContext`in$$], 1, "initial pairs"}, 1, 5, 1}}, Typeset`size$$ = {500., {173., 177.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`ls$124498$$ = 0, $CellContext`fa$124499$$ = 0, $CellContext`in$124500$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`fa$$ = 1, $CellContext`in$$ = 1, $CellContext`ls$$ = 10}, "ControllerVariables" :> { Hold[$CellContext`ls$$, $CellContext`ls$124498$$, 0], Hold[$CellContext`fa$$, $CellContext`fa$124499$$, 0], Hold[$CellContext`in$$, $CellContext`in$124500$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`seq$}, If[$CellContext`ls$$ < $CellContext`fa$$, $CellContext`ls$$ = \ $CellContext`fa$$]; $CellContext`seq$ = \ $CellContext`MortalRabbitsEvolution[$CellContext`ls$$, $CellContext`fa$$, \ $CellContext`in$$, 30]; If[ FreeQ[$CellContext`seq$, 0], ListLogPlot, ListPlot][$CellContext`seq$, PlotRange -> All, Filling -> Axis, ImageSize -> {500, 350}, AxesLabel -> {"time", "population"}]], "Specifications" :> {{{$CellContext`ls$$, 10, "life span"}, 1, 20, 1, ControlType -> SetterBar, Appearance -> "Row"}, {{$CellContext`fa$$, 1, "fertility age"}, 1, 10, 1, ControlType -> SetterBar, Appearance -> "Row"}, {{$CellContext`in$$, 1, "initial pairs"}, 1, 5, 1, Appearance -> "Labeled"}}, "Options" :> {AutorunSequencing -> {1, 2}}, "DefaultOptions" :> {}], ImageSizeCache->{553., {246., 255.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`MortalRabbitsEvolution[ Pattern[$CellContext`LifeSpan, Blank[]], Pattern[$CellContext`FertilityAge, Blank[]], Pattern[$CellContext`InitialNumber, Blank[]], Pattern[$CellContext`ObservationTime, Blank[]]] := Block[{$CellContext`\[ScriptCapitalC], $CellContext`\[CapitalChi]}, Condition[ $CellContext`\[ScriptCapitalC][ Pattern[$CellContext`h, Blank[]], PatternTest[ Pattern[$CellContext`n, Blank[Integer]], NonNegative]], $CellContext`n < $CellContext`h] = \ $CellContext`InitialNumber; Condition[ $CellContext`\[ScriptCapitalC][ Pattern[$CellContext`h, Blank[]], PatternTest[ Pattern[$CellContext`n, Blank[Integer]], NonNegative]], $CellContext`n >= $CellContext`h] := \ ($CellContext`\[ScriptCapitalC][$CellContext`h, $CellContext`n] = \ $CellContext`\[ScriptCapitalC][$CellContext`h, $CellContext`n - 1] + $CellContext`\[ScriptCapitalC][$CellContext`h, \ $CellContext`n - $CellContext`h]); Condition[ $CellContext`\[CapitalChi][{ Pattern[$CellContext`k, Blank[]], Pattern[$CellContext`h, Blank[]]}, PatternTest[ Pattern[$CellContext`n, Blank[Integer]], NonNegative]], $CellContext`n < $CellContext`k - 1] := $CellContext`\[ScriptCapitalC][$CellContext`h, \ $CellContext`n]; Condition[ $CellContext`\[CapitalChi][{ Pattern[$CellContext`k, Blank[]], Pattern[$CellContext`h, Blank[]]}, PatternTest[ Pattern[$CellContext`n, Blank[Integer]], NonNegative]], $CellContext`n > $CellContext`k - 2] := ($CellContext`\[CapitalChi][{$CellContext`k, \ $CellContext`h}, $CellContext`n] = Array[$CellContext`\[CapitalChi][{$CellContext`k, $CellContext`h}, \ $CellContext`n - #]& , $CellContext`k - $CellContext`h, $CellContext`h, Plus]); Table[ $CellContext`\[CapitalChi][{$CellContext`LifeSpan, \ $CellContext`FertilityAge}, $CellContext`n], {$CellContext`n, 0, $CellContext`ObservationTime}]], Attributes[PlotRange] = {ReadProtected}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.448956291515625*^9, 3.449145931*^9, 3.44914598871875*^9, 3.449146028984375*^9, 3.449146111828125*^9, 3.44914625165625*^9}] }, {2}]], Cell[TextData[{ StyleBox[ButtonBox["Mortal Fibonacci Rabbits", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/MortalFibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/MortalFibonacciRabbits/"], FontSize->14], StyleBox[" ze str\[AAcute]nek ", FontSize->14], StyleBox[ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontSize->14], StyleBox["\[ParagraphSeparator]", FontSize->14], StyleBox[ButtonBox["http://demonstrations.wolfram.com/MortalFibonacciRabbits/\ ", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/MortalFibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/MortalFibonacciRabbits/"], FontSize->14], StyleBox[ButtonBox["\n", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FibonacciRabbits/"], FontSize->14], StyleBox["Autor: ", FontSize->14], StyleBox[ButtonBox["Oleksandr Pavlyk", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Oleksandr+\ Pavlyk"], None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Oleksandr+Pavlyk"], FontSize->14] }], "Text", CellChangeTimes->{ 3.448955826234375*^9, {3.448955858875*^9, 3.448955869140625*^9}, { 3.44895591803125*^9, 3.448955939828125*^9}, {3.44895604453125*^9, 3.448956055234375*^9}, 3.448956210546875*^9}, FontSize->10] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Cyklistick\[EAcute] \[UAcute]lohy", "Section", CellChangeTimes->{{3.439987175546875*^9, 3.439987190046875*^9}, { 3.444804453796875*^9, 3.444804454390625*^9}, {3.449037311203125*^9, 3.44903733003125*^9}}], Cell[CellGroupData[{ Cell["Kter\[YAcute]m sm\:011brem jel cyklista?", "Subsection", CellChangeTimes->{{3.4490382348125*^9, 3.44903824378125*^9}}], Cell[BoxData[ GraphicsBox[{{{{}, {}, {Hue[0.67, 0.6, 0.6], Thickness[Large], LineBox[CompressedData[" 1:eJwV2Xc81d8fB3C59rxc617XdlFRSSHr80pREdkqFMooQkRGQyUpRRllhG+a NCiUotKwkpSsQkkDCZGZ0u/8/uHxfHw+Pp9zzuc9znlQ8Q528OHm4uJ6SX78 /3dapVFt7I83lGXaJN/WDjm8Fagtc1dspjanf0rL6pTD0cOWfz3tmqlvx+0H 33yQQ3R3Hf1zaTPlezqKtuyrHPb7Cga9PviW6l+q7VYzKgfhFHM/X4VW6tSy hK2aQkx0hWcGtNi3UvynzkaqiDIRO4kNgfGtVLj69hxZOhP6j77OMH+2UsfT p5nT0kyUmn04G1TdRn2MOmh9QoWJsPYjqwQiOygnn52dkwZMqL5+WM8q6qDm 3MciS4yYMH04/sP1Wwe1/shLj0BTJo4ckVZ2cH5HyR73FH5rzkRgUU+B5fL3 1JaML857bJgI2OmYpPu3k+oW5Toj6M0EbVfyt4kbH6k9IfdOpiUwIbGoVjVk +CPV0OKVI5HIRKv42k+icj3UHdfypydOMeHG+BhM29xDLTkkuWl3ChMl0mfU pT/2UN2mWyTp55mY/90vqW7oE7X+Os+ps7eYUFJLiBKm91LOVgqhbcVMrHWz svNd2ktlD/DlSZYw8bot8vC2vb1U4U+JroP3mHDfXbw0mvszdebKe71FVUws uZm9R1DhC+V4et6LrtdM1MRYKDzDFyrpbNWB3mYmLrDMUlK3f6G6A3D1SwsT VZmmSZE3vlBmjWkeHzqYiM55G2Vn+pW6znXj0tUeJirs44+rb/tG7aR4b6eO MOEke+DenUf9FH+Hqc4nIRY2l4UeOdnbT+38pvxqiwgLf4KO7tvLN0D9ivdM fSfKgtGUeEas7QBVk9tyuobOQm+a7Hv3jwNUjPPbgwdkWJjW69DT4hmkjN2n t/mpsPB2T/0+wfmDFJv1d+yeKgsvrzrs+G0zSHEpLqjkVWfBvq2+WihjkCqz GJuXqcHCyhSz273aP6jfC3T35y5k4T8vB/rGTUNUqIK2gcZyFmTdPuhqHhyi LCriJq30WfjLzW3Nc3mImm+2mXuXAQsRBjwTfT+HqLjiC7SCFSxw366Rczg+ TOlEzKvnMmPBbSCqOaNyhDKf72K4xJIF9fTmZUafR6hA2brlC9awMCp69vMv np/U7KLfSSprWWg5HHCkZOFPirVPdKOAFQsrvLQ8oqJ+UkMHvd3v2rAwwiyL lpQZpc76d/ekObFQfPn7wOb5o5ThNbMhT2cWrNPKN1wzGaW6kspiFriwYKX2 udp+2yj1Pey4yl1XFmiP/F50F49SfLOt+UWbWaiuiXdf/3yUCtLgavZzYyHR XTX0cfsolW7pmKDgzoL+2aahO3OjVO3rtpOHPFhY7NaZ3Lh+jAo4l8ar7cnC /cCeK1s8xygzuBx4TYxN3S9/hY1RMkebD4d6sZDzXlV4QfYY9WK5km6RNwtB C8vKng+MUZ1TebrCPiw0HpzqvnzsF7U9QVLXdgcL7gon5kKyf1EGTO78BmL1 feLmVNEvinY/6IrlThY+JaVMfmn7RWnv2xOwPICFOvfocEeNccrkw6vRiUAW zO3viOobjVOn2RuEPHeR+VeO28vbjlNaYUn3a4l9fcQuDoWPUyEnXnUnB7Ew zlVQU1Q9Tm1oyFtDC2Fh3uMNilfejVNe5UHKm4mrRXsKc4fGKa7/PqbcIp7T WKh5VnqCWrtmzsJuNwsidQozafMnqHnKTsdyiFMGdjxPN52gPmuf39ZPHGt3 VDjHZ4Lyz189HBHKwkm1lB0Xoyao5WXmOQ+IL78NO3r91AQlszGof5b4RIxp RVXZBMXVGuO0N4xcbwi811g/QRl7j4bfJrYa+Le8q3uC2jJUsWyAON9x7MBf 3kkqyHBnov0eEt/lW6qfyU9Sj5NNNOKJzfbOT0zUnaQkbet+3SNmHN750GnN JPX6jdf4N+I7wqbrlDwmqdEhNy1GOAv8dx/LD4ZOUotG+E+bEDc9llItT5ik Mi6ULdxG/EzXe1187iR1xblkNp44Sbj5gHPpJOXx1YbrGnFZSEoR58UkVX// 9Yoa4tGW1rrJj5PUv6aj1z4Rr9J6e69uYpLSeVS2/nf4//OpZke28BT1q/yq Bj2CBec3ww1BKlPU9owL+mrEp+ZSGswNpqjRrr59esR6yn+dZW2mqLLShzMg fqm8f+MP7ylqC5fPTWviRTv9q55ETlE8GxUzHIm/i7NiziVNUT70+Q82ErNm xsJ3XZqi7lLPGG7EPYKbc1c9mKI8n86/vJmYx6byE/P1FKWLjCBX4gH2KZ2f X6coKd11IfbES9ZbBtfMTlGVn8IL1xIn2PqnnZeYpp5GuiiYEj/3jD4RqjlN rZpVqV9EXF4sRK01naYO2IvdUiBWP3orT8FxmuqwtnspSMznw5015j9NBV2V V/9F1iPVrFC+9sA0lSF5sewd8dYke8nstGnqg67coYfEr49eDwgqnKb2XLoe n0u8TjdMemXVNFUocKpmH/Gh3IC/km3T1BuuQWwkVuf2lPgyOE3lGPyaWELs rZq654jsDHXJrpT+nnx/I7eUPHudGerT+2cRhcQOL8VuKa6aofz/LJCLJNYZ 8tQpC5qhPidcFBUm3iJtFn0gboZ6c4bH+zWJP+tbV70ts2aozgj3sRRilaH0 R2+qZ6gHvMdqxYmDlukXt7B/U1lTd9f8Px8a3E59O730NyUV9PzgOeLJp+4L rNcS+34aX0V825Gddj/sNyWcWXc2jeTbk95Yvn0vflNys7mVUsFkvetLHmn0 /KZs18f23CT5a+b1ffrVxG9Khtpivpr4dMv+W7Iqs5R2aEyVP8n3tNxTZgl7 Z6myi6IFp0m9SMlROnEjcZYytLm8kE3sbyq07FXeLEWzn1tzmdQXP03FQMG6 Wcp8E2VbTOqPiFTDiIfcH+rR0+mUAj+Sv2IBxQHaf6jO8YyvKsTzP9Z5R+AP tf5WQvM5X9I/QrX9Dvv/oQ4WZcTsI/XtzLm3UWHlfyiRcWOR+dtYED7v7uj3 8g91TF9eL4nUw6w7iaWuPX8ofru68Z+kXratPPdOR+AvNXGmdm0RqaebOd3m t1z/UvevjC0T38LCsYDpTeMTf6mfFhsXuG9kwTgi7FKh4BzFXtPAk03q+9bR g4XuCnPUbP+P6HZS/81/tt4rWT1HHRrcbbSO9AcLo9qD2qlzlEjGLD/dgYWL QWcWmS3+RxX4fulfYM1C57P3BwrN/1H6rRlxq0j/+Sq77oWEyz+q1aWtctM6 0i9ZWupv9v2jAi9yaAdJ/xp7UXFB4sU/KubN9f4bq1joVnIYrtXlguL1Y+pn jcl8VQRLlEy4oDmg27vbiAVFMRn5PZZcsOrtbLYi/dL8RsV9STcurNSJtxkn /XX+b64wjTguTBgWFHKWkv1Alg93fisXkk8JMbm1SDz3D7RXfeTCF6NrErdJ /7Z7o9nXOcCFxdqvzDw4LPRFlWXyzXGhT0nd4Cbp/9qGkRd0NObhlqrOxYUK LAz3JQ5Xhs9D6H6ZuHwJ0s88cw6fPzgP9OmUt+pkf+Ew6vtz7/F56KjO2nRJ jNTb0Whz1Zx54I/9JJgtzMKRhJXqq5/Pg7PXkX++vCw8lKazyyW4sXu34Lao abIf5PX5YFLADXGZNXbHu5iI6X/zx+sON9Y3F3pVvGeip8f54OEKblS+XVz/ neyXBsq5/ytr5Ea+fnz2ylZi76vdn0e5cZY17NjUyETwoE+7+woa7r0tsQp4 xITDyTqtq89pMHgwufxqDhM/pI1CdRtpuNRidjIum4l5Caybd1tpMHVJXbk1 k+z/rm8cvP2NBtvCyhci6UwIDhqsCBDgAV2z2nPtSSY0n4WUfbMirkj9sTKa iZXSBn9HGniwKaCaWunEhBHceq3f8sDBsTxvwp7MR6JD8eJ7HiS+MXpydQMT E7cVM1YN8OD26TArXmsmvETMfdbz8eJj8tHYyyuZcLwvv34fxYvvdeEt0YvI fvfY0UabW7zgid4muY+Pidy+2c2SZby475wXMkBj4pWgiVJzBS92bV2S6zSP iV3xretW1fNiaeXqHep/5OBnL8z88ZkXwwHCjQVk/98hE23uKscHmnu+yfou OXRe8Viesp8P265k7f1VJIdRbZfplXF8iDuSa/nhhhxsK0ylfpzgg95gzdma AjkS3/M3Ls7gg652+sPki3IYvHpYPvQOH9ag24jnHHmerjrvwFc+uHlNXo7Y Lwfj5+F1F9bygxGtQT+2Vg7OdMOhHFt+BN6JOKdmIQfml6SjaU78OJPT8eDh SjkUft8js9uTH/JiR999N5JDRLjBp769/LjYUXxaS0cOMebNexov8+PZavHK pRJyyOzWmoz7yw+b2+rTCe2yMOxnl0dyC2DpqtJkZossLPM/tvnxC6Dx/Vud a69lsSBv/VJDCQEkjVkdelwvi4aS9WcvqAsg+RlvbluFLGadTF5nWAlAvoeK uponi0fNjVxaqQJQLa4wfe8jC+fbwR6J5wSQp746WMebPG/W3/17tgBuVAdX H9giC94vLtbZlwRwvujOZ3lXWTx83axXXyaAl3cX8GCtLPYkngtzbReAwnfJ B0sWyMJqcVypnawgZOyFnCp+yGDEYLUcS14QefK8z/v7ZXBT1y33o6IgBu9f TZT6KgNu2UH2Vg1BrHVhafh1yyB222e9JcsF8V+7++XpRhm0Ggu7KjgI4udz 64eNt2TQO9uYZHhcEE4fd/5dEyyDzwfs5xJPCkKgm3ufeYAMtLn8RzuTidUO hRv7ycDNZnXw7rOCKGC/6tbaKgNlVylO2EVBcB6qXxq1lcFtoyH3lkpBjNsv EDNZJIOYy92XOUOCyDolXVI5KA2ZRN8NG34KIvCilrNOnzTOv7u2JfyXIKLr 9m0+3yuNw8uPVN2dEYS4mFV6+Dtp3MxykRDnE8LiVI9pqVppMKOFR5iKQvi9 q/2DQL40Wv6aet+3FgI7iLv0tYs0Fm/qfBppK4Rjqav76Q7SmGw/pbTcXgjz n5aWbrCRxnhfRs8lFyGc9fvDrl8ljUjjw4JeXkK4Kurvdn2JNOZtPGBmFyGE CVae1GIhaWyC8wvtXCFse2zwiqqUwreIKf7A/4RwzoE3s/CeFGrm2IsL8oVA d77rJlUihaGrtlYKV4Ugklj06kuBFIwZcxpDRUIYVsxOizonhVVl6yUWPxFC uOiykbBQcv8TetzGXjIeca3wu5pSuOH4tHC+sjCM0h6srk9mYFpj/vGFqsLk XNL95+wJBo4k/rdAW10YdwQ9f207ykAm7XHDfC1hmP9XeXE2moGq6jim7BJh vLY4aa3qy4D3t76IR5QwQucZHrM1IY72ubR9izA6VU5Z6fZLIn369IxOljCu ZNpmnDWThP+7Ze7jEiJ4YZDs0DtCx+IMuvwLhgiWijvG8A7SUWr0681/0iIo ut3ep/WNjmLtwmX2TBHcbfibEtJFx+BdH81HyiK4Vn3fi1ZPBz1qT3zDYhG8 XTLnaZhPh8HPS431tiL48re7f9CJjkU3H2c9txNBW5R9F8uOjhF+1adVDiJI erTDysqaDoF57gsfuojgYrBPTuFK8vd5vuU1W0SQveeM7e5FdJRYLzJSChYB c7rLQ06ADqmuSytmTougy/27+5294qjXynjjmCoCw78n1P13iSNIYI9/cboI dqn9OaW0TRx0vem84CwR7ImvdE21FcfE+47TfJdEsDYkG8kcceS+W2qeeU8E O29/WN71Vgzjwpcc/HpEsCh2qdCArhiUffa+4f8sgg8nw8M7NcWQIaZZXPiV rN+MjuhrBTHk79fKmPouAt5cvbePBcXwylpz660JEbDyenUffBLFUQsupRRh UTCfefxWSBFFpkm/4eoVorjzYX3W43ERuOgYh9NMRBEXskn8yqAIYvYLClab icLnee3HpF4RzJ/YYrZhtSgkGbH/+b0WgbGlhmTsBlEYKq+Yp39DBHy61Fcn X1HsbT5ssm67CE7MjtW0pYtCvKXN3auNxI2Ym/GXDFHIGoi0ZTYK4/ZeY+Px bFHsHhaTbX0ujIDDgp/l80VRy/vur2OJMBQV/5s5fksUhZpdFWGnhdG+STmo t1YUx3jefTK1FkatSqLaqT+iMKpyHmQ8E8KMwtZJfS4x5PpMi0/fF8JYQdev zzQxxEjbjH8sFoKh9vewNcJicLQ/IFJB8kwvfbBwGUsMLLfmodxoIbRKPfh9 zVAMGlJ+fCp6QuB1aPPnihTDauPN7QuuCqLJ/OcdiX1iKOQJa0rKFcTI/p41 GrFiqFTmCEylC+IkQ8V5U4IYqh+LW7fECaKvzIjelyGGEw5VcU+9BdGVZZF6 4YEYvuYGLNmtJAiv/5JMz3KJQ2f9rs1LzwsgUimC7y+POK6+qt9inSaAKLsR QT9BcWyZXzrmf1IAe1otnqyWFEfjYev22/sEIBkUNqGhLo6ia+0T0R4C2HL2 Snz8WnFwFGPSh5QEUGlcwbqTSuJyZ9SuwGv8+P5L0zw2QxyCxy/LKl7gB9+o a759jjj27vz8qCWTH1V7GoXnrojj/fVGCftEfrx41hK1/4E4fjfGceKD+PHr /rVAmV5xJLzN+fhlOT/Oxx3Pb2PSoflxDSOxjg8Wx+fLrGbTkfpBsNXpKR+C 8pIH7ijSIRM8ZalWyYdCgZhbaWp0NMyttXhVRPrylOo1fx062NnMUfdzfLg2 biDhQPKuvWl8wVY/PhiP5Olo7aSDh/8Nl4AwH3b51Q1VBdJRXRe5L5CXD818 z+e5BdMhKdo/3vqPF+H6vmqpe8j1Rau/3hvnxQ7XEDAO0uGmeZVW/oEX9Ozi CIc0OrIMjRdfL+FFdc8C8/rHdGgvO1cQ6MULx+Rg8dqndMw+ctEXcufFNv4L G2uq6XBqDhy76cKLNvcXbvUNdIzF6NAE1vNCYmW/+Kd2Oo492PWaz4AXjzOd Yl1+kvnWLfPQFePFaoGcZ46qEujXaW+zfsKDC+fqYg9yJKB4Mdu0tJIH/p32 eTe0JHA6OUpNrZwHWWFtf4QWS2BgYVO4VBEPFom0KHUYSyD+c2C4RQ4PXlot 1itxloBNl25XbzQPsjfOVvmckMCnLzeyWMbked4vFI6ckkBkg0LfWQMeOO1x T71wWgIOobeYzGU8YBh6Vn86KwFcuW6wWIcHB5Q7tYMvSiDWXjAuX4kH6hoj lg8rJZB3WOzxFV4e3BuWqRt8LIGl2k8WHubmwUCuoJP8Mwn8eJdybts/Gvo7 7ifsr5dAnerxUMMZGr4cF1hv2yaBi4a0rQuGaHin6xuk/FMCW9P0nZe00ZCY 47F46y8JXPhh4h34lgYn4dgfuZMSWLVj5dFbr2mQkDvuqvKXPF/rtqRFAw1C r73bdIUkYZVwLaSiioYn2uoXY9Ulcc6pzOPVDRpqzY+XvdKUxOTDRv/AQhpO Hu8rVVgoiejUjFz6NRrEPG5HPNKVhMJTTnLARRq2n7QeFKIkkS/z/HJAFg1z wlcfvtokiaLI6Vvpx2mwjB83Z3lIouojc/C/YzTYGU+d9/WUxO6XVhp3jpJ9 +z/3hnl+kgjxHcr5dogG+/Obp1bukYTSfdw6F03Daz1egbS9knD6OjXXHEmD tnH312/RknCbuOEitZcGBWtr3uRDkmB69igWhNGQnXy0vD9JEhtKLmnL7yLn BFkeuZUpkuDrP9MUH0De58EwzUon93d+jZ3eQUOYEr3F9rwkHqbYSg77kvlO X2E9KSDjP3NUQNWLrN+elKX1zyUByeK5my5k/TeV79Wpk8R0KGc42pmG42Lz wlIaJJElR83YOJHx28kmbGkm7/fd7sPnQMMkkyHx76MkirXUC6tsaOhtF/nh /1kSa4r2Jj5aT0MRPMLffpNES6h50lNrGvpy5JILhyQRcXbud9c6Gh7FJj3z nJWEZ+7HI26WNNx+/naiaU4SmQ4vjpywoKG1LeMVxc1AhF1E4ePVNJQ7lwar CDKwzTMpyGQVDVq7GPqpIgys0dYTjTOnobSQlsdLZ6CuVKj1zUoarpdedfoh w8Ch+9d7D4KGCttteZ4sBnYVnZ/fQxHfeJzQqsBAiZP4eUvi17Y79J6oMyDc VcyrYUaDzI2HYwZaDIz8mPiba0rDcu4n64sWMqAtNKCmSKzI3fsybykDruND vxeZ0LBxPW3ndn0G4h92Zt4zpiGiaXf5fCMGztiWx64hNi/5fnfElIFFX1WL PxjRsJm+cPvdlQycq7yntZ+YNTbyaL8FA/Ki9EFV4piNk9UW6xi4Kvx0qomc C/+umN0rZsPA5gHPDXHEp45WvG23Y0Di7b4xinib+nj7BScG/v3M/8RNPDTr dSRwIwMGvh4KjYZkfUeetBi4M2Blp3cll1jv8+sXNE8GWmuu7dtL/LbCevvr bQwodJpdcCW+5z2Sl+PHwJVzYVIU8fWayH0BAQw0/HvSpkPM8+HS9IpgBjaJ 5/erER+5toQhGMbAkgcJVirEy3TfveiIYKBzsO8Ph9jltJtiAdkHLjq2iGsp scnQHpHoA2R9feqcLIjVYntTrQ+T77NRcXYrsWqaV4lCPAMLOGd/HSL+l1C0 4+dxBmISUsyuE8u2Hi97doqBpcvCujqJV/DfSj93hgGzprRGBpn/ibp3AoHp DLhP2Ek6Ert/eCG6MpOBcv25wkxiKW3qokwOA7myP8/1EfOUjdf++I8BDn3v OxOy/ta5BdHPLjHQntgTnEl85r3Q0dAbDPhFHzrvT75nqu6y91bFDPQcXq3X SXxr3KVcrZQBtRXzlJ1JPGxLixNqr2Dgv5Uef7aQeHnfKLrv9mMGfpcH/xgm frfk1O6Tzxh4pemtF0/ibch61+dVDQwMnb5e84LEo/CEjYdyEwNv9D0YkSR+ w2+qu/xtJuu54NI9bRLfG3LvPi5/z8C9i0f5b5D4dzM8sWH5dwZUK8druUk+ RSUa5EoPMzCu8bzlO3GB0DevyVEGboVyGb1fQ0Ojnv2q+zMMvNAcFW0i+egX WGG9WlAK2zd7ddFtafgW0KCkJSqF5Gy3m3obSD18N7NFREIKvo2tbR52ZH1f 1jDb5KQQoMjUqyP1YPB0zZYgLSn0dXaITbjSYCM7e01SWwolI79EjDfRoPti 3tp7i6XAc48VcmwzDTPjybHzDMjzKqV89DxIf4gRqMq0kEKa5QxvhzcNa1Qt znd4S0E/qfGvYzAZX0n0w0O+ZHz5X1dw7aZBIOeN2sKdUnDMV+q4E0oDrZRW eWC3FAYZQysWRpB8WxfyTyuWnGPCpRL999MQLxQ1m5AjBRdhBQXpUzSMCGyd XX5BCmdHBF01k8l6Rsnofr4kBel/7UPUGRo62pcZmd2Qgsmx8CVx6aT/XOu7 NvmAOPH53425NFzeHKUZ0iEFO/FIe73bNFx0zTY7yJDG/rzrWlc7afBtdoyM lZVGmbjaoycfSD2o+vrqkLw06jodyj9/Iv2iS/lVnJo0ZH+vbTftp0H8/MhE op40uPPfXbaaIOvx5cJEjiM5F5ZuvFlN54HOkyCj+lRpxM9T/7PChgciK12n Gs5J46ymui5lz4MdPPOLXmVL467TomvWzjyYcUoUbrkojePhy12jPXiw7HKW 24cSaRw1WZS2KIgHLnEfDvx8K42YA9s3jp7mgZzmeWMeKRlopVq/a+3kQZyC TP2orAyWCEolFPTwwK/957KP8jJIFqILxH3lQb1L4qX7ajKwumkebjPCA9VL fS8D9WTAJWnfrkvjBcW+kNLgQM7lVZmWlDYvfg77l/icIef8aIH/PI/wYtIj 6IxNugz2iV3QEj7Oiw+y2vrLM2VgZPp7XWUSL9SGdN7QLshA2F91w9IsXrRf VDHOLZZBtzFTe9dtXmwsrrKvbZIBTXNyF/sTLwaeK/h9E5XFk/DGnQ4WfJDY stb4iIQs5vgpV3drPqAgtlFJWhZD7So1AfZ8YKseXrCRLYvXtAa1bA8+rPj6 vqJ6gSwWrNIqNI7gQ9mL2b7UNbKQ3Lbe8PA1Puy+2/VvJlYWd5uSs2Ql+GEW XX+5e0wWq9ZG/B0e5cf8gg/8pZOymLq18F3/DD+SClMFTvyWxekAgzP98wRg e9vy6zJuOYj0uZ6YkRBA8gtxgXgJOTQZblzvtVQAm46ceS+9RA7nPHu3WewR gOnHhxaDgXJIzrDntvojAL9FHeuDv8phBUdONIkthK0qF1OuP2WitOfyHbcA Eaxa6R2mksHCE8pasPmbGDxKvVumD8hj13KzTKUvdETl2V/9bxMbA+Edu2at JME5cMCuaYMCef9FN4N2BgKLTukKrVaEnaHM54Q10tAdNlobY6mEES/rXK2r MuCpDGkQtVaCxLFot7kbMvg1/U8if4MSnhVc6Gi+I4OL9ZojTRuVcDc0SjDy kQz67q1jrAxQwvmD9bSSVhnYX45cH31aCamtNzYM0GRR3xKe7NClhCMpTTOW W2URUlSp+stEGXUBTistyLoMDzPYGyhlnJvRv+cmI4eH95T/XV+pjKSbI+kh 8nIYK9aN87dUxjbF+Ph0Drk/deDsjw3K2LSzluvlCjn0LWKbq2xThtWf0EcD XnK4aaR8iTqhjELuxJTOYjns2F172adTGZTOtLTeOiYGbWYG9T8oo9aPK83Q lgnpChFPwU/k+UU3rxs7MhHFrfb29jdlhJwezDXyYOKpbNMQfUwZ3q5lzvK7 mRgaf6cvIKiCh4XXhX0zmGD40D50GaggG1e/0L8yUV+5wq/FiHgHx6R6gAmT UbpGo6kKnv5M+RoxzMQ7LWOLp6tUcMHGndM8xYRZrbtoxQYV5CWcZ/kLsbBp T8+Hb34qaHyY9EN8MQurcvfxa2WqQLoroZr6//+f1h/rNTivgviGPS+PRrOw x6F9YG2eCvYJ2/2uO8Ai+0eF/UGXVeB4+uxTy2MsiJfVl9beVsH6macNSiRu xqS6Xe+8UMHS5UnjFvdZcLw8ne73VwV3mBobnGZYKD6ZUHeeSxUit7KNjf+y sH+FstpbmiqSJy+IKs2Tx/vc8A2rhFTxLWHt5m4BecxfW71fV1YVHW4+Hsvk 5DEsLTi+WlcV73Uk1ljpy2PVSLSgpa8qQg8YZ/KHyGOf5xyv7w5VOAYqr7IO k4dO0bvf8YGqUFX5Pe9khDz0nmq9bAhVBeuQXDnPfnlc62/j9jpI3uf9raP5 uDzWxxXuuJ+hijT/kriefHkIhPSoKr1UxRmFdru7zfLYfkzV06NJFekt3fsz W+Ux59xw7HyzKr5E3D4Z1SGPcz7GaQrvVBHXt3Pdkg/yOJpXkrLgmyomXnyR jByQx4OS/MJgLjWE0J/FBf+TR2Ekl0b+cjW8mveuf0yLDU3D7X9Wr1CD7U2B p5cWslHf9aCp30QNVpW3yhwWsTFx9PEOvdVq8J4f/SVfj43Cc/oOLQ5qSCge 1JIyY0Nlsbvm6hA1HD6Vk27owMaJ4j9bJ8PU8KgnYMF1JzYS0+7GF+xVQ3SM 8wOmKxsO+rFZkgfV8NG69Nl3NzZ8GtY+HjmlhqyPdpbuPmwIH7om03pdDcZ5 pptj9rLRV2Z2N71IDcftz5bfiGIjMtxcz7VEDZsGdX69i2HD0kXrSdcDNcRy RUxoxrKRvl5FdKxeDS+7xWfOJLBRUHHUZ3W/GgoeZDuez2BDbN+L8oMcdazY 16q7v4yNPyscVsrNV8fXYD8XoXtsBJ9ZsuO2tjpOzi27nlrOhvjF/JSveur4 sT31Y1YFG/MeDes4m6vjoPz4upgnZPxLDybZbVXHNw3VrsMv2bCoTE0Y81ZH 6NVSx+ZGNhp6FtPTfcl1SuKLQhMbRSVbnnXuUgfzzfZ1BW/YcD0ynBG8Tx2n DVfPnW5jI60wbqooUx2D7X1v8j+yYf/0nsnmHHVYvn28oKSHfJ8Srz88F9SR pHfz6ONPbFSbL/zmdk0d0ryGJi8/sxHH8wLi98j4WRuOlvWxsXzDqP7DB+oQ 8hStu9zPRldVSk7AI/J+u455KQNs3HVdfK++Wh3qh1SctwyysWbiz9SJFnWs 7Uxzqhlm45nDQluTDnW0p1TPPzvCRrPpSaHhTjK/ZQaDXj/JeBfeKHb4rI6s zBM6Q6NszNimnFIeU4fYvMETzeNsjM2d+NkyoY6En1I5hybYWDvCKTo+o460 yMnT2pNsPHT5umKci4Pbl4vlIqbYqLxStbVRnINNHuNH2mdI/Ajk1+xmcGC7 eu9j799smOxaEiMjy0FVWv/sAHGqikadpyIHKobtoT9m2Vg3/suDT5WD5Kap Qr8/bEQ1G5vc4HCQsdXm4wfiQuU/L6e1ORj+9N3gyV82snzf7stbwgH3mY+b tOfY2OrbG2y5jIO8cu+wVGKfj5tZ6cYcPPaJSXD+x8apAvkmE4oDo/jaQ8XE fW+ePvlizkGtm3gQPxfpS/f83ZZbcbDOT1S+gDhn571/3TYcKMbGvfv1/+v+ J7vi7Tn4jxUVbzRPAf92nvq52JmDvzOvlPcTi1tsNXq3kYMzxgFXK4hD+i6X H3bnYPfmZcxJ4jOePDu1PTmYXCoZrs2tAIsPbJu2bRy48Q3f30KsVHTaM9aP A88Dd76dJO5dxXVxQQAHI8XWv+8SjywRZrQGcdCidvVXF3HBYruig6Ec7H1d 8maOeEJpV8SCCA6yNb1T2TQFnBf859saxYG29CUDfeJXCvkHY/dzwOTZ9dCa OLt89NHCQxws6L2t5kG8zTtBrT2Ogz61HTt2Enu++Xf9cAKHnGtOnAojVhr8 6bLoJAdjHvTkSGLeml+q75M5uMIzERhF3F2YJxafykFX2HKNCGJHmUS5pec4 OP236X4QcfwDa+pDFgdpKc81tv1/fLERh07kkniokQp0JLY4kdetn88Bq/VZ AkW8SW+zw+fLHAheaovRJA5grPiQXMBBZr3jauH/j+9f40GTmxw8T1716TuZ v5Bw4fKBYg6eTBfZ1xC/OOExl15K1vPZpbQc4oXSkR3m5eR7BC8uCCE+Fpfw dKSCAz3zrUkU8Z1pdsX5xxxUW1msEiLO7Hhate4ZB3d8x2tek+/36y1f82QN B3ssD8mlEo/ZZ0jYv+Ig3+a0ijCxYtGsydwbDhYqWrRXkXgx69EKut7KgYKY qWso8ZmvPF283RwIJYXcqSPxV6T4XLqkh4O1zOHEXcRiM7s2eH7hQP75Um0x YnVWduWDQQ6w9PpDcxLPT3oGnIJ/c/BKa04kiuQD99kKp8A5DmJPGS0bJflz /oyL5Q5uDdSrDWzeTsyKsZjyFtJA2prz+cYk30RrfTY7szTw5iAX1y2Sry+p b3fsFTVwtncr/xzJ5yVZrUM2qhoYtYrlW0dsRFnQLBdoYEWFX38TqQdHTRUj lhlpYOGQueoFUi+ypl9fX2ymAfN+3qY6Uk/UvvmXLjDXwM5vVwMHSb3RqIrQ V7bSAJ/Wpr0qpB7dDNeuFdisgbsfvpfafWfjfreG96soDWzye7ikgtTDE+u2 va/erwE7+5DUM6Rehn+d5X14SAOqnWOd3qSefr9uE1x4XAMWttrsyS42Xvwo cjiUqQFR4adWH9vZaLwmk6NwXwOWpvozFaSeT/cVu4k/1MDN8h8H0MCGTf6N m1xPNLB65tDnx/VsRBx7TOut04CihM7aoho2DncLIK9DAyExrZF2VaT+/XLR 557WAI94tMP5O2T9j3FMCmY1oHbD6N5QMRtbNobVbvingYbkR/lGRaR/MLn8 s/k08b1eX6z2Oht3dvBf1JbWRIx2v2HhJTY6L1ulLF+qic68utnMdLIvFi1a 2LJcExUdbu8vprJhsMR/SegKTTwOszMvOMPG4nCH8BvQxIDOtaIrp9hYqeP3 mLlBE3Uai4QCj7Jx7aRHf2uAJowFGMoqe9hoC20K2xmsCav2rurPu8n3M8qy mwvVBN/Lg38uBLPh6VUzpRatieU2A4oSAWR+Td5NvgmaCK29Zf3Ai42eHh+T +kuaeP6f7C9DWzac1usMT3RpQm3jlNawGhtTNhG673o0cXO/mesbZdJPO564 VXzRxDefCM0iBTako1657/uhiR1VtWWbZdnQ6+Zt/TmriZDelue7hdgojTr+ /AJLCxWHvhZcGJHHYX87VWlXLbiqFM2x7sqDdaxqxZvNWohmZy9zvSMPuU27 JxO3aEFz1n570i15hLe/dv3ro4WNRnmPh67I4+6G7LimPVo47R70KuScPC6v Gu5enKIFtzdJzxP3ykNevmp7a7oW6k08dkSR/V1ReXloVKYWnjr0rvUOlkeN ah/74X9aeL0l5gXHTx5eqVTk0iItbDh8zH2Pizykhk35Xt7RQtFWfTcTB3ms ZS0X3X5XC2o6OhX/bOQxvlrzYPJDLTzxjy+JtCDPP1H2TfWJFg6mbHVZtFIe /0y3VZU+10JjYFDwRxN5BNyPFbKo04LGK3mek4byAMPr2dsGLUhzfWYuWyaP /wF9dN3n "]]}}, {}}, {{}, {}, {RGBColor[1, 0, 0], Thickness[Large], LineBox[CompressedData[" 1:eJwVmXk4lG0bxu37zGAGY8zYx07J0qaeswUJqVSWlBJakFQUQpYQUpGiRaGU pSKVUiJUlJJSSipKJdVbRBjbd39/zfE7nnu97ms5r2O0fIJX+okICQmxRIWE /v+7a9rzY3TOEOUZ6swJMOHh1bKegMZZQ1TZt05pGPOw0Xt5XJTbEHX64UlR WSMe5JY9824/NkQF/lbJidfnISqi4+9cxj/KKrNmSESbhweFRc/um/6jlGt7 3qdq8mBWHiBOOf2jdt+u/iCrwUNT0tsa3kHCJbE3+9V4eHj3Q/QGkWHqT+7Q KXclHiCdQmVpDlN/A+v5uUyyvngX7d78YUrvpG3POwUeao7N9OqLGKYG+DGH QechJqyJdn5gmJLROX70mgQPM0L729Z8HKFe3vr41P0fFyP8ko8Xxkeo4u+H EmYMciGx+MPSHtVRSlCx5bLEABdjm0d2mq0apb6v0u/O/cXFina/voFHo5S0 TkZWRg8XowkvstRKBdQCsWUHzrdy4bfq16SX/zj1tVIkyKmIi8CbU5IX4sep TNGctIhCLgpH1UTaz41TCzzmHS8s4EL8aSRrtGOcCrh48uPIGS68bAcNZy2b oNjh64MPZnBhl8AMvjN9kppr53smJJKLpL/NqV+/TlGx0Ter/jlxkfx8VG3h UWGcieY+r+tXg+fJHKbnRjFY3y57d3+5Gix954cwAsXw73dEj+syNaQ/dfld FyaGzH3rq744qmGugLNWN00Ma31lb0jZq2GevLhT600xlG85OsdxnhpsBkXa X8mKQ0UmVLfaUA3Wrz+qZF4XR53P0BJDETU4LPVzkq8Rx9ihHbJFUxx8OLGs IbVJHEmVsa/1JzhwGm3YG/VBHFu407drj3Cwo2TxQ0cpCfxpHhDI/MdBW+ci TsZaCeS9pLmcf8uBpXJieZmQJNKopR3PrnJw6a7LzRZZSUTc5Dj1lXKw6Pb5 mT+VJdEqyakRLSbjewqO80wl0fQ9Om36ebLf6wbaRg9JLP8vUDgkm4Ox0oBb vuWSqOCcXZ60n4N18xvr9b2loJDxfqpjGQe+hcEfvm2Vwsl9JglFjhyYNnrt Or9bCmyazszQJRxkN/zuUUyRgmToa3mxhRw8UFv1vP66FPC++8ekJQfLXtQ+ DpSWRpxniJYvh4MTc9X1Dl+VRmglb8uDT6poCZ+5Re22NI4kL+AGflTF7om7 /gV10ph0uVvH6FTFuw6nkMJX0ph48/i18ytVmKXGFuwZk8ZS0ZTL5x+pYsTZ I22enQw2dYfev12iioR5ecdpb2Tw6+z8Y1tCVNEmtcBuoksGkiKKYYVBqohe 6rv+23cZWLjld3RtVQV7htSp4jEZpGpv0HT0UcUWj9OSP9Vl8fSTncvQSlVo XqDnLfeVxfCSL5/PWKgi/0Rk17I+WWSOBmyeNsDG1tn7YnX+yuLVGUOX3F9s vDa88vr3mCzY6Y8bpb6zkTyv0zuYJoe+a1bbnn9k45zJrblS0+Wg+8nUyugp G4bDc6Izd8lhxu6DFyQushGZvk2tM1IOXg42/ab5bLxa+mKXWoIcDJYG3V5+ ho0DJvdUoo/JIXeq9G5yJhuWsYvCWq/L4VWMaGxdDBszV5p+yf8rhwCK0enl xkbHfsMelzE5XA3Y9GzuSjZCtWQvDIjQEKBeZ6PszMZYY62ZqiINd1qLj1Qv ZONXSHBF7zQaWodfTHttSljFxyRhKw3pmz/unC7Kxr2Ml+8Wt9HQr/k770Sx Cg5HDDcHd9Awo9JRWOyCCl5z2zmHu2jo67jlHHhWBTss5pws/kmDyPP11dOP qUDqXcQTVzE6ztULBxyMUkFE89EwX3M6Fr9qH4hyUYGgMy+2xZqOG6bfp5U4 qKBAP9PEzIaO6KGu822LVFCbHznzoR0df0aEnbmzVJDCPz3lvZaOsQ1HZ8do qqBq+7aX5nF0rL4rN5b9RxnsP39mvEik43NVWUZanzL6tAUn/VLpGIq/07iv Rxlm0Rw/v2N0mNRsNHV9o4yAdUXyjRfoyJu7tPRNjTLuJk51TxXR8V9ArfS1 28q4qu0YZ3SFjsoP4ouSK5TB72eruN+k47Vu3lbji8qQCWjsZz6kwzBTPsQ5 XRnX3+3N6W6io/G/hcfpycqwy+7syXtKxzFt5rvmWGWsvnJ9taCNjrDmhd8Q qox4swvWMp/pOFjzU0rKSxlZ/P6UgnE65O51XuMYKmNJYErg5ik6Ciu74jV1 lDGFc4c0RBiIj0p21+Up43BwXHqgJAP/SQhM9RSUkRK1JydcgQEP4abdzFEl 5KvXxX9kMrB+6IezzF8lqDn+rJitzMCR+9u3T/1UAtd6x6/HHAa0RlZf6ulS wqeMjZIbdRjQZiwdOtWohHlXLDZu5TOQtOz25IE6JWR8Nlf212fA/jnr+Pa7 Sjir9v2cjTEDW0UPZMwtU8ImnaDy9TMY2CueV/PghBI+iqqulbFkYNGTVKsL R5XgaF2dUGzFwP3tYnHxqUoozBIPbpzFwA9nn3qbGCWkBRm6RM5nwH8Fqy/f XwlL/LcXPqEYKB1OUY7YoIRKz9XX5BcwkO+7Z9NyTyVYOPEkwxcxwLn1Ol7g rISLyw02nF7MAOvmh63P7JXwZalh+nVbBqTrDmTlLVDCennNtHp7Bor2dX6y tVKCoHj+9qolDER+1FBRmaaE93nnHQodGDB8anDzm4ESBp+sZK5zZID27KxH ElcJ/xRqlAycGOiNOrpjjbISrKKqZvcS1hJzUeHLk/uOeygsWUbsEU+bfV9U CfK5Ku++Ef6kv+th+gQLd8aPD+xzYaBfJkjKa5iFyPMxmySXM7CEpyll2M/C 54Sbs5MIB/FKng31sdBzbl3sOOEeTT2/uh4WIm6/tNu8goEwXn5b+gcWPvyt OP6IcMNOA721b1igRb6K4q0k999d5aP/goUXXEfprYQPDCzP/PuEzP/kY1dM uOfRu9qaByzknr+wsJtw3MYFg6k1LLScfC1Ld2Vg1HG9tfttFl5/Hbg6nXBi jdgR3QoWjNXM5zkQzjUZl+4vZSGgWqjOjXB2k9Dl6kIW3Bqknb0I/9Wsj005 x0LZvVDxNYQHGrdfb81hoTa1RX/x/7/nXbdWzWQhJLvgkR5h8Y9hzI1pLFSb No1MkPOwaQdWFx1g4VXaxpYmwluDT0kORLNQKtbunUK4YJ2P5dy9LIgKd96j CDcUBH1NCGFBnLlNuI/Y49vnuQYt21jI+1trc5CwiMBKjOPLwtUYv0Qe4ZKN VxL81rEgcUVzsJDYVyi3q6J8DQsZMZOn+ISrCv6cmnRhoeG707Ec8l5ltn12 Tg4sCKpO/hUh7FNQe+/kQha0519eeNOZgbTZK2zmWLEQldi0QYgwf1bI6lQz FiCRsRDEP34FzfJ5r8/CDpstZXlLGdANWL8vgcPCk80XAuuJvyn/sj/9lsnC WvMfTu+IP7Zr/mqbRmOhyHRp5y87Bo6exvWPU0xIJC+s7iX+XPgrPXD2KBMa xlP8DuLvkZpvNhwbYCIq7fzguYUMrBBaorHsCxOGEo0e9+cR+y3mdrQ+ZmIe p3TpLhsGJG6e8LBuYKJG9lgmdy7x33u5q09XMyHMzcheTeLRf7FGd2AZE9E+ T3x9STwHXhFnaB1n4suPBTJt0xk4K/rVJuMwE6cueXTPncaAQqyfhvhBJl5Y +mQOknzwsPei2p9IJmb9O8SikfxBfy936t1GJtx8xVctIPll0/Hr7LVrmZjb a3ZhuxYDwibyEZ2rmDBjfPt1ncfAn/yr4z32TGy8G2P5V4mBe+5CqTQzJhSL FZNdxBngqb46XStQxDdB3jZ7UQbevNjY0TyoCLEc/2dzhEm+WMge7vhPEWdG GGGsCTrm9ge0j39ShP145pOsQTpYwQeC3Z4oIrV4dnbPJzqkvF7EbT2tiE1V NgUu1XT0zdknJAVF/GvbW/QniI6IyjCByiEFdPkuXxoTQMerpvlhVUkKoOnt 3kffSscmjcu56+MUcO8IrdXMlw6ji0I/SvYoIHreto69nnRInxvle/oo4IHl v7759nQUSF4sEZmlgIJG69W/tehIn6lzdXuPPF6kWxQVa9Ax6NHFXPBRHrSh U8ZbeHRkq+ypZ3XIo0vt25fvbDqWT28cqmmRx4Yd25dLy9NhVli9hH9HHhYS vodrJ2l4+1OowiBDHmtYMmXLPtBwLEVhSgB5jDPKObM6SX1fpZAaN1cefwQD XnxSz/0Ml6nLWssj8FliiuxrGpZs4yzVMJaHHKcpRPIZDbNitti6KsnjyT2x +Q33aOhdqVnQ/JKB2FXB7/+7S0PDBpnPI40MpFd/fsq7Q8M378oKvXsMJHR+ uZNcScPFyqbviZcYYJi+icwsoyHuJ/XePYqMvzRQGltAw3ITpSobUlck9yea DeaR+epbyqK55Pt/F70CztGwb1Zu431S1zY5i77YfIaGQ3wPW0dSJ3M/LTqf c4KGo1RG3bZWOuCoQJ9xnAbRN1KcG6QuP9JUcGg5RsNA2SEfobt0PFgYtIid QfRJ5N2rOYVEFzDuV/Wk0TDicevM60g6bmd3aJxPpaHJTq9LP4QOrYUPQrek 0HD7Yeq3cH86ZCKSRYSSaRDeVTBdcwX5vu2AcEA8DYXKXM1QPaJzZj/cYRFJ g/Ts+tU2rTSk3Xjh6RpBQ332oiHnRzSMX3O7tyechoU2B4U2VNNwfG2p4Oke GqwXFzofKKIh4kdNQtluGhTtqcC2WBru2ijsGdxFw2F+NvM7GbciovavDeGw Z7X0ySAaQoeYx96F0NC1tmDIwJPY9Y3ggkswDSGWnTZxM2j4eey95q3tZJ2t 4bNzDMg8VQ0rPmH61tLQMnViV4P66TSyTllCS8FHGRp0F+eoJQfS4MP3OTos RMONMzcKJQnXHWi5wRiWQ1LJtvOsABryhjVO4bMclog6cvK3kXuJcNw93soh 2Ex4piXh/hLu4p0tclhwwj7An+hJj41S+efvyKF798gBCcIt8ZHy98rl0Hy1 1rlkCw2a7rIX2y/KYeecS30ihCVem9vJEt3r/vBB3Y3NNIxaNTjyU+TgEDTs HET45cltu6j9cvArvHbIkPC68Qd3PMLk0L5ka3yfP3k/2wM6uwPl0FJ6cHoZ 4fglfkXpPnIofRJ9PIKwx5XpTkXuckj3LrvpQNjrR41MwzI5nBGJz+ARFp0+ +vnDYjnUOrsb//OjQXLt89ejc+SQ9y897iXhL312n1jmctD+FZdzg7Da7wDx 6fpyuLb3UMhpwh9H11KOPDlkrBKXSybcK7/gsD9TDubN87ftJdyXu3IwVpro 9teph4IIK/u+CjozJYuX0232bCbsvFlt7NaQLMQjzhj4Ew79Gn+q7Qf57jiW v5XwIvvIZX+6ZdG/6uy3EMKfJCOZcm9k0RnSOhxNmHlVuk//mSwKH7S3HSH8 4G5V66IGWXxr/RdzkfBkjtlj7ypZnE8PEdQR3npQ8WVkmSyWxx60/UxY4YTm zxOFsmh6Ge0j9X97JmsoXT8ti7RtR1bOIPzv6Sfn5xmy2C0YU974f3sGLz3+ M1kWduqTZccIs6YW/icVI4vqgBdaTwmfS36wmh9K7pNcsU2GvFfU/vbmBQGy eJQYdzCTsNSsie8RbrLYX9A88oXwE1EViXoncp5FY+rziT9UhhhayS6URf4v q+NThHdmFDw9ZSILS0/3vi3En9TX9M3s0ZLF6IK0sXbCT0q/3TRRkcXt48vX PiL+mDZz71C1MNkvfLDUnvjv7b7AmxLDMtD++/z+U8L8yY50l58yyJz0mPuD +PsnheMHu1/LQC2kLjuAxFNHKLdOolQGCyMWTOPsoCH/uJDn8jwZROY6ZT0j XNjxVuHkcRlc/jT79ZKdNCwuevrVNFYG7hUTa+JDiX/qXVnmtkYG1C//rA1h NPivbaDnO8qgwaH96iIS139pymM/IYOXHbwYNZIfaD/Oe8cby8Bu+HaFQhTx Hw4v/ZqQDGxWNU/yokm/NnfNl8khaUQMXZwxPYb0Y+Glex1/SCPkpvVaf5I3 UiyKvL6QPpohG/heNZGGD1KX1nJLSF+utff06iQaXnwyfbXtnDQSG7avOEHy mYKkZu7tLGkITjcXmJD89/nWDwP3/dJQ+ZCoevYIDeK1PsE5q6Ux6qtSKUPy 5wJT8/K+pdJYZa/rvi+TxGPfuLsNpEk+OVcSQvLvepf6r11GZLydTNP50zTc EpntOk1IGptdMwPMimko+bvfvadYCnJericHSmikXgq8gs9JISJyZdndy6R+ RYwNC7KkUHdWOcennIbhvV+mmLFS2BGx/vDQLRpc136sdnaTgkJLcP7sJhrc 5ErsP4tKIaiHzV33hIa5zk57wkclccdR6GTiUxoYwi6R8r8l0ceVLf5B8nLV 8cUKCzokoRsx7jJJ6p9w/JGfpWWSmN7ou8H+PxKfk9/nVqyTRPXR6yLNf0h9 9Lp6191VEoseMxrX/CXx7THNY2qJJHYbvaqPHiH+o7d9xMVSElestlSyRekQ OjPDbUpGEjSH+hVhqnT87FT4efKWBFQKMq98XUrHzl6/199ZEigZPB0lcCb9 4pzXRoGyEqClzuhkkrpyw0dG6o+wBFbrfV7m5kbH8bY9weP/iePJkRNztIi+ MFlbFWbQJI6up8FX6qKJ/rAWPd0aJY4IJ1WTJbfo6LoZSE/tFcNy/092CqTu 7VLlDdt/FMOaTxcMumpIf7tiVErytRhCNMSXHH5EB936cnVqvRg+7QjSs2in Q09lp0hZrhiK5GM/ZQzT8SVT/+GW1WKwrf488x7Rj9M/7Ltc1yAKl2PiVy+Q fqxk2qZntDuiELl2xvwY0asXf3ss9yoXxWfXnRsTiZ6+lT3tuGiuKAIuSl6o 8WVg/LukyL49omAWpsckpRN9ay5irWZMxq+TVYv4xoDdokfrHbNEwPLTbLP7 xcC7L52SimkiWDTv1yvOXwa2hVgqvY8TQVR/QtWbSQaWCvVF798hgvCP7mpr ZOXxsKUuZsJRBLY5X6691ZHHyJYZb9tFyXrGhQmFbvLgZu/f5bRHGHpS2yOb POVhHz1/66JgYfwQTr32e508JGtjTajNwtAaSP9s6yuPQ4Nec2zdhJF+5KGX aog8/DaMO6bNFMatnrli61Ll0TKrnkcbFcL+zbM3eNTJo5WZu0ZhvxDkMpny Xx7I4/xyU+fyvUIoF5yR3t0kD1tpIUW3ECG8tDXsOPVcHmd8J/Sv+wjhCl3v ryLRfffstofcsBWC9sFy6bPj8hj9oPnrnZwQ8ip+m5rNUUDts3UJfdQU1Zmp 3bxnvgLOFkxYF5pPUR4XxxY8WKiA97anuDt1pqjbxrnXAhwVEE6b8X6O5BRl 9cck+6uXAlTmlVZntExSuks+fcrcrwBL2mj4jk2TVOX1tHLOAQW8yW91nrNm knr19InThYNkv+lXm5UcJikNJacvDzIUYHR9k7HItEkqxeVgnOUFBaxdK8Oo GJugPLwGQh8+VsCV+cOlKdkTVOb954cOtijg6cq2gxFpE5T++nrv5W0KKJJZ fCJq/wR1WEzH5Pt7Bah2/C6s3jJBJa08ZGPfr4Dm+oMrDOZMUMPTLZor2IqQ TZt5q7prnBrf1f6gnEd0+bPUFT9fjVO/W7zXV2grYlCltHTak3HKsHdq030T RVjMH6EN3Rin8g6HJUotUATb08wuKm2curLigOmCbYr409PbnzNvnCrTTrjp HayI/Pe7TjhZjlOZTLWc2N2K8LV708QyHqdmX2jb0BKtCK1vY9Zf2eOUXERQ WUYmmV9s1nV4aIySvLTp3Y1qRbSxfn9mVoxRV+o6K6TqFdHh+fKlUckY9WPB 98r1jYq4tE/yrXvBGPX6SIEV66Ui8hTOHhBkjlEbXBcWne9VhGfksLJb2Bh1 cbb9ancWk/hdQVoKNUbZ5Dku7lRl4p3Ndxf12WPUtzUtups0mPAq5JY9njFG zdwvVRxuxMT61vBLQXpjlIqI1fImMPFAw0fjI32MqvVIWONrR9abnrtjjvQY pXTWzUTEiYnCHTM0r4qOUZ9aEyzt3JjYOeEi6BkRUNmVd6x+BzHhXS0180CP gKpTWTbz3C4mlsROqFz5KKD2mH/75BrORMK7BqX+DgG12spLtz6B9JkBfQ8e tAoot8l1dbWnmLh1/WhSaa2AMknOTkzMY2Lg0sEPl+4KqBdnbzxZdpGJz99v yNXeElDPd/fWfb3GxMfq9UupcgFFb1Z4bEH61KCkN4/iCwSUaN/cXZdayHmC pneknxNQYde36mi8YkIuua2n/IyAWuVRckCxiwmVpwIjZAsoHz7D7DDpez/u XpxSkiWgxEKUH9N+MNE6e4vhtEwBFXzapEn+HxPT5rUHxaQLqF96JtpZY0zo b7K0dkoTUI/3lnmqCbPg6p6eYJ4ioE4/OL/aVI6FV87LRmwTBVTe0gu02wos 5JPYCU0QUMvPOR6xU2FBcZxaWR0noCRe87v8tVkQ+dStmh0joJJCDuaPkr7f wqbij1G0gLrrNKCabsrC+uVDba/3CagDn99C14KFT1kq7aciBdTvhMsKd2ex 0LEkQDIiQkClLH+WuHo+C/OatcNCwgXUWsujJ/8sYmGn7AqLuL0CasaP+faH HFjI7OhdVrpHQLmMMZOMXVj4u+rum99hAurCDax6sooFm7n7upwI+1h9vxTo yUKOS2VofaiA0t/Aj2FsYCGi/O1FV8JhX4VaK/xYSJ1pkjixW0B1Lo7M9ghg wbDppcZ9wtseJLUIhbCw+ubz+FzCRbG0HUVhLATSJ2uzCMPv2y7XfSwk/ZP/ Wki4Y3pP22QsC78mTgi/IPwy6mFaSRILQTsFWipkvxl1i7M8DrHQem3P6jDC Xqule6UyWTCJ1Sv+TVgj9Fr07WxyX9dB03hy/gjHFysDclm4V3D+v+nkvn2D /61TP89CCfV8dISwQVJczosiFpYe7/F6R+xziT02mXSVhT/iOvw3xH7RjVVJ 82+wkGxwzvs3sa/CIxXTf1UstGssUtUi72Hm7dV7pZaFxV0N64OiBFT/1MNr Wx6yUBh51aaNvB/PPuWATjMLL7etq1m9X0DVBBQbnG5nwaMr4vOleAG1t838 h8d7FkT7ik9HHBBQm5mbT7I/s+D3nme0OUlAXdlVlp/9Hwu9ezR+H0kVUFqJ Gb88Bln4yXpl8+yQgIoNvifFFbBwW5GTqndEQNntV8zMF1dCt9JKVwPiz+3f Lv/1l1XCDZs73a0nBFTt43BJEwUlmB3JzTl+UkAd2sAwvsVVQv3DFaUhJF5a 1R8eabdQgtU5+fXBlwVUwd/hvbw5Shj7EbuAFCPKtdv65yYo4b72lL/5DQHl 1BjsNOCkBAuW+9nd1QJq+t3GTqa/EsI4pxtiWoi9i+sl1gWS/Vd8uO3aRuwd mxZQuFMJQvI7rZe8FVCZE9vuzo5Rwo/mhd0ZnwXUtfZW943ZStjdplh8dVRA 7X5Bn1mSqwR6nPDB5CkBtf3q2fHB80pYl3yKGyc+Ru0a1mQmlyvhncjvHe0K Y9RAjdCCksdKyJ8s0pQ1GaMmPgRwOseVkLnh0OMT/mPUulnpnhqiysjZLHiz b/sYlZSm83KjtDLCF9QVxpF8qvD0CXqUlEHbvnbXn8QxqqD7+ov3Zsp4s4y9 dlXRGOXOGe3J2aCMF4fP6swaHKO+V67xfuKvDGkb1QK9yTFq489Ir7FAZdAj W0OtpMapiF/25WvClaF0JqO3gjtODYiMxo8eVcaak1VXZ9iT+hCq0/SlThl/ 0uihxvnjVGTVqa8Zjcpoq/qy1vnyONVhJKs6/5ky+DIe+Sm3ximxv4IT6W+V 8aRhmO7WMk5NfvaYUP6jjHafF8etJsep7I/Su6q5KsD9mkOjGyaotrbMk/ba KnDd5GbZFDRB2SdF2bXoq6B2QQ6jImKCitzhKdU+QwWi7kGyr45NUKdC2/Bo iQqsO05kuTyeoDoeS9B1dqtAS3JutvScSarieGhobLgKVD2G1oQsmaSahuQ6 OqNVcOhMc1U/qf+DOuURKQdVINd6X8hm9yQ17Yn0vNpcFSxs0fb8e3WSUn+y Qulwowq6u3bee2E8Rfk1FDokq7Jxpf/AlpkcIZiF+670VmdDozs5vURbCHcy nfJm6LBxJLouzdBYCCu2XB5/asKG5oTM44U2Qgg/I8ltp9jQf+Lk2LteCPo2 OR1mfmy45GlN/31BCFsvW2i/KWVju8r4Ov85wth/UjNhWjkblbbbZPsXCaN+ 7fPyuBtslHfcNYx3FsbY9yubuffYqLML3lK9QRhbhpPEeS1sXKoPuZWUJIwY u4VnV/xh4xtn/4+Nr4Wx3dV5btw0VdD2vNc4u1cEqcx66wILVUSJWxm3xotg cKe7Xs1MVTSaJwtLHxZB5vnOr98oVTj4ryo5eEEE+3grVSZcVNFe+mte8wsR GB31/j0zWBWJ7jqSC8yIXj6VGy9arIr0zP6Gxb2iuHyy/1bSZVUUT53sFx4U xc987mLJclXQX2uL102J4qSfQ/BIpSoKTnimL1URQwn4FwoeqOLPcpeBCDsx SGZYz9TuUsWtgfZP9hfEUOVdZvhdgQPVoz8vMX3FcdUtZ3oZi4NdPpKPbILF If7u/tNdKhwspK/c7x8hjhXWu7v/cDno85nKunNEHG5nD9Hr9TnY+MVTIaCa 9BeOztnNNhysF47ue6UsAaENr11yfTkQ+2MQk90kgXNL53VnlnKwyTZ/0VxT KSgyKv90XuGgx6kk02q2FG6eHm3QKedg1gaVTDNbKdTO7HhbfIODRM/sTO46 8r3nxIGz9ziQP+Lt1JsmBY1L+SsMn3Ogktmbb/NTCj+e7A3908/B3q8ZS58X SeMqz6H7jrkaBmM8j9ZoykJTREfTr0gNnVcWZOkNkb4t7PibJi4Xf5WOrexd Ko/7p2bWbC/kwvdc5d6Eu0TX/n5gHjCTBw/xnZ9teUysWfvvQukbHqSCVsla R7Mw9c9xV1ieOiTcLne1Ciuj0k5nc0O4Bu77W9bytqng7+D+8IooDbT7mocY 7VBB0dM7o+djNZDIGwq3DlPB7gvaSw8f1MCKDcLJTnEqUNnAdovN0cBZvymH HSdVcM88O77ztgZmNOWMZz4m85978iLGNXBzfs/6WUZsUFtXPXq5WBOBLqxZ y7+ycW17m/GInSa+LDD9d/sHGwqH0cRz0ESRR/A+7X42ujNp5YHOmth6aPL1 7zE2Dp+8uEh1jSauOPRHRCqo4sjjHz8ub9aE0PHoaatsiB+9O/mmMVUTvbsa T44cUcUB16vlH9o1cZirULfbioPdq1dWL+nQREnRGXWfORx0+j2Xv96piY9z Ii86UxzwivYfSe/WREN3ooWGAwc/W30EK39owkLWq6/EiwPld5fKVac0kaDd H7U1ngNJyzTrc/pasFovnurTwoHz4pJrFkZacHOtsJNv4+Dc+aVRjSZa6BOx e3vnDQeLXeInh8y1EGMQuFfuEwff/N5WbLDRwuIp6VWZgxx0/9Od2L1CC70f +oytVNWwS79qZc4+LXy2nP3s5gY1mHU7WGXEaMGdudUx3E8NSaK78tPitLCy fPDtrG1qWGxmyk1M1sKZWS94V3ep4ZidaErqMS2oJj37vCdRDacX3TPtKtWC 9C2HxD0lahhR9GVc/UDOO9vBm/1XDXrsN71vurXAbZsqCxsmfrdqla3YFzK+ aV9p65gasprbDnj/IPdpXn4sSowLPdNIVYMRLey8fOh5qRIXt6+W6QsraqPu l72T/0wu3gVOt22x04b3iyOe0/dywdbiuv920IatSr/iu0guFpm5XZZ31gbf 48SRuBgubLft57q5auPYrIIXjxK5OJSZNzHgrY2tq6pmGGdxoRyfZOsfro3j rp93upZzkZgS4299WRsJq5cMc75xUdGYnR5Vpo3f9yW0Pfu4+B468PlBhTYu NVPPsn5xETvhzvSs0sZBs7UFIoNcdDycE3zkkTasNmyWuSbEg23+5S2Wn8h+ sTf0/FV5aMjTi3Nl68CsoFRSZQkP/YwZIlJcHSRLSaSpO/JwMlG0oVpDB+Ky 5hVay3iY/9NSylRfB+7G/7o5q3hYp8cL4ViT+dfHDr7x5kHTeM61aat0MJK3 3S0mjIe46zvvDrvpoNyyWhPhPGTzrwzWrtVBfX3B9vFIHoI+SPet2aSDlGOz j26O5WHeC3rDkZ06qHQLvi+ZxkOeXz997lEdvF/l7bn9HA9HGOFeSlk6sPx3 pOBrPg9Ded11f7J1IIg3cfO8wIOifU9b8Tkd3PiUO2xRzMPbH17fjMt0EFxr MXi1gtz/vcuRDS06MFy1K7fpAQ962+Yop9B1oZb99UDEV/I9z3fWTkVd0G8f vrGql4fVM+/NW6tMvsvZrTTq4yE4KeLnNHVdbFzR+OzRLx6eZntWfDbVBevp 3FtPBnlYdNr/6i5nXVw5wwr7J6yOlAKp9VtX6ELySbtwkqg6ZvGy3nqv1sVa u+QfiuLqMDvaYu6yThdnPs19xZVSx8XUrdTMIF2YaUzrG6GpI3LOykzjQ7oI cnrj08pWR6Dwkc2mR8n50LVVhaOOU8d0BqZl6ULPpee+u5o6ci+d1Z15Rhev 33ZvfMpTR7WDcbvzZV3cAs05WlsdS3a5W68u14XLHttHuTrqYEdEY90NXRxa mJdWpauOtinR5cHVuuja+2fos546ePbKlqee6mK/+pZpk0bqSM43qb/YqovP DWa/R4zVEX70df/1V7pYHXN48D8TdZwJnW7Q+l4X11YFPW02U4f3N/FW+f90 IXLyx3mXGeo4qV9vqT2gi3ceT6N1LdQhy7hkYvlPF2kFo9mDhJNY5i89JnVR UXk8NdFKHWOHLV+W0PmQGap1C5mlDtGdLwMjFfmI0biYwppN7KMYHeWozIfi DqsTFYQV/7pM/eTxMUNgPffLHHW8qdDZfk+Lj4q2c6175qoj1sLL5QifD13p c5SEDVnvkKuvlSkfat+dzinPU4cudS9LypyPv739R7MJ7/X+Ytlpycex9xwP 5fnqqDlTU5lgw0fD4m9+4pQ6FsRMXOlw5MN7xc9t5VDH9ysXTMtd+LhnaSFQ WEDsK39DPtmVj6LcN57bCWdd9pqyXsuHsIxhOmehOjzn5UoxvMl6fo3e2wiv KcgJ+ebDh9GfK0I3CbO0GOtztvHxstP6Chap48Vu8487t/PhMdV0O4awFWv9 HaedfPxqSMqoIvzuzpZ+vTA+uuV6Z/YTHpjU3S8cwQfH1qdIZ7E6emz9/Tuj +HDyDfq6gvDL5qn8ylg+pvfE/BdJmJvfYJl5gI+OO4z7eYTfnk/iBB8k9vLM WFdP2CFezdXxEB+sc/vquwjPvL3yvf5RPsLfLRwYJeyVPlUplsVHxH3373Rb dVxiDXZ3Z/Oxaqv5JQ3C2XoinjWn+f//f8zMhHCY35j6mXN87NQbjLAknDiz fFrkeT6e8O8fmkV46cPBFI9LfLDLlf3/z6fGj0+bVcqHZJSv6P/HNyZs4aqU kfPHqfoZE779cPbyfxVkv5GCFHXCg186ml5V8lG5ImQXjXB+jVryjTvkPa3/ Ux8h583qfXIwq4aPs/sT0z4Qnl9S9TS0no9L1hfu1BI+Kl65cs0jPlYkXy/J JTxWeFhl5hM+2pp4XnsJz/tPUY3dwsefYIdm5//zN7rX6As+vsqeHVMn3L1k xduO13wk2R/4/oO8x5udF4/e7eBjW/fGrOuE1wR8iM/9wIdFUc7kXsJfmVoK m77ycRhFEkPk/U+MNxTZ9vER12N7vpRwsGbEHoP/+Fjr/mjcm/DIosWX/xvi 48z24Xe3iX/1uv6n+GKUxMcXn40bCOdXvbx0Y4KPZS0mZ0UI646HbogS10O5 1dIFc4i/zn5uGnlDWg9x75aFPiT+TJduaPxF08POFMVcZ8KS3Sv+rVfWw8+7 4Y+diP+X/TR6eYKjB83n25obSHxsNrvQ+VxdDyfEb9bMJOywfVbwIn09TIz3 hNFJfPVrmw7tM9ZDcq/07J0k/nJ3RuTdnKaHd4tlvz8n8Zny6am/0Sw96M1j MWJI/H6s/7uH6aCHJOlxj1xrdWRsXCa2zFkPMcHNIW9JPpjGW1qcvEIPFuvM dzAIpxTdspn00IOk1j9uIMkfBbfsl/Vt00Pu/mq13mnkvKxTlQ1pevD6kfDy u7463EJXqAkdJed5vLPrBclvz1rjo+dm6cHVfFrDTb46fNiXba6d0YPdqT7Z YJIfzRpEtp69oodTncPReerq0DfSFd/zXA8yjf9EaCwSjzMjssrb9PC+8Nd4 vqI60Tlj0j/f6MGqy++uhYI6QjfHZG/o1oP/YbckW7o6jl/hcpYM6KH2wxZT I5Lv39Tv1WCw9HFgWW/lPwGphwanN0+p6GNjdJ3jmlEeBEKHon+r6ePtf59R PsxD0q1WxRYdfTBP8Bw9SL3x844oTrXQR2yPdUMIqUerkrLnj67Ux6v7wtvr P/DQcnPh3S9r9PE8amnem04e1ozK/Wn11Mdgo7ne9w4ejo4U7iry0YfMwT7N 8dc8xAv07q3aqY/HEoH3vj/jQXzKc+jkUX1ouoVUf6rmYTR8FzMuSx8D4aeO ld7hoTTg1NMtOfrYpHj9cshtHhIyfRhWefo4rv8y79d1Hs537c1pLNNH7/Cn sNISHpjyVks6WvQh7jk+tTibB/3cnQ2naAaw9S83ehdE9IN5/HVvBQNIiTgX qgbw0Jo3ja6jZIB3x7P3uG7hYaXxquGLXAN8GFjOvu3Dwy0Rh+BiYwOcu7dg vpMbD+gJ8TviYIDoMCQcpXioLJx+/mWCAS7m1LRmyvFw3dTbPjbZAGnLWE/m SvNgmbxP1SzNANlH+VIfxXm4Ita18ECmAbSemjmpTHExIpy92zDfAIGLi/4u 6+fiZpN6gX2NATT8mw91tHHx1f1q5NMRA5S3PfX1yebi3HWns8XjBkiFRxX3 GJfohLa4RCFDBHsPRbYe5qJ1wfaYOVKGGB2zsDVK4mLHRyfJTBVDdM8qmMwO JXryn7SSmLUhFrLeFgSs4KL5qplDW4ghWuU70n4SPdpQvGhvQqgh5m5UFv83 pYaT9R1KFuGG+Lb+nqxAoIYZkRkZqfsNMXzm7JP+P0RPxx91MjxsCI8bxx3P daqBJVF1SqnUEL/vteiNXVPDlN66rnM9htjalPfz9lo1SC1tbPjwzRBV67LN I9aoQba5QVrthyE+PQkTsV6hBqFbPlfS+w1Bi8twPWenhp9Hd5r7TBpC3mqb JEhf98g1o+CWihGc4huiroir4bCeJY/tYASr9oBNG0o4qBR8/K7uZISK/kWX sy9wcMcr64uOixGSPq8Ybj7LwTNNhp/BaiOoVXScMTzGQfBiIR+1jUZ4Hzdc UbGPzDdJd7201whv7HsNGM4cFP3yWeRWaAShDr0RiR+kjy8v/rK7yAjMDzfr 6D2qcKa90DhSaoR/22R9FN+rEntJeNRcM0LkaDFoLar4Xr/rmVCNEfSYF4Je XFNFdG2fP6PdCC6xbNv8cFU8rdr0wVPcGP3PhJtyxFQhsWNKzljKGGssB3pM J9gwlBd6NSJjjDP3V0rWDLFxVO615SF5Y7A19qS8If3flMu+5Tlqxvj7vfbO 90Y2IphBcjA3Rk584ZH0NDY29p336rMwhsOinsUjCWz0lAWtzbA2xq6poQrv KDbkTSQC3801RqoxZ0B/OxujUQLGSjtjDPh+nH/WhQ0Zv2GZviXGMBi7ozpi z4a05L2GGEdj+LtS8i5gI6H4Z9T55cZ4ZDAQOzydDTEr9TgLV2OI3zVUdjBk Q7a4dFntamNscmKPZGuxYRCn+3WpuzEWTdtu+U2Vjffm2o4vPY1hGf+r3UKR jf8Bz5vtbg== "]]}}}, AspectRatio->Automatic, Axes->None, AxesOrigin->{0, 3.}, Frame->True, FrameTicks->None, PlotRange->{{1.9, 9.5}, {1.2, 8}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Text", CellChangeTimes->{{3.449058131421875*^9, 3.4490581519375*^9}}, TextAlignment->Center], Cell[TextData[{ "Cyklista jede po rovn\[EAcute]m ter\[EAcute]nu, p\:0159edn\[IAcute] a zadn\ \[IAcute] kolo zanech\[AAcute]vaj\[IAcute] stopy - rovinn\[EAcute] \ k\:0159ivky. \[LineSeparator]Dok\[AAcute]\:017eete ur\[CHacek]it, kter\ \[AAcute] k\:0159ivka odpov\[IAcute]d\[AAcute] kter\[EAcute]mu kolu a jak\ \[YAcute]m sm\:011brem cyklista jel?\n(\[CapitalUAcute]loha a obr\[AAcute]zek \ jsou z knihy Stan Wagon, ", StyleBox["Mathematica in Action", FontSlant->"Italic"], ", Springer, 2000;\nviz t\[EAcute]\:017e ", StyleBox["Sherlock Holmes, ", FontSlant->"Italic"], Cell[BoxData[ FormBox[ StyleBox[ RowBox[{"Adventure", " ", "at", " ", "the", " ", "Priory", " ", "School"}], FontSlant->"Italic"], TraditionalForm]]], ")" }], "Text", CellChangeTimes->{{3.44903800796875*^9, 3.449038171984375*^9}, { 3.44905788740625*^9, 3.44905792946875*^9}, 3.449063037421875*^9, { 3.449124625921875*^9, 3.44912462896875*^9}, {3.4491515610625*^9, 3.449151592140625*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Cyklistick\[AAcute] matematika", "Subsection", CellChangeTimes->{{3.449055703796875*^9, 3.449055709875*^9}}], Cell[TextData[{ "P\:0159edpokl\[AAcute]dejme, \:017ee vzd\[AAcute]lenost os p\:0159edn\ \[IAcute]ho a zadn\[IAcute]ho kola je ", Cell[BoxData[ FormBox[ RowBox[{"L", ">", "0"}], TraditionalForm]], FormatType->"TraditionalForm"], ". V ka\:017ed\[EAcute]m okam\:017eiku plat\[IAcute], \:017ee p\:0159edn\ \[IAcute] kolo se dot\[YAcute]k\[AAcute] zem\:011b v m\[IAcute]st\:011b, kter\ \[EAcute] dostaneme posunut\[IAcute]m z bodu dotyku zadn\[IAcute]ho kola o \ vzd\[AAcute]lenost ", Cell[BoxData[ FormBox["L", TraditionalForm]], FormatType->"TraditionalForm"], " ve sm\:011bru te\[CHacek]ny." }], "Text", CellChangeTimes->{{3.4490568271875*^9, 3.449056903171875*^9}, { 3.449057193828125*^9, 3.44905726025*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"cyklista", "[", RowBox[{"L_", ",", "krivka_", ",", "tmin_", ",", "tmax_", ",", "pRange_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"predni", ",", "zadni"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"predni", "[", "u_", "]"}], ":=", RowBox[{ RowBox[{"(", RowBox[{"krivka", "+", RowBox[{"L", "*", RowBox[{ RowBox[{"D", "[", RowBox[{"krivka", ",", "t"}], "]"}], "/", RowBox[{"Norm", "[", RowBox[{"D", "[", RowBox[{"krivka", ",", "t"}], "]"}], "]"}]}]}]}], ")"}], "/.", RowBox[{"t", "\[Rule]", "u"}]}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"zadni", "[", "u_", "]"}], ":=", RowBox[{"(", RowBox[{"krivka", "/.", RowBox[{"t", "\[Rule]", "u"}]}], ")"}]}], ";", "\[IndentingNewLine]", RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"predni", "[", "u", "]"}], ",", RowBox[{"zadni", "[", "u", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"u", ",", RowBox[{"tmin", "+", "0.01"}], ",", "t"}], "}"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Thick", ",", "Red"}], "}"}], ",", RowBox[{"{", RowBox[{"Thick", ",", "Blue"}], "}"}]}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "pRange"}], ",", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"PointSize", "[", "Large", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"zadni", "[", "t", "]"}], ",", RowBox[{"predni", "[", "t", "]"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"zadni", "[", "t", "]"}], ",", RowBox[{"predni", "[", "t", "]"}]}], "}"}], "]"}]}], "}"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}]}], "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.449058368359375*^9, 3.449058572109375*^9}, { 3.449058620421875*^9, 3.44905862221875*^9}, 3.44905867365625*^9, { 3.44905870678125*^9, 3.44905871903125*^9}, {3.44905875553125*^9, 3.44905875809375*^9}, {3.44905879528125*^9, 3.4490588559375*^9}, { 3.44905910765625*^9, 3.4490591175*^9}, {3.449059219546875*^9, 3.449059221390625*^9}, {3.449062922515625*^9, 3.449062967453125*^9}}], Cell[TextData[{ StyleBox["P\:0159\[IAcute]klad 1:", FontWeight->"Bold"], " Zadn\[IAcute] kolo jede po kru\:017enici o polom\:011bru 1." }], "Text", CellChangeTimes->{{3.44905892384375*^9, 3.44905894490625*^9}}], Cell[BoxData[ RowBox[{"cyklista", "[", RowBox[{"1", ",", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "t", "]"}], ",", RowBox[{"Sin", "[", "t", "]"}]}], "}"}], ",", "0", ",", RowBox[{"2", "Pi"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.449058585921875*^9, 3.449058600625*^9}, { 3.44905884409375*^9, 3.449058846796875*^9}, {3.44905912225*^9, 3.449059122578125*^9}, 3.449059225140625*^9, {3.449062903703125*^9, 3.449062916921875*^9}}], Cell[TextData[{ StyleBox["Cvi\[CHacek]en\[IAcute]:", FontWeight->"Bold"], " Jak\[YAcute] je polom\:011br kru\:017enice, po kter\[EAcute] jede \ p\:0159edn\[IAcute] kolo?" }], "Text", CellChangeTimes->{{3.449058896984375*^9, 3.449058914984375*^9}, { 3.449058961390625*^9, 3.4490589830625*^9}}], Cell[TextData[{ StyleBox["P\:0159\[IAcute]klad 2:", FontWeight->"Bold"], " Zadn\[IAcute] kolo jede po elipse." }], "Text", CellChangeTimes->{{3.44905892384375*^9, 3.44905894490625*^9}, { 3.44905900303125*^9, 3.449059010078125*^9}}], Cell[BoxData[ RowBox[{"cyklista", "[", RowBox[{"1", ",", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "t", "]"}], ",", RowBox[{"0.5", RowBox[{"Sin", "[", "t", "]"}]}]}], "}"}], ",", "0", ",", RowBox[{"2", "Pi"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.449058585921875*^9, 3.449058600625*^9}, { 3.449058749390625*^9, 3.449058750140625*^9}, 3.449059024875*^9, { 3.449059129828125*^9, 3.44905913015625*^9}, 3.4490592281875*^9}], Cell[TextData[{ StyleBox["P\:0159\[IAcute]klad 3:", FontWeight->"Bold"], " Zadn\[IAcute] kolo jede po parabole." }], "Text", CellChangeTimes->{{3.44905892384375*^9, 3.44905894490625*^9}, { 3.44905900303125*^9, 3.449059010078125*^9}, {3.4490590620625*^9, 3.449059067671875*^9}}], Cell[BoxData[ RowBox[{"cyklista", "[", RowBox[{"1", ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{"t", "^", "2"}]}], "}"}], ",", RowBox[{"-", "2"}], ",", "2", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "4"}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.449058585921875*^9, 3.449058600625*^9}, { 3.449058749390625*^9, 3.449058750140625*^9}, 3.449059024875*^9, { 3.449059077171875*^9, 3.44905908978125*^9}, {3.44905915084375*^9, 3.449059165734375*^9}, 3.44905923028125*^9}], Cell[TextData[{ StyleBox["P\:0159\[IAcute]klad 4:", FontWeight->"Bold"], " Zadn\[IAcute] kolo jede po sinusoid\:011b." }], "Text", CellChangeTimes->{{3.44905892384375*^9, 3.44905894490625*^9}, { 3.44905900303125*^9, 3.449059010078125*^9}, {3.4490590620625*^9, 3.449059067671875*^9}, {3.449059241171875*^9, 3.449059247546875*^9}}], Cell[BoxData[ RowBox[{"cyklista", "[", RowBox[{"1", ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{ RowBox[{"Sin", "[", RowBox[{"4", "t"}], "]"}], "/", "4"}]}], "}"}], ",", RowBox[{"-", "Pi"}], ",", "Pi", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "Pi"}], ",", RowBox[{"Pi", "+", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.449058585921875*^9, 3.449058600625*^9}, { 3.449058749390625*^9, 3.449058750140625*^9}, 3.449059024875*^9, { 3.449059077171875*^9, 3.44905908978125*^9}, {3.44905915084375*^9, 3.449059165734375*^9}, 3.44905923028125*^9, {3.449059269234375*^9, 3.44905934575*^9}, {3.449059498140625*^9, 3.44905950109375*^9}, { 3.44905974340625*^9, 3.449059768625*^9}, {3.449059801359375*^9, 3.449059922078125*^9}, {3.449059962015625*^9, 3.4490600415*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Obr\[AAcute]cen\[AAcute] \[UAcute]loha", "Subsection", CellChangeTimes->{{3.449063064234375*^9, 3.449063070703125*^9}}], Cell[TextData[{ "Zn\[AAcute]me-li dr\[AAcute]hu p\:0159edn\[IAcute]ho kola, jak \ ur\[CHacek]it dr\[AAcute]hu zadn\[IAcute]ho kola? Tato \[UAcute]loha vede na \ \:0159e\[SHacek]en\[IAcute] neline\[AAcute]rn\[IAcute] diferenci\[AAcute]ln\ \[IAcute] rovnice (viz \[CHacek]l\[AAcute]nek S. R. Dunbar, R. J. C. Bosman, \ S. E. M. Nooij, ", StyleBox["The Track of a Bicycle Back Tire", FontSlant->"Italic"], ". Mathematics Magazine, Vol. 74, No. 4 (Oct., 2001), pp. 273\[Dash]287)." }], "Text", CellChangeTimes->{{3.449063080234375*^9, 3.449063192078125*^9}, { 3.4490633099375*^9, 3.44906331828125*^9}, {3.449063767109375*^9, 3.4490637685*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"frontWheelPath", "[", RowBox[{"t_", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"P0", ":", RowBox[{"{", RowBox[{"X0_", ",", "Y0_"}], "}"}]}], ",", "t0_"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"P1", ":", RowBox[{"{", RowBox[{"X1_", ",", "Y1_"}], "}"}]}], ",", "t1_"}], "}"}]}], "}"}]}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"t", "-", "t0"}], ")"}], "/", RowBox[{"(", RowBox[{"t1", "-", "t0"}], ")"}]}], " ", "P1"}], "+", RowBox[{ RowBox[{"(", RowBox[{"1", "-", RowBox[{ RowBox[{"(", RowBox[{"t", "-", "t0"}], ")"}], "/", RowBox[{"(", RowBox[{"t1", "-", "t0"}], ")"}]}]}], ")"}], " ", "P0"}]}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"rearWheelPath", "[", RowBox[{"t_", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"P0", ":", RowBox[{"{", RowBox[{"X0_", ",", "Y0_"}], "}"}]}], ",", "t0_"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"P1", ":", RowBox[{"{", RowBox[{"X1_", ",", "Y1_"}], "}"}]}], ",", "t1_"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x0_", ",", "y0_"}], "}"}], ",", "L_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"xf", ",", "yf", ",", "xb", ",", "yb", ",", "\[Tau]"}], "}"}], ",", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"xf", "[", "\[Tau]_", "]"}], ",", RowBox[{"yf", "[", "\[Tau]_", "]"}]}], "}"}], "=", RowBox[{"frontWheelPath", "[", RowBox[{"\[Tau]", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"P0", ",", "t0"}], "}"}], ",", RowBox[{"{", RowBox[{"P1", ",", "t1"}], "}"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"xb", "[", "t", "]"}], ",", RowBox[{"yb", "[", "t", "]"}]}], "}"}], "/.", RowBox[{ RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"xb", "'"}], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"1", "/", RowBox[{"L", "^", "2"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"xf", "'"}], "[", "t", "]"}], " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"xf", "[", "t", "]"}], "-", RowBox[{"xb", "[", "t", "]"}]}], ")"}], "^", "2"}]}], "+", RowBox[{ RowBox[{ RowBox[{"yf", "'"}], "[", "t", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"xf", "[", "t", "]"}], "-", RowBox[{"xb", "[", "t", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"yf", "[", "t", "]"}], "-", RowBox[{"yb", "[", "t", "]"}]}], ")"}]}]}], ")"}]}]}], ",", RowBox[{ RowBox[{ RowBox[{"yb", "'"}], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"1", "/", RowBox[{"L", "^", "2"}]}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{"yf", "'"}], "[", "t", "]"}], " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"yf", "[", "t", "]"}], "-", RowBox[{"yb", "[", "t", "]"}]}], ")"}], "^", "2"}]}], "+", RowBox[{ RowBox[{ RowBox[{"xf", "'"}], "[", "t", "]"}], " ", RowBox[{"(", RowBox[{ RowBox[{"yf", "[", "t", "]"}], "-", RowBox[{"yb", "[", "t", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"xf", "[", "t", "]"}], "-", RowBox[{"xb", "[", "t", "]"}]}], ")"}]}]}], ")"}]}]}], ",", RowBox[{ RowBox[{"xb", "[", "t0", "]"}], "\[Equal]", "x0"}], ",", RowBox[{ RowBox[{"yb", "[", "t0", "]"}], "\[Equal]", "y0"}]}], "}"}], ",", RowBox[{"{", RowBox[{"xb", ",", "yb"}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "t0", ",", "t1"}], "}"}]}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"frontAndRearWheelPathSegment", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"P0_", ",", "t0_"}], "}"}], ",", RowBox[{"{", RowBox[{"P1_", ",", "t1_"}], "}"}]}], "}"}], ",", "p0_", ",", "L_", ",", "n_"}], "]"}], ":=", RowBox[{ RowBox[{"frontAndRearWheelPathSegment", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"P0", ",", "t0"}], "}"}], ",", RowBox[{"{", RowBox[{"P1", ",", "t1"}], "}"}]}], "}"}], ",", "p0", ",", "L", ",", "n"}], "]"}], "=", RowBox[{ RowBox[{ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"\[Lambda]", "=", RowBox[{"Norm", "[", RowBox[{"P1", "-", "P0"}], "]"}]}], "}"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"\[Lambda]", "<", RowBox[{"10", "^", RowBox[{"-", "10"}]}]}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"P0", ",", "p0"}], "}"}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{"{", RowBox[{ RowBox[{"frontWheelPath", "[", RowBox[{"t", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"P0", ",", "t0"}], "}"}], ",", RowBox[{"{", RowBox[{"P1", ",", "t1"}], "}"}]}], "}"}]}], "]"}], ",", RowBox[{"rearWheelPath", "[", RowBox[{"t", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"P0", ",", "t0"}], "}"}], ",", RowBox[{"{", RowBox[{"P1", ",", "t1"}], "}"}]}], "}"}], ",", "p0", ",", "L"}], "]"}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "t0", ",", "t1", ",", RowBox[{ RowBox[{"(", RowBox[{"t1", "-", "t0"}], ")"}], "/", "n"}]}], "}"}]}], "]"}]}], "]"}]}], "]"}], "//", "N"}], "//", "Developer`ToPackedArray"}]}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"bikePositions", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"P0_", ",", "t0_"}], "}"}], "}"}], ",", "p0_", ",", "L_", ",", "n_"}], "]"}], ":=", RowBox[{"{", RowBox[{"{", RowBox[{"P0", ",", "p0"}], "}"}], "}"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"bikePositions", "[", RowBox[{ "positionTimeList_", ",", "p0_", ",", "L_", ",", "n_", ",", "frontAndRearWheelPathSegment_"}], "]"}], ":=", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{"FoldList", "[", RowBox[{ RowBox[{ RowBox[{"frontAndRearWheelPathSegment", "[", RowBox[{"#2", ",", RowBox[{"#1", "[", RowBox[{"[", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "]"}], "]"}], ",", "L", ",", "n"}], "]"}], "&"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"positionTimeList", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}], ",", "p0"}], "}"}], "}"}], ",", RowBox[{"Partition", "[", RowBox[{"positionTimeList", ",", "2", ",", "1"}], "]"}]}], "]"}], ",", "1"}], "]"}], "//", "Developer`ToPackedArray"}]}], ";"}], "\n", RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"DynamicModule", "[", RowBox[{ RowBox[{"{", RowBox[{"frontWheelPathBag", ",", RowBox[{"loc", "=", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], ",", "bikeData", ",", RowBox[{"\[CapitalLambda]", "=", "2.5"}], ",", RowBox[{"T0", "=", RowBox[{"AbsoluteTime", "[", "]"}]}], ",", "Tnew", ",", "frontAndRearWheelPathSegmentLocal"}], "}"}], ",", RowBox[{ RowBox[{ RowBox[{"DownValues", "[", "frontAndRearWheelPathSegmentLocal", "]"}], "=", RowBox[{ RowBox[{"DownValues", "[", "frontAndRearWheelPathSegment", "]"}], "/.", RowBox[{ "frontAndRearWheelPathSegment", "\[Rule]", "frontAndRearWheelPathSegmentLocal"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"frontWheelPathBag", "=", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.", ",", "0."}], "}"}], ",", "0.0"}], "}"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"Column", "[", RowBox[{"{", RowBox[{ RowBox[{"Column", "[", RowBox[{"{", RowBox[{"Button", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"frontWheelPathBag", "=", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.", ",", "0."}], "}"}], ",", "0.0"}], "}"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"loc", "=", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{ "DownValues", "[", "frontAndRearWheelPathSegmentLocal", "]"}], "=", RowBox[{"{", RowBox[{"Last", "[", RowBox[{ "DownValues", "[", "frontAndRearWheelPathSegmentLocal", "]"}], "]"}], "}"}]}]}]}], "]"}], "}"}], "]"}], ",", RowBox[{"Dynamic", "@", RowBox[{"Deploy", "@", RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"bikeData", "=", RowBox[{"bikePositions", "[", RowBox[{"frontWheelPathBag", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "L"}], ",", "0"}], "}"}], ",", "L", ",", "n", ",", "frontAndRearWheelPathSegmentLocal"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"GrayLevel", "[", "0.8", "]"}], ",", RowBox[{"Thickness", "[", "0.0012", "]"}], ",", RowBox[{"If", "[", RowBox[{"sb", ",", RowBox[{"Line", "[", "bikeData", "]"}], ",", RowBox[{"{", "}"}]}], "]"}]}], "}"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"Darker", "[", "Blue", "]"}], ",", RowBox[{"Point", "[", RowBox[{"bikeData", "[", RowBox[{"[", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "]"}], "]"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"Last", "/@", "bikeData"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Darker", "[", "Red", "]"}], ",", RowBox[{"Opacity", "[", "0.66", "]"}], ",", RowBox[{"Line", "[", RowBox[{"First", "/@", "frontWheelPathBag"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Locator", "[", RowBox[{ RowBox[{"Dynamic", "[", RowBox[{"loc", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Tnew", "=", RowBox[{"AbsoluteTime", "[", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Norm", "[", RowBox[{ RowBox[{"frontWheelPathBag", "[", RowBox[{"[", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "]"}], "]"}], "-", "#"}], "]"}], ">", RowBox[{"10.", "^", RowBox[{"-", "3"}]}]}], "&&", RowBox[{ RowBox[{"Abs", "[", RowBox[{ RowBox[{"frontWheelPathBag", "[", RowBox[{"[", RowBox[{ RowBox[{"-", "1"}], ",", "2"}], "]"}], "]"}], "-", "Tnew"}], "]"}], ">", RowBox[{"10.", "^", RowBox[{"-", "3"}]}]}]}], ",", RowBox[{"AppendTo", "[", RowBox[{"frontWheelPathBag", ",", RowBox[{"{", RowBox[{"#", ",", RowBox[{"Tnew", "-", "T0"}]}], "}"}]}], "]"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"Not", "[", "is", "]"}], ",", RowBox[{"loc", "=", "#"}], ",", RowBox[{"loc", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Max", "[", RowBox[{"Abs", "[", "#", "]"}], "]"}], "<", "\[CapitalLambda]"}], ",", "#", ",", RowBox[{"{", RowBox[{ RowBox[{"Max", "[", RowBox[{ RowBox[{"Min", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "\[CapitalLambda]"}], "]"}], ",", RowBox[{"-", "\[CapitalLambda]"}]}], "]"}], ",", RowBox[{"Max", "[", RowBox[{ RowBox[{"Min", "[", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "\[CapitalLambda]"}], "]"}], ",", RowBox[{"-", "\[CapitalLambda]"}]}], "]"}]}], "}"}]}], "]"}]}]}], "]"}]}], ")"}], "&"}], ",", RowBox[{"UpdateInterval", "\[Rule]", "0"}]}], "]"}], ",", RowBox[{"Style", "[", RowBox[{"\"\<\[FilledSmallCircle]\>\"", ",", RowBox[{"Darker", "[", "Red", "]"}]}], "]"}]}], "]"}], "}"}]}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "\[CapitalLambda]"}], ",", RowBox[{"PlotRangeClipping", "\[Rule]", "True"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameTicks", "\[Rule]", "False"}], ",", RowBox[{"ImageSize", "\[Rule]", "320"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"Row", "[", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"Length", "[", "frontWheelPathBag", "]"}], "-", "1"}]}], "}"}], "]"}]}]}], "]"}]}]}]}], "}"}], "]"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"L", ",", "1", ",", "\"\\""}], "}"}], ",", "0.01", ",", "3", ",", RowBox[{"ImageSize", "\[Rule]", "Small"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"sb", ",", "False", ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{"True", ",", "False"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n", ",", "4", ",", "\"\\""}], "}"}], ",", "1", ",", "24", ",", "1", ",", RowBox[{"ImageSize", "\[Rule]", "Small"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "is", ",", "False", ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{"True", ",", "False"}], "}"}]}], "}"}], ",", RowBox[{"ControlPlacement", "\[Rule]", "Left"}], ",", RowBox[{"SaveDefinitions", "\[Rule]", "True"}], ",", RowBox[{"AutorunSequencing", "\[Rule]", RowBox[{"{", "1", "}"}]}]}], "]"}]}], "Input"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`is$$ = False, $CellContext`L$$ = 1, $CellContext`n$$ = 4, $CellContext`sb$$ = False, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`L$$], 1, "wheel base"}, 0.01, 3}, {{ Hold[$CellContext`sb$$], False, "show bike positions"}, { True, False}}, {{ Hold[$CellContext`n$$], 4, "bikes per step"}, 1, 24, 1}, {{ Hold[$CellContext`is$$], False, "restrict bike path to square"}, { True, False}}}, Typeset`size$$ = {320., {178.5, 187.5}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`L$47268$$ = 0, $CellContext`sb$47269$$ = False, $CellContext`n$47270$$ = 0, $CellContext`is$47271$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`is$$ = False, $CellContext`L$$ = 1, $CellContext`n$$ = 4, $CellContext`sb$$ = False}, "ControllerVariables" :> { Hold[$CellContext`L$$, $CellContext`L$47268$$, 0], Hold[$CellContext`sb$$, $CellContext`sb$47269$$, False], Hold[$CellContext`n$$, $CellContext`n$47270$$, 0], Hold[$CellContext`is$$, $CellContext`is$47271$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> DynamicModule[{$CellContext`frontWheelPathBag, $CellContext`loc = {0, 0}, $CellContext`bikeData, $CellContext`\[CapitalLambda] = 2.5, $CellContext`T0 = AbsoluteTime[], $CellContext`Tnew, \ $CellContext`frontAndRearWheelPathSegmentLocal}, DownValues[$CellContext`frontAndRearWheelPathSegmentLocal] = ReplaceAll[ DownValues[$CellContext`frontAndRearWheelPathSegment], \ $CellContext`frontAndRearWheelPathSegment -> \ $CellContext`frontAndRearWheelPathSegmentLocal]; \ $CellContext`frontWheelPathBag = {{{0., 0.}, 0.}}; Column[{ Column[{ Button[ "start a new bike ride", $CellContext`frontWheelPathBag = {{{0., 0.}, 0.}}; $CellContext`loc = {0, 0}; DownValues[$CellContext`frontAndRearWheelPathSegmentLocal] = { Last[ DownValues[$CellContext`frontAndRearWheelPathSegmentLocal]]}\ ]}], Dynamic[ Deploy[ Graphics[{$CellContext`bikeData = \ $CellContext`bikePositions[$CellContext`frontWheelPathBag, {-$CellContext`L$$, 0}, $CellContext`L$$, $CellContext`n$$, \ $CellContext`frontAndRearWheelPathSegmentLocal]; { GrayLevel[0.8], Thickness[0.0012], If[$CellContext`sb$$, Line[$CellContext`bikeData], {}]}, { Darker[Blue], Point[ Part[$CellContext`bikeData, -1, -1]], Line[ Map[Last, $CellContext`bikeData]]}, { Darker[Red], Opacity[0.66], Line[ Map[First, $CellContext`frontWheelPathBag]]}, { Locator[ Dynamic[$CellContext`loc, ($CellContext`Tnew = AbsoluteTime[]; If[ And[ Norm[Part[$CellContext`frontWheelPathBag, -1, 1] - #] > 10.^(-3), Abs[Part[$CellContext`frontWheelPathBag, -1, 2] - $CellContext`Tnew] > 10.^(-3)], AppendTo[$CellContext`frontWheelPathBag, {#, \ $CellContext`Tnew - $CellContext`T0}]]; If[ Not[$CellContext`is$$], $CellContext`loc = #, \ $CellContext`loc = If[Max[ Abs[#]] < $CellContext`\[CapitalLambda], #, { Max[ Min[ Part[#, 1], $CellContext`\[CapitalLambda]], -$CellContext`\ \[CapitalLambda]], Max[ Min[ Part[#, 2], $CellContext`\[CapitalLambda]], -$CellContext`\ \[CapitalLambda]]}]])& , UpdateInterval -> 0], Style["\[FilledSmallCircle]", Darker[Red]]]}}, PlotRange -> $CellContext`\[CapitalLambda], PlotRangeClipping -> True, Frame -> True, FrameTicks -> False, ImageSize -> 320, PlotLabel -> Row[{"straight bike segments: ", Length[$CellContext`frontWheelPathBag] - 1}]]]]}]], "Specifications" :> {{{$CellContext`L$$, 1, "wheel base"}, 0.01, 3, ImageSize -> Small}, {{$CellContext`sb$$, False, "show bike positions"}, { True, False}}, {{$CellContext`n$$, 4, "bikes per step"}, 1, 24, 1, ImageSize -> Small}, {{$CellContext`is$$, False, "restrict bike path to square"}, {True, False}}}, "Options" :> {ControlPlacement -> Left, AutorunSequencing -> {1}}, "DefaultOptions" :> {}], ImageSizeCache->{615., {215., 224.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`frontAndRearWheelPathSegment[{{ Pattern[$CellContext`P0, Blank[]], Pattern[$CellContext`t0, Blank[]]}, { Pattern[$CellContext`P1, Blank[]], Pattern[$CellContext`t1, Blank[]]}}, Pattern[$CellContext`p0, Blank[]], Pattern[$CellContext`L, Blank[]], Pattern[$CellContext`n, Blank[]]] := \ ($CellContext`frontAndRearWheelPathSegment[{{$CellContext`P0, \ $CellContext`t0}, {$CellContext`P1, $CellContext`t1}}, $CellContext`p0, \ $CellContext`L, $CellContext`n] = Developer`ToPackedArray[ N[ With[{$CellContext`\[Lambda] = Norm[$CellContext`P1 - $CellContext`P0]}, If[$CellContext`\[Lambda] < 10^(-10), {{$CellContext`P0, $CellContext`p0}}, Table[ Evaluate[{ $CellContext`frontWheelPath[$CellContext`t, \ {{$CellContext`P0, $CellContext`t0}, {$CellContext`P1, $CellContext`t1}}], $CellContext`rearWheelPath[$CellContext`t, {{$CellContext`P0, \ $CellContext`t0}, {$CellContext`P1, $CellContext`t1}}, $CellContext`p0, \ $CellContext`L]}], {$CellContext`t, $CellContext`t0, $CellContext`t1, \ ($CellContext`t1 - $CellContext`t0)/$CellContext`n}]]]]]), \ $CellContext`frontWheelPath[ Pattern[$CellContext`t, Blank[]], {{ Pattern[$CellContext`P0, { Pattern[$CellContext`X0, Blank[]], Pattern[$CellContext`Y0, Blank[]]}], Pattern[$CellContext`t0, Blank[]]}, { Pattern[$CellContext`P1, { Pattern[$CellContext`X1, Blank[]], Pattern[$CellContext`Y1, Blank[]]}], Pattern[$CellContext`t1, Blank[]]}}] := (($CellContext`t - \ $CellContext`t0)/($CellContext`t1 - $CellContext`t0)) $CellContext`P1 + ( 1 - ($CellContext`t - $CellContext`t0)/($CellContext`t1 - \ $CellContext`t0)) $CellContext`P0, $CellContext`rearWheelPath[ Pattern[$CellContext`t, Blank[]], {{ Pattern[$CellContext`P0, { Pattern[$CellContext`X0, Blank[]], Pattern[$CellContext`Y0, Blank[]]}], Pattern[$CellContext`t0, Blank[]]}, { Pattern[$CellContext`P1, { Pattern[$CellContext`X1, Blank[]], Pattern[$CellContext`Y1, Blank[]]}], Pattern[$CellContext`t1, Blank[]]}}, { Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`y0, Blank[]]}, Pattern[$CellContext`L, Blank[]]] := Module[{$CellContext`xf, $CellContext`yf, $CellContext`xb, \ $CellContext`yb, $CellContext`\[Tau]}, { $CellContext`xf[ Pattern[$CellContext`\[Tau], Blank[]]], $CellContext`yf[ Pattern[$CellContext`\[Tau], Blank[]]]} = $CellContext`frontWheelPath[$CellContext`\[Tau], \ {{$CellContext`P0, $CellContext`t0}, {$CellContext`P1, $CellContext`t1}}]; ReplaceAll[{ $CellContext`xb[$CellContext`t], $CellContext`yb[$CellContext`t]}, Part[ NDSolve[{ Derivative[ 1][$CellContext`xb][$CellContext`t] == (1/$CellContext`L^2) ( Derivative[ 1][$CellContext`xf][$CellContext`t] \ ($CellContext`xf[$CellContext`t] - $CellContext`xb[$CellContext`t])^2 + ( Derivative[ 1][$CellContext`yf][$CellContext`t] \ ($CellContext`xf[$CellContext`t] - $CellContext`xb[$CellContext`t])) \ ($CellContext`yf[$CellContext`t] - $CellContext`yb[$CellContext`t])), Derivative[ 1][$CellContext`yb][$CellContext`t] == (1/$CellContext`L^2) ( Derivative[ 1][$CellContext`yf][$CellContext`t] \ ($CellContext`yf[$CellContext`t] - $CellContext`yb[$CellContext`t])^2 + ( Derivative[ 1][$CellContext`xf][$CellContext`t] \ ($CellContext`yf[$CellContext`t] - $CellContext`yb[$CellContext`t])) \ ($CellContext`xf[$CellContext`t] - $CellContext`xb[$CellContext`t])), \ $CellContext`xb[$CellContext`t0] == $CellContext`x0, \ $CellContext`yb[$CellContext`t0] == $CellContext`y0}, {$CellContext`xb, \ $CellContext`yb}, {$CellContext`t, $CellContext`t0, $CellContext`t1}], 1]]], Attributes[Derivative] = { NHoldAll, ReadProtected}, $CellContext`bikePositions[{{ Pattern[$CellContext`P0, Blank[]], Pattern[$CellContext`t0, Blank[]]}}, Pattern[$CellContext`p0, Blank[]], Pattern[$CellContext`L, Blank[]], Pattern[$CellContext`n, Blank[]]] := {{$CellContext`P0, $CellContext`p0}}, \ $CellContext`bikePositions[ Pattern[$CellContext`positionTimeList, Blank[]], Pattern[$CellContext`p0, Blank[]], Pattern[$CellContext`L, Blank[]], Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`frontAndRearWheelPathSegment, Blank[]]] := Developer`ToPackedArray[ Flatten[ FoldList[$CellContext`frontAndRearWheelPathSegment[#2, Part[#, -1, -1], $CellContext`L, $CellContext`n]& , {{ Part[$CellContext`positionTimeList, 1, 1], $CellContext`p0}}, Partition[$CellContext`positionTimeList, 2, 1]], 1]], Attributes[PlotRange] = {ReadProtected}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.4490635206875*^9, 3.449063575890625*^9}] }, {2}]], Cell[TextData[{ StyleBox[ButtonBox["Bicycle Rides", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/BicycleRides/"], None}, ButtonNote->"http://demonstrations.wolfram.com/BicycleRides/"], FontSize->14], StyleBox[" ze str\[AAcute]nek ", FontSize->14], StyleBox[ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontSize->14], StyleBox["\[ParagraphSeparator]", FontSize->14], StyleBox[ButtonBox["http://demonstrations.wolfram.com/BicycleRides/", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/BicycleRides/"], None}, ButtonNote->"http://demonstrations.wolfram.com/BicycleRides/"], FontSize->14], StyleBox[ButtonBox["\n", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FibonacciRabbits/"], FontSize->14], StyleBox["Autor: ", FontSize->14], StyleBox[ButtonBox["Michael Trott", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Michael+Trott"], None}], FontSize->14] }], "Text", CellChangeTimes->{ 3.448955826234375*^9, {3.448955858875*^9, 3.448955869140625*^9}, { 3.44906364003125*^9, 3.449063671734375*^9}}] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Cesta na M\:011bs\[IAcute]c", "Section", CellChangeTimes->{{3.449124448140625*^9, 3.44912448434375*^9}}], Cell[TextData[{ "\[CapitalUAcute]loha a obr\[AAcute]zky p\:0159evzaty z \ \[CHacek]l\[AAcute]nku Andrew J. Simoson, ", StyleBox["Pursuit Curves for the Man in the Moone", FontSlant->"Italic"], ", College Mathematics Journal, 38(5), 2007, pp. 330-338." }], "Text", CellChangeTimes->{{3.449124520375*^9, 3.44912455015625*^9}, { 3.44912458153125*^9, 3.4491245928125*^9}, 3.4491246444375*^9, 3.449145876640625*^9, {3.44915144878125*^9, 3.449151462390625*^9}}], Cell[TextData[{ "Francis Godwin, ", StyleBox["The Man in the Moone", FontSlant->"Italic"], " (1638):\nAstronaut je p\:0159iv\[AAcute]z\[AAcute]n k hejnu \ labut\[IAcute], kter\[EAcute] jej doprav\[IAcute] na M\:011bs\[IAcute]c. \ Labut\:011b se vznesou ze Zem\:011b a m\[IAcute]\:0159\[IAcute] st\[AAcute]le \ \[LineSeparator]k M\:011bs\[IAcute]ci, cesta trv\[AAcute] 12 dn\[IAcute]. \ Jakou rychlost\[IAcute] musely labut\:011b let\:011bt?" }], "Text", CellChangeTimes->{{3.449124689359375*^9, 3.449124790859375*^9}, { 3.4491250625625*^9, 3.449125114*^9}, {3.449125168640625*^9, 3.4491252743125*^9}, {3.44912536803125*^9, 3.4491253781875*^9}, { 3.449125725734375*^9, 3.4491257348125*^9}}], Cell[BoxData[ GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJzt3Ql4E9X+P/6ht/qv4MXCD718/frFEFrWy1YJFMrSlaUWQtmhgixlkwtS MYAgQrHRVqAsEQQVaVgElMhiWYIgWy6rNQWEUpGypFikpl68JfShPE//n+bI MCRtSNskk+X9evL0Sc5MZk7Sdt5zZs6caTz2zQFj/8Zx3PVaHJfsx3Hlz8sA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAnM9oNJpMJosSjZlSqVSY 6fV64Qy5ubkKK8J52BK0Wm3uQxarAAAA8DUUjiwx5XI5ZyaTyXbt2pUrcPLk STbP4sWLVWabN2/WPE4loDU7deoUn7YGg4HNwwc0rUin0wlrwuah4EZAAwCA d6Boo1zjE5Cilp6wcKQQ3LRpU6LZpEmTOAGLJq3Gbmq12uK9fLKzl9SUZnOy tKV9AL6eVMi/hepp0dYGAABwZxbtx5s3b1K8Dh48mIUvPWeBSM/5NGRR6Oy2 J0Utn/ssglnaUjTzAc3qQzNkZ2db14da1lR/vs58dgMAAIiF0oriidq2lGWv v/46O2nL0pZFG01y82O8LKDpU7DK8zWnNjU7g8yqzRKcNbRZdlPbWey6AwCA j4qKiurduze1c/v06cMOILOGJKWV2FWrERbK7Pg5252gljtrAle2I8EOg6OB DAAANUdRQm1Ayp3WrVtLpVKKoVq1alHmpqSkJCcnh4eHUwnFE+sB5bYtXEeh Bi/fBKYPTt8DfQnLly+nJ/QyODiYRTY/lSbRDGLXGgAAPA8FCoVvdHQ0BcrI kSMpeiiA0L6rEH0tlLassUwRTDskFR6gZt2/WUvZu3dXAACgSliX4NOnT7OW L6UJwqKqKGRpR0WlUsnlcplMRk/opfALZC1lFtaU2vhuAQB8GYUsJUV4eHhI SEibNm3atm1L+YsGb83RLg3tzLDj0pS59Fz4lVL4pqSk4LonAADfRCnQokWL Dh06UEYMHz6c2rzo3+sM9D2zpjG1iymLbXzP1EbGrwAAwIvxnawoeemnResM nIodc6AslsvlGo3GYioltdwMu0MAAF6Dtufp6endunUbOXIkS16Lc5TgYpTF 9erVYweoLX4R9MuiCGZZTFPFqiEAANQQtXA3b97cokULSt6ZM2cied0K/Tr4 wxHW54XZaCGiVAwAAGqIwrdRo0Yvv/xyeHg4ktdt0a+GjX4pk8mo/WvjvMCp U6dcWTEAAKgqdm8+diSTnuBUr6cwGAzsTLFCobC4kRPTp08f/E4BANwQbbQX LlzIDmyyuxGJXSOoDtaDmt+Dsjh8Qb9WNhw3/aLxKwYAEBc1iNRqdVBQEDvg bN29BzwUG6CM7VBZNHvpV8wGw8TvGgBAFLT5nTdvHrv9Hz1Bm8grUfiyo9No 9gIAuAmdTjd48GBq/NruwAPegTV7KYhtpDALa8Q0AIDzbNy4US6XJyYmVthj B7zYjh076FevUCgqzFk+piubAQAAqoc2sHv27ImNjbXdFAKvxzpr2QhirVaL nTQAAIegjaparW7UqBE754vDzlD2pCBmM9BUF9cKAMA7UNSmpqZS7AYEBCB8 wRo78tyhQ4fg4GDWcdpGB2mDwYBGMQDAE7F+NbRRtb4sFKBCfMdp67s/MBTB 7Og0zmIAAFTo8OHDrOVrfSkowBNRvFLIUtTaODqN/loAABbOnTvXv3//wMBA imCEL9QEy1mlUlnhHxLfcVqtVru+bgAAboW2k6NHj65Tpw41XhC+4BCsCx/l bGX3WqIZcEtiAPBx69at4zguNjb27NmzYtcFvA07Lo2oBQCwRtvGiIiIPXv2 iF0R8FoajYb163vinNRqxgliAPAFJpOJ9V/duHGj2HUBL0d7eolmtpvDts8g AwB4AQrf9PR0bOvAxexpDrM9w/bt27usVgAALrNv377nn38+KCgIR/zA9Vhz WKFQ2N73Cw8Pp9lcVisAAGfLz8+PjY0NDAxcvHix2HUB38X3lNbr9TZmwy4i AHiNdevWUfhSBN+8eVPsugCUUf7iumAA8HrU6FAqlY0bN96xY4fYdQF4xGg0 sj5a9nRIMBgMGCgVADyLVqultobtwfMBRGTPQWn7ZwMAcAfUslAoFDaG6gVw E+xapCdeOMyOXSuVSuxPAoA7W7VqVWBgIDUcsLECj8BuovTEwzXsrAqawwDg nvLz87t160b5e+TIEbHrAlAFFK8KhSIxMfGJ+42Uv5TXrqkVAIA9aMM1fvz4 gICAQYMGYcAN8FBsXI5atWqJXREAAHvxAwDimiPwAhzH6XQ6++fXaDQ45wIA orCzNwuAp6BdSvqTtj+F1Wp1vXr1nFolAAALrHcKuj2D92EprFKp7Jzf398f e6EA4DKnT59++eWXZ86ciUNw4JX4btJ2zsxGn8a/AwA42yeffFKnTh3a4Ihd EQAnojylYLUzhdldlpRKpbNrBQC+bOTIkZS/Wq1W7IoAOF2VUhgAwHmMRmOb Nm2aNWuWn58vdl0AXAQpDACiMxgM7du3t2fsAgAvgxQGABHpdLqqXiwJ4E1Y H+kqnX+hmeVyOb3RebUCAK9HO/+08cGWBHxcVa8XLnt4szDsuwJANbDjb3be UxXA61UjhdktltB9EQCq5ObNm82aNevQoQNO/gLw2HBwVTooVKVLjAEAyswj 5Q4ePFjsWgC4HZbCVTo0RPuxGD4LAOy0ffv2OnXqiF0LADdFTVpcHQAAzrBn zx7K33Xr1oldEQD3pVAoMBYWADiWWq1+5ZVX9u3bJ3ZFANwa66xYvcPL9F50 cQQAIZVKxXEcbVVw/RGAPeg/xd/fv169elXNU3ojLrQHAIb2yQcPHoxzWwDV oFar6X+nqu+qxvVNAOB9KHa7dOmCi48Aqi0oKKga70IKA/g4lr+dO3dG/gJU W+PGjXNzc6vxRkphXKwE4JuQvwAOwYaDxv8RANgJ+QvgQEqlUq1Wi10LAPAA /ODPyF8Ah6B/JZlMVr3D0QDgO3DzUwBn0Ol0NTwcrVAo8I8J4MWQvwDOQxla k8PRrI80DmgDeCXkL4BTGY3GGt5cG1cqAXgl1v+qGmMIAID9NBoNtYVrsgSk MID3CQkJQf9nABeQy+U1DFCWwhgqFsBrBAQEIH8BXECv19f8MmGj0Yh/WADv kJSUVK9ePbFrAeArFAoFhr0CAPL+++8///zzly9fFrsiAL6CHUlGMxbAx9Gu eFxcXH5+vtgVAfAtKjOHLAoHpQE8kU6nQ6cOAFFQbnIcV9VbCVdIq9ViLDsA z6LX65G/ACJyYEOYloMrCgE8Au0t0+73U089hUsLAUTEGsKO6pdFi8LAWQBu DrdAAnAfbLwsh/wz4mJhAPc3YcKEhg0bIn8B3IRCodBqtWLXAgCcLi0tDdcf AbiV3NxcuVwudi0AwLn27NlTp06d7du3i10RAHgMRbBerxe7FgDgLOw8EY53 Abgh+sdUKpVi1wIAnMJkMtFuNvIXwD2xixQcco0wD2NgArgJ+mfEXYAB3Bn9 hzo2MdmBr9zcXAcuEwCqSq1W+9TIOQvSF1y6dMkFK6K1LEtfmrEuwwXrAq/H bp/k2GWy4e8c27gGAPsdPny4YcOGPvU/6Mf57dy5ywUrorVIG70cGR7pgnWB L3DGVb1sD9yxywQAe1DyPv/887Nnzxa7Ii6FCAYPpTZz+GIpgjFqFoCLmUym Hj16REdHi10RV0MEg4eiJrAzLhCmTQGGogVwsVmzZvnaIWgGEQyeCyNMAniB w4cP16lT5+TJkzVZiLGo6NeCW46qUnHx3Wv5N5842507f9J6bUw1PGkhFUYw e+O9kpKarJ25fbuQHmVVjOCiP/5g76p5BazRRystLbVdYoGm0jy0OttLpj8A 51UbrDm8XzQAuF5QUNCSJUuq/fZNm77s2qUr5Qs9ZCEdFi8qXxRtiilu6PH7 w5Y1JVrvXn2opODxpP7wgw+p8GJOebdkmpT6YVp0VAxb2rAhw06dPsPPSblM cyYkjKTnmZm7e8X0YrPRE70+W7jMvXv38VPbtGo9UzGrssoLI/jWb7/Ne3de 967d2RubNgkaM3psTs5j/aXnvDOHKmCxdlqdxWLpw6pWqPiv5aUXX7Inginp 1q/fENvnVZpTUr+BMkVZ9HhUrVr5CS1h//4DWVk/2q4A7/CRo/SWpenL6Nt7 b958+jboLS2bt0hNTaPVzZ49my+ZM+ddmsfi7RdzchJGJNBXwdYVHRn92WeW nbqv5F2dNnUaWw77GxDWvKSkpLLfmo1qgz30ej16TwF4OolEUu33rlz5CW1O Q2WdPkhRpn2YOnjg4KTpb7FJ/eL60aTTDzP0+ImTbNu7YcNG4RLiYl+ljTZ7 fuDg97S1p20+LSrw6QCWg9euXednZiXrvshgcTBieEJI23b0vHtYN77RumNH edhR+fx57y1ZtGjUyNcpyiurvzCCDx06TElEsUvvokffuL4swfMFTekpkyc/ 7SexWDs9KFz4eagmQ4cMZe+dPWv2svSlEs6Pdj9sRzDF32sJr7GaL0xeyNXy o+dhoV3y8q7y89CiqDBlYUqnDjIbFRCifRiamjQ9iapEX92ggYNZxNNDqfyA +xsnLJn6r2nC99KqQ9q2p3dNmTyFVq2YoaDvh3vxJWFS084PFbL9JfrSqOb0 x2BR88p+azaqDfZgY3Q47xLCXDMnLRwAiEajqfaO9IMHD1jb55creXwhf7gy 3ZwXX6z9gr2kMKKZ6UGZyM9MadWyWXOaxL+kJhU/dfbsd2gJq1au4kv49ulX X21jJRQH48aOK0/29X8le6+evenlMd2/+Xf9p/IjqMII/u9/i4UtdGokjho5 ihZFTWO+kCJY6udvvXbKHf5YLjUwWcn16zdYCTX3WM1tRPDC5PdphpjIqNuF hWzJLMfj5fH8klkE08d/d+48GxUQYhFMb4noEX7tYX0++2wta/mGB0WwErbf Qo+LD1v9tLS42Dj67VCLm19aXt5VSYN/UHbzJWNHj6F3UbzyJdY1t/Fbq6za YCeFQuG88aJpyY66NyIAWKD/rD59+rRv377aPTp+NxopwmhDOnrMWBYcQtnZ 5yQv/M+A/gPKzEEgqd+gXmB9elCE7diRyeb54IMF0tp/P3rM8jQ0baJXrPh4 1YIF5VvyXv358odBFi6cmXYApM/WDY/6K038XiqfZ0B8fz5xbKjsXLA+++ze vdrFS5bTorinn+EnUQT7cZzl2hu8QLOpVMvNnzpbGvCMtG7gPu1+4Wz/bN3G RgRnZGyhr4Xz88/KerQ5pfo/Xcuf3hX+8POyCPb/m7+w45xFBSywCKYZTgsO 6RNaJpUvW7CML+FqcVTSsEFD9jIoqCm9DA4KtligJCCAPiALU6o2NfDr12tg MY9FzSv9rVVebbBTWloa9/gfpGOtWLHiqaeewnC1AA73/vvvBwUF1XAhV/Ly qB0U3FhKj0EDBmWsy6C2JD81LTWtRXDTuybTW0lvNQsK/vXXgus3DDTnSPOZ wfv374d17jJuzDh+fsq+Nas/jYt9leaJqB8+fOgw2kTTT34GtjE/9XiakE6y jny6/fbbb29OfZNWR3P2i+v3sepjGz29hRFMa1+yeEnPqBhae1RE1NBBQ2j/ ga2Rn58imKtdx2IhtGqahy1n//795Udlhw63mMf2ueC5c+bS1OlvTrcoX5T2 EZW/Zv66yh5G8IjhCTYqYIFFsPV6FTMUVL47M5MvYQuncvayt/lgwokTlntH QwaXt3BVy1fw1b569Zr1eoU1r+y3ZqPaYD+nHosuMx+OxqhZAI518uTJmveC 5hnyby5atJgdlO7fV84fWixv6TR6+eDBQ0GSoEkTJrHCUSNfp0J6Czs7nLHu 0TgA7ADmhPET+TZ1NSKYoSVQmstCOrAzxXcr2UYJI5gFyrtz5/HH0qmSVY3g 7/Z/R88HDRxsMY/tCJ4/7z2aOm3qNIvyD1KUVD7x4Vfnygh+NTaOXh4/fsLi jfHm3RI20iar9hXBaYgKa44IdiqFQuHsM7ZqtRr3ZgJwFNpnfumll/71r385 drF5eVdZzxzhxja0Y+jC5IXSFxru+vavrf3XX2+jebZs2fqRuaF07vxPrPz8 +QusCxOfgPdKSqodwQwFMesddNrqLYwwgruFdevRrYfw1OQV8y5ElSL4/Pmf 2KewuKZp7edrbUQwfRs0NaJHhEU5RTmVU9ucvXRlBNP+gPkM+waLN9LeVHk0 m1vHrNrbd+y0Xq+w5ohgp6J8dMGlSTgjDOAoFL4Uwc74n6J0sNiojh+XSO0m iaQx3422oOAWa/EljEigqLp//z4rt24nZp89V8MILqsoa4SEEWydbrv37K1q BJeUlLD9EL7rUZm5axPrX11ZJek7YRf+HDhw0OLjC7tIuTKC2WdPHGvZVY9r +CLt1bAdDKp2cGOpsMNYhTVHBDuVTqejhrDYtQAAuzj2ELSwdUlNTnaxSe7P l/nC5ctXUCQ1lzYXvmvYkGGdO3Wmmfmj02UPW8H0yHl4jXDvmJ7ViGDrS4np LRcuXKyw/hatYNol4DtF/3z5l7DQLlWN4LKHPaJpUceO/TXQ3/Tp09k388Qe 0ZRu7ONfybvaPawblbz99kx+HldGMOsRTQm7Y8ejxR46dETq579ly1d8CesR vXBhCp/C1jVHBDuVk0aqBACHo5Zvz549Fy5c6JCl0caWHT6lJu2UyVNYysye PUc4z8GD35dvges/1mk2Y10G2yzzR6eZ10eNlpovlqGltWzRYuiQod27dh86 aAg/wxMjmDWxKd9pCVQrdhT6tYTXKvsIwghOnp8sNV+WS29MHDeeqjFt2pus ccrniz0RzF8XTI9ePXtTYlIc79qVaTuCaRVT3viX1HzxDu2ZSCSN6Tl9IcKL cF0ZwWXmL7Nzx/IvML7/ACqnHSd67lf778LlXL78C+sD0KNbj6TpSex7s6g5 ItjZnNopGgAcRa1WO/CYldFoTFmYwvrt0IZ30MDB69dvsDgmeft2IUVG//7x wkJD/k0qpIfFcEz0UpmipAAt39Rz/rSolJQPZs58dPMm9q6LOZZ3+J08eUpS 0gx6UlRUlJ6+tF9fOQUZPejJqpWf2Bhqsn/8QP4K4jt3/nxn9hyKYHojhc56 82lQWiytkR93cfmyFQPiLQf6YPMIr0Smmq9bl8G+GVpgbGxvVvk33phq4/ss K79Me3vCiISWzZrXrx1onU3btmloIfSdPLECPPquaBL7coQ++WQNlZ8UdHhm C6dy4Wx5eVdpZ6Zjh470QcI6h9HOifCyKSY//+a8d+exMc3ow1L9LWpe2W/N RrWhSsIfv+DLeWgDgq7RANWDiwsAvFJMTIxrVuTYfXgAnyKXy3GJPYD3cdnN GkwmE21GnDceF4C3qslAlADgzpYvd90IYxi1EqCqjEYjx3FHjhwRuyIA4Hjx 8fFPnslxlEqlWq1+8nwAYDZ48OCQkBCxawEATuHiCKZdemoIV3tseQCfwi4E PnfunNgVAQCncP1FSchfAHuYTKY2bdpMmDBB7IoAgLPgumAA96RSqRo2bIgL kQC8GCIYwA1R8gYFBX366adiVwQAnEgul+PIMIBbyc3NrVev3ooVK8SuCAA4 lwvuV1iZJUuWjB8/XpRVA7gz+q902QX7UFX67LOnTp/hb4sMUBMiRrDJZJLJ ZGKtHcA96XQ63DzFneEOBeBAIkZwGbY2AFY6d+68fft2sWvhMYqL76pWqCq7 ZUBpaSll5ZjRYzt26NiyWfMA/4CarxERDA4kbgSXmU9GUxCLWAEA97Ft2zaO 49yqF3R2dnZN3n7t2o3jJxxzg2ML90pK1q3LYPc0rDAT79z5M858wyN6dO/W XRbSgZ68ZXXjoapCBIMDiR7Ber0eDWGAMvOpmZdffjktLU3sijzy7tx5XN3n qv327/Z/Z3EfWwdidy6mQHz/fWVlmdivX//Fi5YUFNyi5/fv3/d78f9ozgMH DtZkvYhgcCDRI5jgFjAAZQ8vBHarQdQpPWsSwbszM50Xwb9cyaNWMLWF2a3t K8xEaggLX06bOo3mTBxXo16giGBwIHeIYAAggYGBlMIuW11x8d2vv942ZfKU V2PjKFZGjRy1Yf3G0tJSfgaKzoge4X4BtekJPbZs2Vql5aemfjR86DBKK1oI W4LFPeUdxUYEW9i69Wuas3evPvYv/PTpM0nT36K30OMD5YeU+NYRTK3slStX UbLHRMXEvdo3PT2dlRuNReyDX8m7arHY5ctVVP7d/gPsZeoHqfH9B7DfArXu Hzx4YH8NwaPhumAAN+HiJvDsmbMpSkLathsxPGHQwMFNmwTRy9cSXuNTmJ1F 5R9VbcyyqBI+aEVO+BxViGCN5huak8LO/oVzAbXpLdGR0VT5f7ZoOXTI0LDO YRari46KMe9pRNA83cK6Shr8gx36JvH942lSysIU4TJvFxayb/tiziV6mZ9/ k97CVkG/jjatWt+/f9/+GoJHw+hYAO6AwtfF/4xZWT+eEHSU+vnyL6zDkjBc XHAgOifnEq3RxkNXUVdnIfsjePas8r2Od+fMtbP+W7Z8JfXzz8zczV7euGGo sPcXzfDLlTz2/K7J5BdY/53Zc9jLzZu30sz0xQoPL7Cz2P3i+rGX1Mrm/J9m z2m2H7J+tLN64AUQwQDuQKPRuPIodIVWLF9B0TBxwiS+xAURvHzZCovGssVj +NBhttdifwRLJc35tucTURpS4HINXxQWHjumq6wDNo+rXYcas+x5cfFdatXS /IcPP7rj87Ah5cfnN6zfyF7GRMX4Pe2Aq6XAE7lVBMtkMrfqiwLgGmyYGlGu Rfrvf4vPnj23b+/eTRs3Kd6eSdHQM7onP9UFEXz3rul3o9HGw6JLlTU7I/g/ //mP37PPffbZWjsrf+ToMVpsu3btLMq7hHapcHW3bxeePn1Gs03jV78BzVBw 6zdWvmKFil4OGzqcvczPv0kvaSH0zbOSd+fOo4odPPj9XWz9fE94eLjYVXiE WgEYlw98kChNYIq2OXPeZScl2dU97CwnPeHncece0Tw7I5iq4Vc30P7FrlR9 XOH5a+vuWFfyriaMSGBfY0i79n6cHz0x5N9kU/mGcPbZ8vs+064OPV+z+tEN OKi5LWnwAhXSbKmpaTS//ZUETxcfHy92FR6hVgAawuBrRGkC379/nw1bkTA8 gSKMnalkWeaVEbzui/LTrwrFTPsXuyx9qT0RfP36DZaw7703P/fny2UPu7Hx EUzmvTuPShbMX0DPZ76toN0evr8WQ83nKW9MYbtDfXr1Likpsb+e4NGWL18u dhUeg4Yw+Br6m2/Tpo2LV3rixEmWtsJuQqJEsAvOBbP8HTxwkPDDPtHevVp6 V8cOHS3KLXpEJ01/i17OVMziZ7CO4PM/XeA7ZfWMihlfyYXJOTmXWI+4o0eO 2l9P8GjulncGgwENYfAd9Kf+0ksvuf4o9OYvN1uHI7ts1jKCa9ep9lpYBCdN T7Ixz8kTJ6m9aeOx7euvba/FdgSz/KWG6pW8vCpVnhqq9EaLjlIsTIWr692r j8XauZcaWUQw6RfXjwp379lHP/dp91e20rQPU809tTZUqarguaKjo8WugiWF QoHxssBHbNu2TZQRsb7d9a35CtlH56GKiooieoRbRPDyZcv9Xvzfaq/ltDkc oyOjq9T8rCobEczyN1TWKce+XtAWJk2cxDXi+PsS/ve/xXGxcexwMb+6oebu zakf/jWs6IMHD6R1n7OO4A3rN7KatGvd1uLbEPY3e8vcpt6zZ081agueyK26 YzFGM7FrAeB0tKXlOG7q1KmuX/WvBQVSaZCkwT8kfk9Jnq1L1egSytHWoLzd J7hKIvvsOT8/f0phSf3nl320uKpr+eOPP6RSiTTgGS6wHi2hsaSxQz/EXyqL YIm08V9Hs+sG+nF+wscpwSVCNlBDWOLP0dslL/4vV/e58J7h4ZFRtZ4OoGWq 1evZPJs2felX//9JJRIKa0lg/d7hfTh6S6OXDz9+9xnKWXZJlCSoqbC8fM9H Ei7x4+i3IA2sT1+UP/fUH3/8pwbfB3gMg8HgVhclAfiUPn36JCXZOkjrbNQc O3/+gj77rI1euJQdP2T9eOVK1Y7iCtHCaRW5P192alvYeYxFRZTyF3Mu2Rg3 kj4jfUs25qGvMaRtO2pB821qIV32WVoFrchhlQZPoNPplEql2LUA8EW5ubkU wTjg4yPeNl9zLey1BaBWq92tOxYPmybwbrT367b/feBA1PZfuDBFah6Ou8Im MPgsd75Nkkwmw/0jwFvRHibHcej57/VOnjzVN64v5W/TJkFHj+me/AbwJe68 EXCHIXMBHIgTUKvV+PP2BQcOfk/52z2sWxZuvgCPo/ZvYmKi2LWoFJoJ4DW4 SohdL3C64uK7u/fsvYfRrsAKNTNpV1zsWtiCk2Xg6SoLXwQxgI9TKBR6vV7s WthC7XS5XC52LQCqyZ78RQQD+CB2f3D3P8xLEey2HcYAbLMzgpHCAL6G2r/u fCKYZzQa3X8/AcCa/fmLCAbwNSqVCuMwAzhPlSIYKQzgU3DVLYBTIYIBoEJ6 vR7dnACcChEMABVSqVRufjmSBZwOBo+DCAaACnncUWidToehhMCzIIIBwJqn 9IUWwkhZ4ImQvwBgQalUemJfaKq2TodBzsGTIIIBQMhzm5OUvx7XeAdA/gIA 7+9///vy5cvFrkV1sOG8tm7dKnZFAKqM/fUieQF8mac3JKkJ71m9yAAYT//X A4Cao40ATqcCuJ6HdsAAAEfBXYcARMGOQhuNRrErAgCiUSgUuPcugOtR+HrW SDgA4FjUBJbJZJ7YERoAAMCjeVMTWGcmdi0AAACezMuawJ44uhcAAPgmagJ7 U29MdG4BAACPoNPpvK8jNAarBE+BP1QAn0UNRspf79sI0CeiFBa7FgBPYDAY vG8HGADspNFoFAqF2LVwPDbStdi1AHgC+gfETTYBfBPllMfdF9h+tGXD6WBw c4mJiXq9XuxaAIAIqP2LAQEAxML6DXrNlQgAYD/a9/amC5EAPA79D3rlaSAA sI2Sl/IXR8AARKQxE7sWAOBqSjOxawHg04xGIw5DAfiU/Pz8gIAAf39/X/jf NxgMjRs3FrsWAAAA5SQSCaWSL+QvI5fLvbXLNwAAeBCdTsdx3ObNm8WuiOuo VCpvGnsTAAA8DjV7KYw4M99pApdhmCxwV0ajEd2hAbweBa5Go5HJZNxDYtfI pQwGA312sWsBYAk7hwBej92CgXuc2JVyNS8eAQw8l0qlwhVJAF5Mq9UKG7+M D+546/V6nzr2Dh4hMTExNzdX7FoAgNN98cUXbdq0YRHsfTdFAvA4bGhKsWsB AE5HmUtt4fPnz/tgXywA90TtX2oFi10LAHAu1hmJDUSZaCZ2jQCgfMcYJ4IB vBvLX/7Is9ZM3CoBAAB4PXYjBuGetslMxCqJSG8mdi0AAMD7UdQmJiaqVCqx K+IucA0mAAC4APLXmsFgkMvlYtcCAAC8GfK3MugNDm7Cl08JAXgx5K8NCoUC IyGAO1Aqlbg8H8DLUP727dsX+VsZjAcIboLjOOwNAngNdmP6WrVqpaWliV0X 96XVatVqtdi1AF+HbgkA3oR2p4UX/wKAO9Pr9bhHIYB3YINPIn8BPIXGTOxa AIADNG7cGLfhA/Ag1ArGiWAAT2cymZRKJcZ8BgAAcCVq+VL4UgTj6sIqSU5O FrsKAADgwfR6vcXgz2Cn+Ph4sasAAACeaunSpfzNB6GqgoODxa4CAAB4HqPR mJiY2LdvX3oidl08FcdxYlcBfJrJZML/L4DHYRcfYWSJGqJ9GHRGBRHhiiQA z8J6PlP+IjtqDsNEg7gwOjSAB2E9r9Dz2VGoAaLVasWuBfgu7AQCeAS+8Yue VwBeQy6XYywdADeHxi+AV0KHQAB3ZjQaFQoF7Sqj8QvgZWiPGhEM4LY2btzI uj2j8Qvgfej/Gn2xANwTNXtjYmJwnggAAMAFjEajSqWqV69ecHBwz549sYfs ArSfk52dLXYtAABANCaTicKX4zj6icPOroSrQgAAfBYFrkajkclkFL4Yqs71 MDYCiEWv12N/G0AsFLgIX9FhhEAQC47AAIiCnfNlh50RvuJCBINYEMEALkb/ cQhft6LT6TBGJYgCQ2MBuAxt6hMTE2UyGbW5cAIIADAuB4ALsHO+QUFB6PYD ADxEMIBT6fV6pVLJDjvjpA8ACCGCAZzBYDCo1WqZTCaXy7VaLQ47uzPOTOxa gC/CYTEABzIajRS47IQvNXvR0cKdcZUQu14AAFAFfPKyA864pZH7qyx/kcIA AB6BGrl88rIRlnDA2SPYzl+ksG2G/JsZ6zK+3fWt2BUBAB9F7dxatWqxo81o 83oceyIYKVwZxQyFtNHLy9KXil0RAKg+j9vcsTYv695MLd/k5GSxawTVYWf+ OvZvsrj47u3bhfYUCt258yc1OUtLS20v/F5JCc1GS3tiNX4tuEUzP3E2xlhU RIt98OCBRTki2FFMJhN24MH1PKjpwccu69tMbV6dTochrTyayyJ49qx3IsMj L+Zc+umnC9wLDSm26OX33x+iSTduGIYNGUYl9OjapeuOHbsqqGeHWmyGpk2C xowem5VVwbZ6585dgwcOZrPR49ln6wqnnjnzA60xY10GpbMyRdmmVWu2tEkT J+Xn36ys2ud/upA0/a2OHTqyZYZ2DN206Ut+Ki3Nj+OoPKRtO1o4PVJTP6JH tb8lX5abm6tQKMSuBfgWF7c+qor2S+n/QqPR0L8GH7uUwujb7DXsj+Aa/imy 1uIX69ZT9gUGBspCOrAEzM4+N3jgIHo5YngCK6THoUNHhO9d90WGpLF0YfLC JYsWsbCmN1Lh4/Oso/KWzVvQiqhNOmXyFKmf/1tJM/hWM0UwzZA0PWnQgEH0 9kEDBw96mNdhoV2KiooqrHbKwhSq8MQJk2iZaR+mdpKVZ/Hnn61lU7dt0zSs 9/+opHtYN6o/PT75ZA09avJF+SxEMLieaxogttFfPjVmWc5SyNLqatWqlZyc 3KdPH3pOhWq1Gq1db+XiCKY249y5yfdKSqgpGhERSSWSBv8I7xnOgpLKo2N6 ls/2bF3jw0wMD4+kMPXn/PlFUfj6vfi/VBgVHsFKli9bIa1br137kLy8q8KP Rotq+LyELZxFML0r4u/hVx7OlpNzqXadZ6k8wC+gwmpTA/nOnT/5lydPnpLW DaTHiexs4efCgeiao00QbWrErgX4EJdt/RjKUD5tqTHLGrac+UyuUqmkQr1e j+atr3HZXyCLqg9SlHwJJSNrhFqcAg5p244Kf8j6scx8gpharPSSD01m17eZ VEjtU/aS2rMtmzW3OLFbUHCLLf/8+QtlDyM4rHOYRcUOHz7Kms+260+7BFSl b7/NZAeld+7cJfxciOCawy26wMWcEcGUoblmWq2W/UnzbVvO3KQlVEhTaR40 bMHFEWwRVSwif3/87zAyvLx1fOr0GXquzz7L5iktfawf1NWr11j5zV8L6CXl b0xUtPVKu4V1o3koN8seRjAt3GIeWhFbVIXVvnHDkLwguUe37s2CgmOiYoYP HdaudVtEsDMggsHFqhTBmoeCg4MVj2ONWYbSlhVSO5fNf+rUKbRtwQZ3jmBq wLJ57t+/L5wn9+fLrJwdJabmcFRElPVKWYv14MFDZdWK4NuFhez09NKly/gm 9ojhCYhgZzCZTNhSgStVL4KXLFmS+zg0ZqGGnJ2/ZdWNYP5A9OVffhHOs2XL 1vJOUF27s5eDBg6mVqrFgehfruSx5V+7dr2sWhG89vO1VD5syDBhIevEhQgG 8HRVimCxKwteztl/e9WLYDJm9Fh6+dmaT/kZSktL+/TqTYXKh2eW16z+lF6u W/dYH+n33ptPhX3j+rKX1YhgVmf6yZdQY5ydquYjePbM2RbnuKF6qBWM1gS4 EiIY3IpT/+qqHcHZZ89RQ1gSFMxeUlP3ndlzaAZZSIfbhX/147pz58+Qtu3b tGp9/PjJRwt/OoBmO378BHtZ7VZwWGgXfqCPz80lwghm8/SMjrFnMBCwARcl geshf8EN0ZbQ4XdzrnYEk8zM3RKJZOKESUnTk7p26cryN8vcZZq3bZuGLS1h RAKtq19cP6mf//r1G/gZqhHBRUVFobJO5SNyyDrRqkeNfP2V9iEJ5nPBGs03 bB5D/k12qJx2ANjQHxmPN8bBTohgcD1EMLghZ0TwJ5+sGTE8gYJSWMiGsxBe eEuSkmZQ4cWcS8LCBoENWjZvQWH3amzcokWLKxxJ49DhI2NGj2UHiiPCI/sP HCScmpNziRZLC7d410VzOT0qrPb16zemvDGF4pXWPmzIMMp9+ggWH+T77w/F 9x9AdQvrHEblFp8R7IQIBtdD/oIbor86nJUDF0MEgyiQv+Bu8IcHrocIBhEh fMF9YEsIrocIBgAAEIXJZNLpdGLXAgAAAAAAAAAAAAAAAAAAAADAkQwGAzqm gij69OmDmyUBgC/DtSEgFmcMywYA4EE0Go1arRa7FuCLEMEA4OPYbanFrgX4 IopgvV4vdi0AAETjoRFsNBoVMxQdO3SUNno5OipGtUJ1r6RE7EpB1Xjo3x4A gKPodDontUSKi+/u+jbTGUsuLS0dPHAQhe+oka9PmzqN3SxpaP/+zlgXOA8i GADAGX4tuMXuq+uMhX/+2Vpa8ubNW9jLoqKimMgorvbfnbEucB6DwYBzwQAA DmfIv0kp6YwIpsY1NXt79+wlLDxx4qS09t9pksNXBwAA4EE2rN8wZfIUFsGK GQp6GIuKHLXwXd9m0mIXJi+0KJe88D8HDx5y1FoAAAA80ZTJk1n+8g9qFDtq 4fPnvUcL3LRxk0W59OmAtA9THbUWAAAAZzOZTM5Y7BMPRF+/fmPnzl22HxW+ ceRro2ixBw8etCj34/youe3AjwAAAOA8zhsa64kRTAlr0VK2flT4xt69+tCk M2d+sCjn6j43YniC4z4BuIJer3fSTiAAgJujDaBYEVxSUvK70Wj7UeEbI8Mj EcFeAwNkAYDPct6Fmc7rEU05S4s9fvyERbmf/1M4EO1xlEqlVqsVuxYAACJQ q9UeF8FJ05Nosd9YVVsaUAfdsTwORucAAJ/lvMOAzjsXvGHDRpq0fPkKi3Ku Ua2DBw85qPrgIjqdjhrCYtcCAEAEiYmJzo7g0tLSCme4dOnSsvSlth82ljzm 9dHCwvM/XZAGPIOhOTwO7pUJAD5LpVI5acmUvGyAytOnzzh84f/617RmQcE/ X/6FX9eokaM4/6ccviJwNqPR6O/vL3YtAAC8TXh4pB/nJ6nfQBJYz7FLLii4 1e6frdtJ23ENXpAE1OFeaCh5ti6tzrFrAQDwJocPHV6WvvTSpUtiVwRcJ/fn y0eys52x5HslJefPX/gh68c7d/50xvIBALxJ8oJkaaOXKxv1CAAAAJwEEexu DAaD2FUAAADHO3X6TMrClNu3C/kSRLC7CQ4OFrsKAGUYnQPA4axvkYMIdism k4njOLFrAVCGv0PfYSwq+rXglkMWVVx8l/LFnksR79z587//LbYx1f5budGc 9tx6ldqeVbpG8l5JibC5ao192JKSEhvz3DWZhB1jnhjBtEzbKwWnwiWZ4Cac d306uI9Nm77s2qUrywVZSIfFi5aUmaMqMjzyzWnT+dkojHr36kOFBY8n9aux cVR4Mae8Ny9NSv0wjfN7ii1txltvC/OOntOcCQkj6Xlm5u5eMb1onmZBwTMV s4oeT8+9e/exqfTo0a37v3X/rqzy165dHz9ufMvmLdjM9EFUK1QWIZswYmRq 6kdUTp+OzTZq5Os5OU/ufhweGc7mj+gRQd+ScBL7pNFRMWyGNq1ap6am8esV ftJ1X2T8s0VLNpwClbCx9OnRvVt3ek4PffZZPoKpVlQ3/rNYrBRcQ6vVOu+6 YAD7YaRor7dy5Se0tQ+VdfogRZn2YerggYOTpr/FJvWL69exQ0d+zuMnTrJo 2LBhI1949dp1Ftzs5YGD3zdtEvSMXwAlzrAhw2jShPEThaujEpqBUomeREdG jxieQPFU/rx3b36eHTvKB+gLadtu/rz3lixaFNu7D626wsrfLizs2rlL+YhA o8fSGt+dM5feRS/79OpNk/jZKM3Lb6Va+9n4/gOGDhnGBkag0Lx+/YaNb6a8 knUDqQ7K91PYYheZd06EnzRhRAJ9abTqnuYsFn5Yeknf3pYtX7EvjUVwUtIM NpY+PQYNHEzP6UF7LyyCP/ggjWpFyUuF9Bths9EvyEYlwRkofzE8L7gD+jtU q9Vi1wKc4oEZbfNpO//LlTy+nD9kmp6+VDhp9qzZNDM9qJnGz7xvn5bmoUns JbWUr+Rd5adSQtHU7LPn+BIWKxReX321jZVQAJVnot+jcWB69exN8xx72PK9 f//+vUoO81LkBTeWUpOZL6HkjYmMordPnvTGowXG9KJVBAYGspf5+TfDQsuD e8obUyr7cqjO9JamTZrzb2Et6IsP284Wn/S3335jLXH+w7JPSkn69tsz//jj D+HCKzsQbQ7cVWzcQvr5zuw5VEKLLbLjADs4EO4TB24C50S8GLvxKNvyV3gJ f3b2OZq0ZcvWMnMiUAZRpNKDsok/4ro0fVn5/dEqaaV+uuZTmrpm9Rq+hK1u zjtzhLNNmzpN4veUxTwXn3SgmMKOZnttxGsW5adPn2FLyP35Mithx7SFnZ02 b97KGsKVLZya1TTDgQMH+RIKRyr58IMPK3vLxAmThB+W1WHYkGHWc1YWwePH jRfORr8UFuv79x+obKXgDDqdDndLB3eAnoFej52apOak8Mgtr33bdlMmlzcV T5lzjWKIJdGubzPZDOPHJVI0Www4TwF9/vwFCg7F2zNpZuG9Sln6HHv83O6m jV9yTz/Dv2QnQwfGD7hm80DxR2kf0Wwfqz62nhQdGU2T1n6+lr1kESxsSlM6 s5pU2OuJ6k+7GRR/wrew4/Dx/QdYz0wfllri7MA7/2HZ8rfv2Gm9/MoieOvW ry3mpNVZ7MMAgE8xGo1iVwGc6Epe3tjRY4IbS+kxaMCgjHUZwi7KExLHB0mk 9OStpLeaBQX/+mvB9RsGmnOkuaPR/fv3Q9q1T3n/0R21qOG2ZvWn/pxfRI+I wQMG9YyOqTCCTz0+QD21T/04P/7lb7/99ubUN2l1NGe/uH5ff72twpqPGT2m fGegooyb/uZ0mjRLMYu9ZBEsnIG/W02FPa7PnvtJWslN4iIfDrfLPmlc7Kv0 bdCHHTJocLcuYdYRfKqiofif2COax04cV3ZnHAAA8AIUB4sWLWbnhfv3lfOt 2i/WfiF56WXWKpw0YRIrZK1UegtrGF679qitOnTIUCoZO2Yce7k7M7MaEcxQ q5wyjp2BXfdFhnWdE8eNp0k7tu+wnkQtd5q0MHkhe1nVCP4h60eaFNY5jKZa PPhWM/ukwqMHy8ynzhHBAABQDXl5V9nJRz44fvghi8Jxz959woPP1Cxl54g/ SvuoR7fu/NvPn7/ATrDyZ5YpH6sdwQwFXLvWbamZaT2JHYi2vkE56dypM03a pvmGvaxqBBuLimycIq/wk5K0D1MRwQAAUG1sm89nwV1zZwCKFYpmvgtWQcEt mmfa1GkJIxLenDqNfy+9S3iolqwynziuSQST4UOHWQQow7pjxffrb1Gembmb dSTm26dVjeCy8pOw8TT184dnky1Yf9Kyhz247IlgdlUU31usDBHsTnAZJgC4 jPC+4ZRZ7AJYYTrUDnima5eu/FFoZtiQYdTSpJk/XfMpX8jahvTIeThMR1ho 52pEsHAq5X4nWUfrTlDMhPETaWmrBb2VKJfZR1i6dBlfWI0IPnT4CE2VSCTC Qn70LYtPWj7/94dYiT0R/GpsnEUNEcFuIjc3NzExUexaADxGbSZ2LcDBsn7I ogfn5x9RO1z6bF1qNgb+LVDq97fZsx+7YohawX4N/3fHjkxhYUZKBhXS4+TJ xy5HGjRoNOf/lIR75tXevZ+u9VR4ZATNI+xUz951+Ohj70pesIB7GMG//nrL r+5zAU89I20sado4KOCp/y9IIjl+/ESFH+HOnT+jo6IlgfWf9n9aUv/5Fxq8 EEQNTK6WQjFT2Em7Z3Q4rVT4xhvXrrOa0JPKvh9KdqoVVV4aWL9pUNOe0b1p b+TOf/4j/KTNJS2kAXXowwZJm/Ts1V/4YSv8pMyK5Sou4BnpS43oM9YJCLh1 +/aCBQtoZvoeLOakClD5gsVLrBcCzqBUKhdY/RYAxKXT6XB1MAB4PZlMhtsU grsxGo30lyl2LQAAnIjCFxs6cE9RUVFiVwEAwIm0Wq1SqXzyfAAut3z5crGr AADgRCYzsWsBUIHk5GSxqwAAAAAAAAAAAAAAAAAAAH/Jzj73beZusWsBAODW MCgWOMrt24Xbd+xMmv4Wu8uM8AbrNYG7FgKAV8rNzZXL5WLXAjxbaWnp7j17 Xx812uIOp/H9B/xyJa/my1coFHq9vubLAQBwKxiDF2ooL+8quz06e3Tu1Jla wbu+zSx6OLB8zWk0GpVK5ailAQC4icTERLQvoNpuFxaGyjqxY84Lkxee/+mC M9ZiMBhwrAYAvIzRaBTeSQSgqtLTl1L+ykI68LdOcxKKYIxhDu6A/tSlLSX0 Zz/ytVFX8q6KXR3wYDqdDuNSQk0kjhtP26K1ldxe3IFUKpVGo3H2WsDdXMy5 lJ19tkpvKSoq2r//gJPqs3fvvqZNgoKaBE2ZPKVZUHCbVq2zz1ategA8imAc hYaamDtnLkXwwYOHnL0i+kNF131f8+7ceVW9a7w++yy9JTI80hn1yc+/SZlL EXzo8BF6uWPHTlpX97Bu90pKnLE6AADbDh8+ImnwAteE27FjFyspLS3NytKn py+N7z9AWreutH4DyQsNjx+u4O7hVYXdRS9TXHz366+3UXPy1dg4Cs1RI0dt WL+Rv9/92eyzEa+EU8ZxAbUVMxT02LJlq+0FGouKIsLL3+LHcewt+7X7HVVb ytnmzZvTwqNjerGSBw8e1H6mdnlHiKbNHbUWAIAqoW3mqpWfyEI6DBs6fOKE SdRMEF6XROVJ09/6yTndtMCjzZ45m/5CQtq2GzE8YdDAwdS6pJevJbzGUnh3 ZqbFNW4UqbYXaMi/afGWKrWgbTt//gItsGXzFvxOAjl48BAVhnUOc9RaAADs dPjw4Yx16rlz5vaL69uyWXO20esW1nX8uMSl6cv27dNevXZd7DqC+8rK+vHE iUeHR36+/Asb0WXnzr+OqFDmVjVGT50+88QD0VlZelqFjccx3b+t35WZuZuW TA12YeHFnEvsz97+GgKUmftCo38pVNv27TvKjzM/PgrHZ59+XlBwy3pmajXs 0+4/cuSo6+sJnmXF8hX0tzRxwiT20kkRzBZr40Gtcut3rVm9xnoS3+6mJ/ZX EkClUmm1WrFrAZ5qy5attNmR1G/ARuG4fbvQxsx37vzZplXrUFkn4RG86qFd R4zR4WX++9/is2fP7du7d9PGTYq3Z9LfVc/onmySkyKY1vi70WjjQX+x1u9a Zr7+DhEMDiGTyTDuLlQbtXZXrlxl/0AcUyZPoc0UbR5ruF6TycRxHP50vQMl 3Zw577JTwCw3wzqHCQPUSRFcPTt37qIlDxo4WFiY+/NlHIiGqsL1HeBwRUVF P2RlVTiJtrQ9uvWgzdTevQ448KJUKnEAx9PdN4uLjaO/ioThCZSb7AiJRYC6 VQQfP3GSltyxQ0dh4eHDR9EdC6oKR6HB4d6dM7d/v/4WhdRMXrRoMRvBsmXz FhWeKa4q7EB6gRMnTp4wJxplpfD0hGsiuHrngmlPkjXYhcecLU5eAzwRDuWB M1AboVlQMLs1YVaWPmVhStcuXYWXJn3//SFHrUsmk6EzoUfb/OVmelhfZ7R1 69fWEbxk0SL7l8wiuHu37jbm2a/dT7Fu47FtW8XjsCWMSKCFfy4YCy62TyyV fP31NvtrCD4uNzdXoXjC5XUAVUVtmTatWieOGy9MXmo1jBr5Om2gHHLXYJ5K pcLtvTzat7u+pYe5I308X1hUVBTRI1wYwcuXLS8/Uj2igjZpZfj+Ub87oZVx 6PARtj95u7C8/+HJk6foZaisE0bHAvuZzMSuBXgP2hxlrMsYNmQYn7wtm7cY M3osJa8D71coZDQaMV60R/u1oIAe7Lju+HHjNZpvVq5cFRbahd31ko/g7LPn 2F8UpTC1iL/7zq6Rn3vF9KK39IvrS2/JynLwiGoKRXmf7Zca/t+mjV927dyF PoIDD+8AAFTV9es3hCNifb3tG8e2ecFb7d9/gPUTYLtt77234M6dP9nBE36e RYuW8F2m7TwpnJX1I79YfpQPRyktLV28aIk04BlaeCdZx6PHdI5dPgBAVe3Y sSs9femmTV/SdunAwe/Frg54DEq08+cv6LPP2thto1z+IevHK1fyqrTYs+d+ ct61urrss1TnEhx/BgC38bvROG3qNNy7DQAAwPUePHiQk3Pp2rVrlc1w/Hi2 K+sDAOAmVCqVToczF+BE7DLJ8ePGW0/65UreokWLpYH1HXh4EJ2yAMAj4HJg cIHbhYWsJ8z8+clsIA76mbEuI75/POseI3nxpeMnHHDvYEYul+fm5jpqaQAA TqLVapVKpdi1AO93/fqNqMje0pYSqZ8/H7t+dZ/jXmrUL67frl3fOnBd1Aqm HUtcZAcA7oxaCtRe0OsdfIkcQIVYm7dNq9azZ80+XdGtGSq8E0310I4lDkcD gDvDZgpc6dtd327evLXCy0wu5lyaqZjVtUvXmt+4kGG7lw5ZFACAM9BmCgfr QHS/XMmTBNZj4zCcP2/vjQ6fiPYw0ckBAADAGjV492n3jxr5Oj+CllL5IUbQ AgAAcKqffrrABv5lj/Dw6LWfrw0L7dI9rFu+0wYvAgAA8HGUv2z4aDbMr0r1 MSsvKLglC+kwaMAgcasHAADgrdjB5wnjJ94uLOwb1zcyPPLBgwdsEhvEw4HX CAMAuJvo6GixqwC+i5rA9GCXIO3bu48y98iRo2ySWr2eXq5ZvcZR6zIajRj8 DQDcCiIYRNSnd2wnWUe+5ZvyfkqLpu3OnPlh7edrO7R/hSL48MNErjmKYAzT AQDuIzc3VyaTiV0L8F3r1mVQzu7T7udLJLWf5btmLVyY4tjVqVQqXP8OAG5C oVBgiwQiuldSEhbahR63CwtZyerVq8eMHpM0PenAgYMOXx3b50RDGABEh80R uIPjx082bRIUFxtX2XBYlMUOvEYYu50A4A4wKCW4ib179x09VnFHqfPnL0gb vTx0yFAHjleJPU8AEJ3RaMSGCNyNRrO9X185f1yaLF26jFJ41cpPHLUKtVqN 8SoBAAAscHXLx4hWpjy6bya1fyPDI1s2byHMZQAAAHCgU6fPSBpLInqEh7Rt J7xf4ebNW83XCH8qYt0AAAC8WN+4vs2CJMd0/7YI3F8LblHJmNFjRKwbAEDN mUwmnAgDN6T790nK2WUpy+j5U/5PSRr8Y/2WLWzSYXMoR4ZHOnB1iYmJ6AsB AK7EuoPu2LFD7IoAWLpXUtKmVetVK1eVPTz/yzL3dmFhRI9whx+IVpk5cIEA ALbhokhwZ8oUZe+IKPZ8w/qNFLtL0pd1D+tGT+inY+8gzMarxBEhAHANvV4v l8vFrgVApe6aTA0CA99+a0byguRJEyayYSqbBQUrZih+++03h69OrVajIQwA rkH5izvFgJtTfrAsOiqG3UG4X195evpS512LZDKZZDJZbm6uk5YPAMAYDAaF QiF2LQDci0ajUSqVT54PAAAAHI32TsWuAgAAAAAAAECliovvpqV+lJr6kdgV AQAA8C2lpaVxsXHSRi8fP3FS7LoAAFQqNzcXFwKD99n1bSZF8JTJUxy4TK1W 68ClAQDgQiTwSkrlBxTBI4YnOGqBuEAJAByL2r+4EAk8WmlpqUXJnTt/znjr bTZqh2OHrKSdVYxdAwAOYTQaaa8eF1yA51qY/P5rCSOFJadPn+nRtTvL37lz 51kHdA1hBFcAcAjamKjVarFrAVB97703n6L2wIGD9PxizqWxo8ey8O0b1/fo MaecXqFdVgwcDQA1RFsSagLjXmzg0e7c+bNnVEwnWccRw4YHN5ZS+Pbv1393 5u4HDx4IZ/vdoYmJ0zcAUEO4KTB4uuLiu6oVqjatWrOW77Ahw7Ky9NazUUw3 bdKioOCWo9ZL/zvowQgAAD6rtLQ0NvZVCecnrf2snx8n9fMPj4gUznD+pwuD BgyiqZL6DaR1A0+dOi1WVQEAALzYMd2/75WUsOd3Tab33pvftEkQax2PGvl6 TET5nZXGjU107A2FAQCqRKfT4fgzeLH8/Jvx8ngWvtQKprYwK1++XEUlr48a 7djVGQwGdKgAADvVq1cPEQxeiVrBq1Z+0rJ5C4paWUiHr77aZjFD37i+Dh+y UqVS4VaGAGAP2l1/5plnxK4FgFPcufNnqKwThezYMWPpufUMihkKmpr2YaoD V8qGzNLrK+gGBgAgpFarcTEFeLHMzN1rVn9qcUUSQ23kHt16UASvVH3s2JXm 5uZSCuPgEgDYgA0F+Kzi4rvTpr1J+du0SdDFnEsOXz52bgHANrlcjvu8gG/q GR3OOmitWKFyxvJNJhNudwIANmAsaPBBBQW3pr+ZROHbsnmLTZu+dN6KjEYj bqIEAABQZh67Y83qT/8aO4vzu3b9htg1AgAA8H5Hjhzt0imUwvefLVq+M/ud c+fOs/KcnEsb1m/4KG3RypWraJ779++LW08AAAAvwy5QmjPn3aKiIlaSn39z 2JBh7Iww/+ge1u3ny7+IW1UA8FYajQZXLIJv+o/g0uC8vKvskmF2N4edO3cd PHhowfwFTZsEyUI6UDo7cL06nQ79LgCAwhdXIQGQjqHlB6VD2rY7dOiIsPzo MR2VT5o4yYHrov3exMREjFoJ4MsoeTFoDwAj9fNv2bxFTkVXBI8ZPZZS2IG3 MiQKhUKlcsrVTwDgEWg/XK1Wi10LALcg4WqpKrkieFn6Uorg/fsPOHB1bNRK XCYM4JtoD5wiWOxaALgL7ulnrlzJq3DSxAmTKIL37nXwqDVsMDqcFAbwQQqF AqeiAHgSP/8FCzIsCm8XFkaHR0gDnuHq1vulkoCuCa1Wi1ErAQDAx70SGtqm VetTp8/wJQcOHOwe1o2NmvXTw3sKAwAAgGNlnz1LEdy0SdCoka8rZigG9B/A LlCiwu+/PyR27QDA42F8WgAbcnIu9Y3rKxyXY9LESfwVwdlnz61cuYrSecni JVlZjr+OwGQy4fJAAG+l0+lkMpnYtQBwd1evXT9z5ocffsj6448/6GVJSUlG hjoqItJi1Ky+r/a97NBRswwGAy7SB/BK1P7lOA59LwGqpLj47tAhQ1nmjh83 njV+75WUaDTb27RqPTJhpGNXp1arMWQHgJdhe9e4AhGgqmbNeofCt2mTIMpc i0mHDh1p3Fjq8DUqlUr0kQbwJj179tRoNGLXAsDDXLt2g7V/16/fUOEMz9QO cPhKqQlMDWEMnAXgNZKTk8WuAoDnWfv5WsrfXjG9KpshMiLmmO7fDl8vpbBc LkfnSQAA8FlsXMrZM2dXOLW0tNSf86cZduzY5fBVm8wcvlgAAACPsGXLVkrY aVOnVTh19eo1NLV/X/mVvKsurRYAAIC3KyoqatOqdcvmLSzukXSvpGT+ewso f7mA2tQWFqt6AOC2DAYDDmQB1JBGs52iNiYy6vzDASrpSVxsHOumtWbNZ/yc Bw5+76Q4xpXCAJ6FjcKB/1yAmsvM3B0q60SB27FDR3qw8KWm8aZNX/LzrPsi gwoXLVrijAr4+/vjin4AT0H/rRzH6fWOH0APwDdR81affXbggEEsf7uHdePv 2kCT5s9PZuXW1w47BLuvKA5qAbg/jMIB4HD5+Tf795WznH1j8ht37vzJyunJ 66NGs/KmTYIiwyOnTJ6SffacwyuAFAZwf8hfAIf7bv+BkLbtWMiu++KxGwpH hEew8qXpy06dPvP119sieoTTy7179zm8GkhhADenUCiQvwAO8bvRyNXiJH7+ 0hf/z5/jFDMUN248OiFL7d//afgix3H+frV+/vnRzRpKSkq4lzgJ59c7vLfD q0QpjGHuAADAF6xe/anwsLMQNXip/ZuYOD5U1onayIcOHWHltwsLqSFMk5Ys dkrXLAAAAF9g4yKjtA9TKWcPHvw+L+9qTGQUPU8YkZA0PYn1nW7TqvW16zdc WFMAEIHBYMCRZwDX27BhI0Xtvn3aMvMNDZOTF7Zs3oL1ywoL7ZKV9aML6qBU KnFqGEAs6HwFIJY7d/6UhXSYOuVfwpJTp8/os8/eKylxTR3QQQtALMhfAHF9 //0hjuPErQNSGMD1kL8A7oB7tm68PD4//+YT5/z58i/URnZGHSiFaWuA4bMA XMNoNCJ/AdxBRkbGuLGJTxwa+l5JSXRUTNMmQVu3bHVGNTQaDW0TnLFkALBg MpmwxwvgWbKyfmzZvAWlsJN6SmObAAAAUJmhQ4ZJG7289vO1YlcEAADAh+Tl XWVXLW3fsVPsugBAlWm1WrGrAADV8c032zu0f4Xyd/q06ffv33f26rZudcoZ ZwDfZDKZFApFYmKi2BUBgKp58ODBwoUpbMgOpfJD4aQKx710CNpWqFQqXKkE UHP0f0T/UBgGB8AjFBfffX3UaP5OSZ9/vpblr8UtlmiGV9qFOGkQLX6nHRsN gJpg1//SDq3YFQEAu1y/fiNU1qlpk6Cjx3THj59s2ay59S0OKX+pkHJ53Fgn HtrC9cIANYHxNwA8UV7eVVlIhzatWlPOBjeWWtw7mM/foUOGUpPZqTXRarW0 DUFbGKAacP0vgIdKS1v01/nfFKXFpKZNJK7JXwbbEAAA8B3rvshg+Vt+Q+Fx jx1qpiaw1M/fZfkLAADgO24XFkaGR0oavfxW0ozMzN2REZGs5/OOHbvK279+ /lwDjuVvUVHR9DeTuMD6XN3n6CF9oeEroaHHj590avXkcrler3fqKgA8kVar rVevXnR0tNgVAQAH49vF06a9yQaUpqSOiYyikn+2aDl/3nvL0pdOmzqtaZOg ls1b/PTTBefVhPJXJpNpNBrnrQLAs5hMJqVSSXunOGsD4H3ulZSwtOXzl1rB rKRNq9bCwD11+gxFcHz/eKfWh7YziYmJCoUC3bQA6N+BwheX/QJ4MWrzKlM+ 4G+olJqaRvlLaWt9XfDS9GU0yVhU9MS7L9UEbW1wyRJAmfkuYxh5EsAr7d9/ 4I3JUyxGwaImMDV+KWfXrP7U+i3HT5ykSfu030VHxTj1iHSZ+aB0bm6uU1cB AAAgirhX+1KefvXVNmHhkSPHqDCkXfu7FR342rFzV3kDuVnzdq3b7tr1ratq CgAA4FWuX7+x5pPVFoeUDx8+SiEbGR5pPf/twsKw0C40NVTWKS/vqkvqCOBz tFotjv8A+KY7d/5kdy28dv2GsLyoqIj10Qpp2y4v76qLa6XT6dRqNXqkgHcz Go1s+HR6InZdAEAcK1aoKGoHxg+g2GUlBQW3hg4ZyvpIW/fRunTpkvNuq8Tw 12WgdQDeivYzZTIZdjUBfFxpaSm7gyE1eGcpZk2ZPIW1i5s2CTp1+oz1/M2D g6mBfP3xVrMzsDGlsY0CL4M9TACwcPr0mdkzZ48bm8jnr8UNHXiSF/83VNbp dmGhC2rFjtTRxgpH6sBrUPLiDtoAYG3Dho1s4CyNZnuFMxw/fjKosSQn55Ir a6XT6RDBAADgxfLyrrZr3Zby1+KGwsIZ2rRqHSSRurRaAAAAXu12YWGorBPl 79Kly1jJvZISixm6h3WjGWbNnCUs/7XgFm60BFAZdjJFp9OJXREAcFP8bRr4 uxlSqg6MH0BxfOfOn6WlpQcOHGT5SzFdaD4LXFBw653Zc9jIWvToF9dPo9nu 1HEseaybFm6xBO5Po9GgSyEA2EBpGxcbxy5BunHjr1GaDxz8nr/LMP/gx5Gm nyFt27FCevJqbBzL4tdHjXZNi5jyVy6XU+MC54jBbfXp0ycxMREjnwOADdev 36AmsPUlwFlZ+oXJC+mxes1nrJt0ZuZuKs/JucQCl1rE+7T72cyUvPPnJ1Ph G5PfcE21qVlBTQyO4+gnmhjgbmgvsX379mLXAgA8wO3CwiNHjlY46ffff2/a pDnX4PkVK1SshPPnJM8+J5E0tr4uKSDgGUrh5IXvO7e6AtTEoLYwbi4Dbgh7 hgDgcFyDFz5K+6jCSRnrMiiCV65c5eIqAYiLdgWVSiWOOQOAs3GB9Xfu3FXh pGFDhlEEb/+m4muKXYDaHTKZDIemwWWMRiO72zX+6gDABaR1n9u08Uvr8u/2 H2AdtK5eu+76WvFyc3MVCgVtEnEZCDgV641Af2kUwegWCACuIfF/qk+v3hY9 n7OyfmR9tCZPclF3LNsoiOVmuHYJnERhhoPPAOBKixYtYXdWOv/ThTLzbQ3X rP6UdZmOiYyqbOzozMzd1Ex2bU3LR7akjaSLVwoAAOA8S5cus75qOC42rrL8 LSi4xa4j/nrbNy6uKoCj4FQvALiJizmXZs+a3btXn8jwyDGjx9oeGmvC+ImU v2GhXZx9o+EnMhgMuEMcVEN0dLRSqRS7FgAAVUPpzJrJFd592MXYOWKM2Qt2 opYv/anQ3wxFsNh1AQCoMmkzCeXvwmTL8Tqo1SzW/R2wUQV76PV6mUxGO2w4 cgIAHsqvEdc9rJt12n7+2VoqF7FpjEOLYJvRaET4AoDn+uqrbRUegr6Sd5V1 oubvjQgAAACO8scff7Rr3dbvxf+zKDcai8K79aD8nT5t+oMHD0SpW4VyzcSu BYhAp9MlJibK5XKxKwIA4Bh792rL72bYqp1FuTJFyS5isuhEXVx815B/04UV tMTugUi0Wi2uQPEFRqORjXBF+YseegDgTVgEd+/WXVhYVFTUplXrpk2CcnIu 8YWZmbsHDxzMOk7T1LFjx7m8so9QELMhLlUqFcY+8mL0i+Y4jn7LOPQBAN6n oOAWRa2fnz9fQs1edo3wypWf8IXsRsP0aNm8xdAhw+L7D6B3VTbKh8tQ+0ht Jm41wHlMZmLXAgDAWShqpbX/vjR92anTZ7T7v2O3UoqKiOQPQZfPYM7fd+fO 4wfuaFi/Qf++chtjfQBUFbvCF0ebAcCnNG/enHupkd8LDSUtyy8QljZ8cePG jWzSyNdGSv38/Ti/t2fPFr7lg5QPaM7GjaVi1NcWjuOoXRwVFSWXy+kJDlO7 Oa1WK5PJ6Je1fPny4ODgxMRE3LYDAHzT1KlvUrBmZu7mSzp36kwln3++1mLO M2d+oPIRwxNcW8EqoC25SqWibTuOZLozg5nYtQAAEF9paemevfuEJewQ9EVB vyxm546dVD5m9BiL8l8LbtHDubWsGWzwxcJ2itDIBQCwU9MmQRS11hcizZ71 jrnL1ir2srj4bmpqmiykA4vskLbt5r07T/Q7PlSI2sWsK7VOp0MD2QWMRmNK SgrHcYmJiRqNBt85AICdEkYkUKTu3rPXorxlqxYtm7dgnaLpZ0xkFAvf6Mjo pOlJsX1epedDBw91z/5a1BDWarUKhYLlAi54cR4KXPqSKYIpiMWuCwCAhzl6 TEdhGtEjXHgJEj33C6i9YoWqzHzsun9fObtYWHgSmZ4HN5ampX4kQqXtRgGh 1+txaNpR2L6N2LUAAPAe6enLKGFDZZ1Wrly1c+eu9PSlIW3bcfUbsBbu+vUb WPuXwtrijZMmTmraJKjAvU8NW9DpdDKZTKlUUpQgmu2Rm5ur0WjYSCmsF7rY NQIA8Cp6ffa8ufN69+zV9p9tQtq1j4t9NVWZSuUlJSWyV8rP/y5butz6XatX r6FJmzdvYS8PHDh48uSp+/fvu7TqVceacqw3NcdxFC44fVkZ+pYSExPZiXUc agYAcKUfsn5kTeAKe14tX7aivMuW6mP2smXz5vSSgti1dawRdi88iwjW0x5J drZYVRIFfQ/0qVlrF1ELAOAOTp0+Q6ka1jmswqlvTHqDph48eIi99Gvwj8jw SFdVzYkoiah1zO4UT8+9+CobNha3xYfFMQEAAHdgyL/JBo627vlM7eJ2rduG tG1XXHyXXt4rKZE0+MeG9RuF89y69dua1Z+657VLT8Q3DK3Pfmq1Wk+5qSLl KdWTfRDri3bZQQA0ewEA3FN8/3iLAbXKzN2kFYqZVL506TJW8tVX26R1AymI hbN99dVXNM+oka+7rLauQaFMbcbExETOjLUfxa0Si1qLMDUYDKx6rIa054C0 BQDwID/9dKFpkyDhFUm3CwvZvZa6du7CZ25sn1i/2s9avHfShIked3a4qlj2 CTtXU4lMJmPpTDHNJ6DFG3MfZx2Owqk6nc7ikDjNT4tlPcrcZ08AAAAc6+gx HRsXq2OHjpHhkWxALfp55MgRNsMx3b/Z8Wrhu4qL7/6zRUua3+Ig9s+Xf9m9 Z697junhcHyGWlwARTGtVCoVAhbpyRKWRzNbn5W2XiwAAHifO3f+XLXyk359 5RSpMVExihkKSlJ+6qQJkyiCp02dJnzLunUZVEg/LRY1UzGLyme8NcMV9QYA APBqbVq1FnaNLjOfLKawplYw66zFu11YyBrR1HB2bR0BAAC8jdFYxK4dvnbt Ol944MBBKpk0YaLFzIsWLaby2D6xrq0jAACAd2KDcnC1OHr+y5W8sWPGcc/+ nUoy1q8XzrYhI0NaN1DS4B+btmwRqaYAAABepaSk5OOPV/rX4oIbS3v37DV/ /gLWLi4tfcDP88cf/+kk60iFGs03IlYVAADAi90rKQlp247SVvfwhG9x8d2h Q4ZSSd+4vuLWDQAAwLutXv0pBS41e5csWpT2YWr3sG6sXazRbBe7agAAAF5u 06YvQzuGlo/g0aXr3Lnz2P0QLYbPAgAAAGd48ODB7duF9CT1wzSK4EWLFotd IwAAAN9yMefSTMUsQ/5NsSsCAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADgwf5/ wdEeOw== "], {{0, 481}, {641, 0}}, {0, 255}, ColorFunction->RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable->False], BaseStyle->"ImageGraphics", ImageSize->{453., Automatic}, ImageSizeRaw->{641, 481}, PlotRange->{{0, 641}, {0, 481}}]], "Text", TextAlignment->Center], Cell[TextData[{ "Perioda ob\:011bhu M\:011bs\[IAcute]ce kolem Zem\:011b: ", Cell[BoxData[ FormBox["p", TraditionalForm]], FormatType->"TraditionalForm"], "=27,3 dne" }], "Text", CellChangeTimes->{3.44915141115625*^9}], Cell[TextData[{ Cell[BoxData[ GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJztnQlUVFe2hqsrNkvfSicsu5vmlf3SJcFEbTM7RHHA2dedxBkcYmIMStAI arcDaBSnDjhHFBPjGEQDiQ8UohJEjSJ2nEBJoqIiKIkDAiqIRs2qt6u2nr6p Kooabs3/t66sU7fuPfdUlfe/e++zzzlNR0UNGPWYQqFo8xuFIov+acsaAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAPYkPS2t trbW2a0AAACXpqysLDQkZFNSUkVFhbPbAgAArgupZXDnLgFP/SU+Lr6goMDZ zQEAABeFFJKkkjc2Mkk/nd0oAABwOdLT0oRaSjUTdiYAAEiJiY7RU0uxkW/u 7NYBAIBLUFtby0FLww22JQAACIqKigx1ktxwZ7cLAABcCxJGPanMzs52dqMA AMC1IDc8NCSERbJd6zadgjpyrBKZ6gAAIEXkDuXl5ZWVlY2NiKByTHSMs9sF AACuBQnjqsRELpM9SWWSTec2CQAAXI1aHc5uBQAAuDEVFRUYzgMAAKYZGxER 3LkLki0BAMAE2dnZ3O+Tnpbm7LYAAIDrUlRUxEN7ViUmIqoJAAB1IfKI6C/U EgAA6oIUMiY6BlIJAAD1Ap0EAAAAAAAAAAAcT15eHuZtAwAA04jpNRDDBACA uiCFZLUcNXKks9sCAACuCycRBTRshKHiAABgGqWfX3DnLnDDAQDABKsSE9G/ AwAAAAAAAAAAOB4sPAEAAKapqKjgedvcTi1ra2vRlQ8AcBgkOG6nltTmwQMH Ng8MdHZDAABehFBLt+gcJ0nv2L4DtTbx0fqVAADgGNxFLal5vC5Gdna2s9sC APBGSC1DQ0JcNgD4cLTRU3/pFBRUVFTk7OYAAIDLwcFJ0snw0WMqKiqc3RwA AHA5RHASy6sBAIBREJwEALg4ZMIVFBQ48eoITgIAXB+e4tIp+ZYITgIA3AXO IFL6+Dj4ughOAgDcC/J8zTEs6bD0tDTayGWmrbFvYyrTWVYYhAhOAgDcEbIq SbiM5luSGMbHxbOy1bWFhoSQ+pmjmQhOAgDcF9JDXsJMbydpoBBDnp6I9I39 ZdJVtjNZ+nijY0wIpjQ4CacbAOCOFBQUCPkiTePuHla/es0/OpFcaaGrpJ9c CRVovxDPBgolV2jXDwIAAA6ALUw2Mi2NQ5Iw8jDzrl2CpR46ueccn3SjqY0A AMAoZASqlY8pnvqLukEDqztcSF0VTz1lJKT5X48HqtXyNhgAABwMG5NkE9o4 mQb3pxvdZGopAAA4BzFTuu2TDtUllR3bd5ClqUxtbW3Wrixb+tBramry8wtO nTot3Xnz5q0jR46Wll40cSIdc72ioqS0xOpLAwDcFO7FlivLsd8bfQ2lUt7e nKyvd1OdX2VmWnd6ZWVl56BO3LBBAwaR+tHO4uILI99+J+/Qv98f+/7SpcuM nnj//v0Xn3uBzlI+pbC68QAAN0Xp46OXKWQ1ZJe+/tprejr5QqtWsmcH2SKV M2fGkklJhYMH81q1aLls2UcVFZWtX3rl2LHjtPPGjRuvvPRyVtbXhieu+nj1 7t05ZHl+sz/XlsYDANwRpZ+fLAnhYrji4kWLyIzkcT2hIaH26Pu2Wipram4X nDgpXs76YOa4iIiM7RlU4fVHPf4TJ0wc+95YvROvlZePHh1+GxmhAHgl2uii v8r2esRwRT1V5OilLFbr+eLiObPnJidvWbRoiZDK48fzY2JmJCUlh4dHJH2W tHNX1tDQIStXJN6+rdW0ktKL8+b9q7Kqqq4658yesyJhZfKmZKrwQkkp71y2 ZOnf+vxN78iMjK9efvGlvzZvMX7c+0VFZ23/OAAAN4LMP4Wvry01SIcrGu0Y 4oR2G6cPqq6uafNy64KCExqtZl4QUjli+Jvbtm3XaLPoT3YK6kSF1197fXr0 dD6rsrLyyy+31lXngwcPunbp+tPly+RTU4Wfb/mc95N+vva3vxs95dtvjwS9 2qFDUHtbPgsAwO0I7tyFNqtPN2e4YnZ2tu3dRpkZmS2btyBx45dCKlNTUsvK fqTCycLv27VpS4Xdu3OocP/+fSp/8vFqftcoe/fuW748QaPTzNCQ0J7de/xw 6nR2dk6P7j1HvxtW11nkiQeqn7blswAA3AsSOtKc+Lh4808pKChIT0tLSUnR /HouNXmvYkjch3HdgruJl0Iq79y5Q3bjhg2frV+3gaWSGDxw0PKPEm5VV8fO nltXhVVVN1at+kRoLxWydmVt2bzl28NHWj7bfMsjC9Movr+1yQ4HALgXpHti 1Ha9kOKR6Sj6tf8xaZLR4KRR6DByw21p6vx58595OvDevXuiQpbKqPGR6ela B/xS2Y9CKnfu2EkHr127vqSOJMmbN2/FxMy4e/eu4Vtr164jF9t0902cbbIP AHAvSCRJc8zs/pbqJG9tX2ltZtY6BzNtaep2XSd1auoXGl0vNpUztmsV8tnA ZuQRU+HQoW9JKllL7/78c59evcPHhButinRyxYpEktbrFRW0ZaT/pyf97Nlz Q0KGnC8u5pdVVVUpn6fQ5ah8/nyx0M/Zs+fY8lkAAO6F+VJpdBjOlMlTzLyQ 7VJJDnJkZFSzpgFh746Ojp5OtY0fH0WiN3DAwFfbtIscH5WUpO3FfvdRks++ fftTU1MN6yFd7dmtu/RTDBowiN/avTvnvfCIcp3wMqSTdMCePXuoPKDfALI2 N274bNq0mMLC72z5LAAA98J8qeSuGb2tU1CQmReyXSqZw4cP5+TkkJm3/5v9 ZDrSnvLr18kTLynRjjQ8ePA/s7LHxS2ounHDsAZSVzIdpduVK1dra2uP5+ef PXdO72C6EOkkX+jK1at0oby8PKNuOwDAg7HRqjQ/W1IuqayXkpJSsidPnixM 0HVtAwCA7ZgvlZWVlS2ffVZPKs3sD9I4UCr5QiOGvQnbDwAgFzz3Wr0ZjyJ5 UrpZ1KMd3LlLaEiIbY01i9u1tfkFJ0QKEAAA2A671X/y86vrgE1JSUofH7W/ iv7y0jk8uFua4lgvubm5dJUXW7SUo8kAAOAE4uPi1Q0aGO6vd7iiRZeQZTJM AABwFuSDKw2sShlXVyRDNEC35qMtlQAAgNNR/HouCzOHK5oJVSLjvMEAAOAs 1E88KVSxrrnUrINNyuDOXbDwNwDA3QnRLeFdWFgoV3BSIO9SFAAA4ER40oxn ng6UJTgp4KRNG2fJAAAAF4F87RdatSJZ69Gtu1w6KVbLtXFGXwAAcBGUfn4k a++MHMlGoO1qyTpp/pxFAADgypAqkjaqVU3Kysq4zIk9tsQq5e0YAgAA50J6 2KWTdjnsMWFjxE7O7bFofLe0QhZb8ruRcA4A8ACEj2yYPJmdnU1ax+YlHWaO P07CKDQ2JjoG8UkAgAcgZK0uH5nHevMxJJtULigoMBTAoqIi0lW2JIW02r/5 AABgX0RA0pzkSRZMtjClc1TSFvxqB71ZhiCSAADPQAQnLU2eJOsxPS2NFFIY kAqdZpKQkkLW5W7TJXgyIpmaDwAAdsdEcNJO8BoT5s+UDgAAzqXe4KSdYCsU AxsBAC6ORcFJ2SHvO7hzF6Njdqgx3CtErj1tVKCX8NYBAA6GDEh1gwZqVROl n5+MI7stReuG+6sCGjZKT04ObttW6eOjaNiIxJP+qp94kl4qVSrt5uNDL8Vb 9JIK6Zs3O6XNAAAvwVket1HIViStDlD9mfOO6jVuOUtTq5mu0X4AgOdB1qNW l576S5dOnVxhyIxYeIKMRossWzpYrXyMToyPi8d0lwAAeQlUq+Wa9cJ2xFBH +muFbktPd4WPAwDwDDgjyGHpQKYhoeP0dWqP1ULHyZlQSwCAXLCkKH18nN0Q LaLnXcYFeqCWAABbcLX4pObRgrYy2rdcIf2Vq0IAgFdB2tgpKMiljC6OA8jb HqoqVLcGUEFBgVx1AgC8BMcPV6wX0jQOUcpu3xYVFfH8RS7yRAAAuAUulTwp 4NXH7CTdWFUcAGA+LhicFLBJaachirywOBmW9qgcAOBJuGBwUsDr5No1GsD9 O4hYAgBMIIKTm5KSnN0WI7CDbFcdYzWW6+PTs+bjjz+2+vSampr8/IJTp05L d96urb1eUSG2qqobemfRAXTW2XPnrL4uAMAELEQd23dwqeCkFO6ktuiUIh3m H0/iRpd4c/hwWXz8rK93q//wB+vOrays7BzUiZ9cgwYMunnzFu9/a8Tb0ini hw8dJj3rfHFx29Zt27VpS28tW7rM1g8AAJAggpODBw50teCkgEXM/Ll809PS SPZZTzoFBZnTWUOffcrkKdLVK2wPQVgtlTNnxpJxSIWDB/NatWi5bNlHVL5Q UjJj+gcHDuQeOXKUtlmzZq9bu0561rbtmSSqv/zyy44dO1947nkbGw8AEIjg pCzKYD84mcdM15jnSNfbTFvL9Nn5e5Bu9ASxsdnWSWVNze2CEyfFy1kfzBwX EUGFa9fKpYe98dob54sv1FVJaMgQKy4NADDExYOTUlgqzVxA3FD0aBvQr7+J U4yqq3W5UuQFz5k9Nzl5y6JFS1gqjx/Pj4mZkZSUHB4ekfSZ9qveuStraOiQ lSsSb9/WPp5KSi/Om/evyqoqoxXOmT1nRcJKvZ3FxRde//vrdbXhh1On9+8/ YGnLAQB6kBGlbOCjaPz7QLXaZYOTUsyXSrKTjYqe6Thnw4YNjZ5ipjgL0jMy 1Wo19z2RycdS2bBRww0bNmh03UZtXmrNRz7++O9eeenl+/fvUzkubsGmTclG K9y9e5+i8W9+unxZb7/6CXVq6peGx5NFOm9+bCNFw4Bnml8rLzc8AABgJg+d bn+VK3vcelhkVQ4eONBQ9Ex708LA1tss6hUi4j6M6xbcTbxkqbxz586XX27d sOGz9es2tGvTVtLOQcs/SrhVXR07e67R2qqqbqxa9cmDBw/09t+9e3fc2PdN NIMO6N2j16erV1vUeACAwI2cbikslWYmVXLOj6Wix31b0s2KHM758+Y/83Tg vXv3+CVLZdT4yPT07VS4VPajVCp37thJB69du54ccMOqbt68RW47iZ7hW9sz Mld/Uo8Mzvxg5ob1GyxtPwBA4w4ZQSbgxHgzDyZhFAuLx0THmNOzTzY2PT6a BzbjTnNLXW9m+/YMOj019QuNzhcOaNyYCs8GNmNf+NChb1kqWUvv/vxzn169 w8eEG9ZDOrliRSJJK+dPZmR+VV1dI94NGRxy+vQZ8TLl8xS6ll4NE6MmXsfK awBYiFtkBJmGpc+uQQMe22jL8uLkLEdGRjVrGhD27ujo6Onqx58k0Rs4YOCr bdpFjo9KSkqm+qdOiyl/FEXct29/amqqXiWkqz27dZfat4MGDBLvlpX92KNb D+nx6oaN9uzZQ4WOHTrGzoo9kHtw9py5Bw7kWv0pAPBO3CUjyDRk8tl7+g6O TlhnT0o5fPhwTk4OWXr7vtlHL8uvX/8qM7OkpESjy5OU5rfHxS2ouqE/4obU 9ezZc9LtypWr4t0rV64UniyUHp+ZmUkGKhUKC7+jC+XmHpSaoAAAc3DT4KQh 3LVti8lXL2y4OsDqLikpJXvy5MnChOUJ9r4WAKBe3Do4aQiPbbTTzELcc2R+ ONQWeKHJEcPeNNprAwBwGB4QnDSELWQ7GZYsX455pmgntSg4YZgFBABwJJ4R nDSKnVZ24NE6dvXuAQAuhccEJ43CbnJw5y4yuuFiqVyPMb8BAKbxsOCkUbgr XK7Jh8VSubZ3fAMAXB+PDE7WBccVbVdLeZcUBwC4OB4cnDSKkDj6a7UnTl+a qMQbvjQAgNLHx1ODk3VB4sZL4QR37mJFtCE7O5vjk2RPQicB8AboZlf7qzw4 OGkCXu42wF9l0RRA2r4hfxXikwB4CSI+2SM42NltcRraUTw63SM/mmxFE/44 vUUHcLoRbQcOYPJbADwcsiHVDRqoVU3Uyse8JD5pFFK/jRs3+vr6zpkzR/34 7wJUTUg2tZ61v4q+GfUTT2o35WO8U9GwER1Ah9E31qF9B4/v/ALAy/GGjCDT 0KMhNzd38uTJCh1hYWGGxxRJcHwLAQBOxKsyggxhhUxISGjTpo3iEX379vVa oxoAYIi3ZQQJzpw5s3XrVmFDSiHNvHTpkrMbCABwFTx7uKJpjIokQ0ams1sH AHAJyID08uBkRUWF1OMWkCdue81komOWDADcHbqXvTk4KVi/fr2eTsoVouTc IW/+bgFwd4qKirwzOCm4dOnSxo0bjZqUZ86cqf98M+DIBsaAA+Cm8AyKXhic pIdCfn4+KSTZjaLvZuvWrWRgh4WF8R56V8Yr2nVydQCAnfDO4CQZkLm5uaSB 0t7thIQEkk1xDActZc8OgmEJgDsyenSYNwQnhTYadnCTDVmXf52vQ96WkPDy 1BneGeUAwB0pKipSq5p4ZHCStDErK4sMReFHS/to5s+fT+/KFYG0lOzs7PS0 NM/7zgHwSDg+qVY+5uyGyEZd2eOsjWw9QqAAAGbiYfFJHoFIYigNPEIbAQC2 4EnJk/n5+VKF/O1vf0tuNcYeAgBsxDOSJ6nlJIkivYcKGzdudFbgEQDgYXhG 8iT52iJLnExK2XuoAQDeCXncY8LGKP38FI1/H6hWu2lwkiSxWbNm0hHZHpDF PWfOHAU9uWRNcQcAWAF53B3bd3B3j5ssSVZI8rud3RY54RxL2tz3pwHAA/AY j1vhuXNFciqCm5r6ALg7HpMORPLYRodH6qRGFx7hRc2c3RAAvA5PSgfisTae 3XcTEx1DPxYW5QHAkXhGcJJh11veiX1ckIKCAnIB3P2hBoAb4RnBSUHfvn3J 9XZ3wQcAuBQkKUo/P3cPTgrI6fYGkxIA4Eg4Pqlo/HuP8eMSEhJIKj21NwcA 4HhEfHLShEnObotssPft7FYAADwED4tPCsiknDx5srNbAQBwe6TJkwUFBc5u jszw/OTOboVDoR/RA/IWAHApRPIk/fWY+KQU0knPTqc0BCN3AJAXEZyMj4uH EeIx0COPE2Kd3RAAPAERnExPS3N2W4DMYOlbAGzHs4OTQPPoOUh/nd0QANwV jw9OAs2j2TPItnR2QwBwSxCc9B7oJyaphA8OgPk89LhVTdT+KoWvL4KT3gAe hQBYBDxuAACoF39/FTxu4Eh27Nj56adrnd0KACyAe0LhcQMHwHHRny5ffmfk O5P/gcGkwD0QGUG+vr7Obouc3Lx564svvjTcf/58sdH9JrhVXZ2Wll5W9qNM TZOHU6dO5+zOkau2Mh1y1WaCs+fObdu2ncuzY2dDKoFb4Knxydu1tcmbt9Dn Mnxr7px5rVq0tKi2LZ+nUFVHjhyVp3FycKGkNDQkdJx8S+QoVSp6YlpxIknf sWPHq6trxJ5r18qPHj1GSn7//gPeQ+/Szmvl5aWlJUMGhyYnb6msrNI8kko6 7PvvfygpKZXlgwAgOx6fEWRUKu/evUuGpXi5Y8eueuu5rks+tEUqycTdnLzZ 6tMFDx482LXray4vW7JURqnkRW8tPWvRoiXbMzI/+eTT5//63A/f/6DRhR9J w7/Zf4D+Rk+Lpj3ZOXtbNm+xaNHioPZB/+3r36lDUET4e5+uXq15JJWxsXMG DRzcPPCZghMn5fo4AMiFNwxXNCqVUsgcenvE2/XWY7tUzp83n5TN6tMFc+bM +2jZci7LK5UchLFoTBZ9Ias/Wc3lEW+OGBsxlgqjRr6TlaUV8x9OnQ5q34Hf 7RTUaeqUafSQysjIHBo6ROqADx0ylAxOjW5xtMjxkXJ9HABsx07DFY8cOUZb vzf6Xr16leyEbsHd6KY+X1w8ffoHPbr1WJW4ig/7+OM1m5K3LFmyjO6sCxcu 8M7Cwu+WLv1o7dr1744K27fvG9pzqezHGdNnLFy4eFPy5uAevU4Y2Bv0KZZ/ tHz9+o3LE1ZOnDCRLko7t23PeOO1NzIyv3pModTopDI/v2B02GiyZ8hyJpOM zkpL3/bm8BH07nfffT9syNBuXbomfZZ0+vQZUfPnWz7/6KOET9esGz50OMsj S+WGDRvHRozr2qXr1ClTb9y4QftjY2OTkpKpkbSH7EZyJFNSviApoDK9m75t O5Xpg2zfvp2+atIQutCvv7GjGzcmrVm7fsSbb+XmHqQ9Fy9enDdv/pYtKePf j9y44TPac+58sW9j35iYGb2696RrtX7plXffeZfqqbpxg6RybPh7JDvhYyJ6 dO1+6NC/bfn56H8CfUaLfPClS5bRBySzkLdFCxdrdL62RueVT5k8tV2btnwk /WcQn11PKkWskv63DBs63JaPAICM2C84eVcH1bw94yuN1mDLb/ls8+TNW6hM jtVLL7zIh5GKcmHmzFn9+/anwrXycnLfLl68xEfSWZcvX6Ey2Rh0AJXfGvH2 zA9m6l2OtDd2ViyX586ZG/RqB7r6qVOnqQGkP/HxCzQ6qSRZJoWkaukSm5O1 jTlTdFbcwtt0aqZX87OBzbgwI2b6Pyf9Q/NIKhcsXKTRCSy5k4sXLdZ9ltl8 5MSoidRUuhCpHx15XdfDe/bsOSrTXyqT+adnVd6/fz8qcgKXN23a3KVjZ43O +GRJyf5aa/Oz7AQHB5devDQuYtzt2loSE6lVSfp5vvgCladNnRZls0lmqQ9O QrcpaZPeTnqozZ07f+fOLBJ5SCVwUxwQnJT6vIZlEpPAADXvoVuJdpaUXNz6 5daXHwkp0b1r9yU6VaGbaLZOi4x6mv3e6JeTs5fLBw8epKrIrGJ1IhvVsAGT /zn5rRFvaXT2qmmpXL36Uy7M+mAmX1fPASdBGz50GBX8/uj/sJ70bXTAmTNF 5kvlgdyDfV97nXbSRm3TTu9TWfnNN/s54rd37z5Rj/I3CnGWnlSKr8XoB7EU 9jXMf4Amrkx8Z+Q74uW3h4/QX9L8yspKza+/Z0glcCMcE5w0LZUXSkoCGjcW O1987vmMjExSnuDOwWLn6HffZQfZtFSS7Xfo399y+afLV3QLWGySqpNeA9at XUc3rMYMqSRffs2adWSaRr4/3qhUHjhwsHfP3teulat1bj7x/Q+n6ICdO3aY L5WJK1dOmjCJjhQbPUd++eWXbdsy1q5dv2TxUlGPomEjcZZdpZKepHl5eeY/ Q4uKzv61eYtxEWPT/u//Pl71MQvgcy1bpaVtu3jp0urVa+j3vVBSSo4M/b6f rl7DZ40Y/mbch/FknNPnnTlj5qSJD5dnWrZ0WcjgUBs/AgC24Mi51ExL5U8/ XVao/ix2kmQdPXZ84YKF9C65z7yTbv9pU6Zp6pPKF1o9n7zpYZ8yS9muXVmm pdIcq/LO3buv//31a+Xl0uvqS2XuQbIqa2puKx5JJV/36LFj5kvl2jVr33jt DfGyquoGVbhyZeKWLZ9rdGFMx0ulFWR/nd2+Xfvn//rc0qXLSPpoT2LiKmr5 2Ihx9HE6vNph4cLFeYe+pWZPmjT5nC7xICXli2eeDqTDzhSdjYqaGB4eUXT2 XFnZj9Onf/D2WyOzd+9x/KcAQOPwzEnTUkmMfHskF6qqqvr06iPie7sfZVMP DR36vc4JNS2VUZFRJDX37t3T6OKHrV96pbKyyoRUTp485d86K1RPKgcNGKTR 5WHynp07s17729812ljig2lTptJ1ScP1pHLG9Bkpn6dQoVePnmQHUoEc5+5d u925c+fEyUI6srj4Au3Mydmj9cqLzmp0Uhn/YRy1VjwRSi9eatHsGbKoqdnV 1TXrN2jXH6dLHzt2XKNLuaFzy8uv0yl6UslhUnr8uYJUAuAZODJzku592uha p06d1ujGkuiVC7/7nsrBPYLJAjl9pmjkyFEHDz5c1WX9ug09u/egncuXJ6xY sZL2kET079c/bFQYld9/7/1+b/S7f/++9HLkJge92iE+fkFJSenECZMKTpyg nfv2fUMXYsOM6NW95/j3I7la7lAmdmVlk/POPUc/nDrdrGlA5PjIA7oOaI2u j6nls82HhAyZEDVxzuy5pMDLl68kIf3f3n3efutt0r116zYs1HX1Er5P+K5e /en588Vjx75fWnpRo+vbolb16dU77N3RdKT2m1+g7Qyi759Mr0kT/yH9FGvW rOWQCG1ff62dXHfqlKldOnYeFzHuwzitpT1x4j/INuvftZ9Q8nnz5rdr3Wbc uPE//nT5vfD3BvYfwBXGxcV37RJ855EOAwDMx8GZkyWlF2kji462W9XVXNAr 3/35Z3q5b+++3dm7yaqUnk7v7tyx4+y5hwbhtWvX+JQrV67++9ujVLhkMK6Q BOTAgQPkA5Zfvy4q4Y21hS53+PCRrF27LjwaCULPC3EMjyUhW/HkyUJptWfO FFGdlVVaY4/qZ7+SyM8v+CozU5isGl1i+d69+3Jycqp0uUMMudJ0+sWLl6qr q48fz2ezk8q0k/VZCj1E6FOL5pEw0mEk/tQ2Kly7Vk6fmq4oTiQppiuSnpOh y5+CDqCrc/lCSYkFPxgAQBsywkIPAABQJ+R0t2rRXKFQjAnzqGHdwDHs27dP 6ee3bNkyZzcEADviDcMVgb2xbjw4AG4BVlcEcmFpLrppbt68ZTgPxtGjx3n4 JwCOxFPnUgNOIS8vTy7H5KefLg8bOsxwUsrWL72yePES2+sHwHzIhvTsudSA g+EVb8fKNG2R0fl7Sy9eEnlTFy9e4kGRANgPevQjOAlkh3RSrnCl6anOHzx4 MCFqAqQS2A8yIMmMRHAS2AMzlwU/ceJk1IRJY8LGDB44+IdTp2jPlStXY2fF Llq4eMmSZV06dr5z9y5L5do161o2b9GtW3c65vLlK5P/OXnZkqU3b9765+Sp zwY2C39v3LKPVtj3IwGvpKysDMFJ4FwqKiqHhA7hoZo7duwMat/hytWrpH6j Ro4aEjLk8OEj06ZOu11bS1LZv2//7N05hYXfqf/7f2pqaiqrqt4cNlwMiu/d szesSmAPEJwErkDypuToqdHiZZ9evT/814ca3eD9GdNniP1SB1zhr+KR+NL5 QyCVwB4gOAlchHlz5s2c8Z8pl8PDRvOEk2KeE0YqlQGqP3+VmamBVAJ7guAk cCmWLlk2SjK1L6nfLN1k9SakUu3vz2t/QCqBnUBwErgahScLX3r+hSu6VY2I 0JBQXr2ChHHWzFniMJJKMX9v1+CuPEuJnlTu2bvvhmTKEQCsA8FJ4BTGRkSE hoSYOGDx4iVduwST0E2bFp2SkqrRLQL+v7379OzWXazrvX17xgvPPb9q1Sc5 OXsnTtBq5k+Xr/Tp2Xv40OGVutmlxo97v83Lrefr4pwA2IL6iScRnASOJyY6 Rrvoj8nEoQslpUePHrv+6Jiamhpe/6JSMsledXVNfn7BqVOn2aS8efMWH3P7 tva5f6u6+tix43d//tmeHwV4OByfVPurEJwEjof7EPF/D7g4Ij4ZFhbm7LYA b6SoqEi3vltS/YcC4CQQnwROh/7jyTgYHAAZeehxP/EkOd0KX1/EJ4FzUTdt GuCvQtIFcCmQEQQAAKaBxw0AAKbBcEUAADABhisCAIBpEJwEAADTIDgJ3Ag8 yoFTQHASuBH0HzUmOsbZrQDeBYKTwO0IDQmh/7HObgXwLsLCwhCcBO4FP9zx PxY4DDIj1f6qVYmJCE4CN4LjRXl5ec5uCPAKHsYnVU2c3RAALAPzZgDHII1P 0v86ZzcHAMvgeTPQswPsijR50szllQFwNehZj2wNYD9E8iTikwAAYBSRPJmd ne3stgAAgMuB4CQAAJiAPO5AtTqggY/Sz29MGIKTAACgDzxu4NkgCx3YCDxu 4PFgzA6wEaQDAW+AnSZYAsA6kA4EvAT6r465sIB1IDgJvAce3kgmgbMbAtwM siEVDRshOAm8BwxvBJbyMD7ZwAfBSeA9hIaEBHfu4uxWALdBxCcT4YwAb2JT UlJ8XLyzWwHcA8QnAQDABEieBAAA0yB5EgAATIPkSQAAMA2CkwAAYAIEJwEA wDQITgJgSEx0DNYEBwIEJwEwCkslbgovhz1u9RNPqv1VSpUKwUkA9MD8QgAe NwD1gvmFgK+vLzxuAEzD8wtBKr2WTUlJSAcCoF7I4YqJjoFUeiFkQ3Kk2t9f 5ey2AACAK1JWVjZ44EDEJwEAoC7y8vKQEQQAACbg4CTikwAAYBQRnMRwRQAA MAqCkwAAD4BMvvS0tNCQEOkeuSpHcBIA26H7CAN2nAt9+SSS0lXhCgoKgjt3 2ZSUZHvlCE4CIAs8tpEE09kN8VL4UcWbkEr+UZQqmzIeEZwEQEYwYMeJ8MBS flSRGSkW0GRTUOnnZ3XNCE4CIC+QSrtCGljXd0sKRtooTHq2AFclJrIzTpvC YH48+rHMWWQTwUkAZAdSaT+MzkZC2sX6OTYiQvouSyVv9FZ2dnZAw0b8FpmI dIrQUtMXRXASAHtAto00SgbkgiSRjUbRO0NfNQmd0EOWRHE8aSZtpK7CXw7w V0kP5o0OEKfQY04vyDxpwiQ6plNQEIKTAMiOI6WSBCRrV5aNN/L588WFhd/d v/9ArlbJDnvKUj1cvnw5vyT/mvOC6k08iI2Npd+FNqqKTmGZ5VOE6pLBKY6n sqLx7xGcBEB2SLiKfo29r5j19W66wb/KzLS6hoULF8fFxaelbYuNnS1jw+Sl gVKpDTYGPE1mntLPj+xDha8vySMbgaRpDRs2VDRspFSpAlRN+ADpplY+pvTx UTRoQAopdG92bCy9FeznRxv55tr6H/X7kOFKx2vnMG/cGMFJAGyE85zJK6Tb Vsl3HN2VTzwpNiXfgw0b0a2qbtBA3NryYotUNm2qbuijYHuyqbppoLrZ/fv3 ZW2dDHBMQ89ZZkgkRUySfgiyDOkb1ntC8fMrOztbodNDduH1BFAbydRFI0VG EJxuAGSBbisOnXHXgOFdLOB+B3FHk/8oyz14vrg4dvbcRYuWCKk8fjw/JmZG UlJyeHhE0mfagN7OXVlDQ4esXJF4+7ZWGUpKL86b9y9pJUHtO3z11Q4uHziQ S1UdOXrM9rbJC6dK0heo5wiLlbXNfAbR6fxoY12V/mTcd3PgwAFkBAEgF8Lw 4P5W8x00UkjpiVY3oLq6hrY2L7cuKDhxvviCkMoRw9/ctm27RttTfLJTUCc+ +PXXXp8ePZ3LlZWVX365VVoVnfvt4SNcPnLkKL3kGlwKoysWjRo5khXPUkOd fi/RqS26v/l3efG55/lZVnjyJF0UViUAVkMeH/cg0A0l7QIwHx5kRzXEx8Vb FwfLzMikrWXzFg8eaB1nIZWpKallZT9S4WTh9+3atOWDd+/OoTK71Z98vJoP ELiFVBrtcFH6+ZG+WR1IJBmU/gqdO3Y07ByHVAJgHXSH8v1VbzKeaci54yRA +mvFzR73YRxt3YK78UshlXfu3CGjccOGz9av2yCkkhg8cNDyjxJuVVeTw65X FZmme/d+w+U9OXtc0wHXW12ds4ZsGXoj6uFfoXfPXvS3XZs22dnZJI/0LOMr 0kvrnoYAeDMir89GnRS18X1qRW3z582n7ZmnA+/du6eRSGXU+Mj0dK1NeKns R6lU7tyxkw5eu3Z9SelFvaqGDx22ds1aLm/ZvOX5vz535+5dqz+UjJBGkb1H G6kWf+2835bvzZBz58690KoVq6U0OMmXYAff9qsA4FWYObjDfMRdb2nccvv2 DNroxNTUL2pqblOBXtP+ZwObXSsvp8KhQ9+yVLKW3v355z69eoePCTesKuXz lP59+3OZPuCnqz+18UPJhXTWC95YyjjMKEvaqhiu+EKr56Td6zzeKjQkRCrR AABz4J4F6WAQWRAevUWO3gMdkZFRgU3V0dHT6fTx46Nu3rw1cMDAV9u0ixwf lZSUTDunTosp1yknsW/f/tTUVKNVhYdHpKSk7sr6OjJygjyfSg5E9g6/rNXB IkbfmO25jqJnh5OLpNVW6KACB6VtvBAA3gO73rTZI4GENcE6MykuLo6syv3f 7Ce7kV6WX79OnnhJSQmVDx7Mk7Y2Lm5B1Y0bRishtaSDDx48yJW4CCxfejNM smFvIi/LHKSZk+IJxT1HUvOe98joRADg8RjeR/LCd649+ltLSkrJnjx5sjBh eYLsldsV8XgSBiSLp42ut3QuNalpqnc5vpZ1nW4AeC3BbdvK4vTVhSwiYBQW 4RHD3rzrGp01FqH3hOIx4LaYlNK51AzfZZecXX4RrrT6WgB4IUofH1nWGjAB 3ZXqx38ne7W3a2vzC05w+qWLQxpIVhyJGIkVhw54PCM/pAgrtIsUjycX4sec WvlYQN0T1PPlRDiaY8jS6TXoRAzhAcAEioaN7J1fp41YqprY9RKuj7TXmySL Hk9sSVKBZ6o0/4FFvxe52KK2jh06jBk9Wq1qYvp35IQE1lXDLvgAzFoJgEms yHa2VFrp+IA/2JpT7QGwFywG14tNOmGaOXBAUm8bWZ9Rylc39PHJmGQDFR09 ANQFj6Ez/3i6oTggRnermbc2XWLK5CkBdUx641WIPH9SJ57bnBPROW/HzG+m LoOwXpUzOsu6FDuFlAHwAOj2UT/xpJkHi7luzB9HTJrA0io2c1Z78WCMmnYW pTga/goBv17AsS6MZiixSUnt4WgArEoAjEL3ncLX15wjuetBb6tX9/SWPODN m4ceGzXtLDLnNmzdyl+j7389rgAAAJPs37/fDkpmd4yu42ap58uGpepP/n/6 wx95Gzhg4NZfk5ube8aA/1Gphg0dun79+sSVK98Lf++Pvo3pazQ8DLgL3hzO cjAWWZV6rrQ5VqUYYQerktEb0sjwiGyL6uEJgngzs9va0AEPUDXx8ngIAGZC t4/5sUq+zf+To9K+Q72iRwLbKSjIot4Hz4ZDgnrfG+fS29tCMPT9LepOAsCb 0S7b92j9aHMgtRzQrz/dX1MmTzHTOKyoqGApIGn18gXEtUlTxlLN2fa291y7 hj1K0iE8AADT2D6LbL1YKsieCieBGw6o4fwfe4+ZkqagM2xnBjyaAg4AYAIH jNbRdkN492gdEihOBjDafWPdwEaL0BvYKMAUQwCYidLHx953ip3GgLsLpIRi xaK6AoMcw7SfD67na5M9Sc+vP/n5BWA6dADMw94zC7GX5+U9rayEJJV1ubr2 m39JY2zON5bugPpWLgYACDhJz34dLnxXevn6gGLGXdKrupYMlmVqX6OwSSn9 iXmPvaOjAHgSYmCyPSKWtsyC7nmQWIm5Msic03t8yLhgRL3V8k6EKAGwCBY0 2afFFmvroINVQN+wVDDpOzfM3pExWCGeg4bGqr07kgDwSOyxYiO73kjbMwpP 9qs304W8i9sa1kZ7xGNLb/1xAIA52PsmBYZwog49UKQmH0kZ2YG2J7uKn4B1 mCx86dQlYuY3G68CgBfCNynfR7Z44nRXQifNgXMDDAO52ox93X6rfwWqQS89 iV/y8hCi+xtSCYB1kFqyytHdZF2fNbnbrLfQSXPgb5vkSy+cO2rkSO6LqWut nLrgWKjecHvOP5dqMv24dFHZV34HwHuge42TAPleM79Hhu4+Dn8hPmk+wk1m KePlwOibpK9dTMpEjy1zBFPaYaSnsTz23PDhhYkyALAR8g2Fm0bKKZYFNIRu ahJG6f3uzXOsWQFLHA9oUqpU6ieepC3AX6XRSRx9n7RT6efHAUylj4+6QQO9 Se3ogABVE4VCoVY+RpWQJOr9WDzGfGzEe076iAB4MnS7kQbSLazw9dUunNqw EW10t/K9TJtC95JuarpP6Q6lm9rL88xlhKVSD14sjJ5cYqZK3njN3LqeUCIE jUcYAA6DO1IXLFjATqKzm+OxGJVK6+COby+f/g4A4JFYIZUjdT1B0rR27rtB qjkAwFMRsUqSO14GV6+nTC8ayR03JJIiaExniTJMSgCAR2K4IJE01YcjltLj yW5U+vhwmdRVOnDSoe0GAAAH8mKLlpwuzvakcKLJVhTJ5HykGIYjzQUSqyBZ mpYJAADui5juUmpkciqR2KPXwc07kTkJgFOoqKhARpDj4cRIVkgxqRp72bSH s9b1TsFsGAA4ER40B7V0MCyPondGmJcmRkUhlQsAJwKpdArcDy5ecugSKeUA uCyOWbEamMbGqZ8AAPaGI2C4TwEAwAToLAAAgHrB1NkAAFAv8XHxWBEVAAAA AAAAAAAAAAAAAAAAAACAu4OkSgAAqBeepcHZrQAAAJdGby5uAAAAetTW1kIq AQDANHpTJno8/w86sc+K "], {{0, 309}, {441, 0}}, {0, 255}, ColorFunction->RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable->False], BaseStyle->"ImageGraphics", ImageSize->Automatic, ImageSizeRaw->{441, 309}, PlotRange->{{0, 441}, {0, 309}}]], "Text", TextAlignment->Center], "\n" }], "Text", CellChangeTimes->{{3.44912582753125*^9, 3.4491259300625*^9}, { 3.449143903265625*^9, 3.44914394171875*^9}, {3.44914398478125*^9, 3.44914399171875*^9}, {3.449144029640625*^9, 3.449144190109375*^9}, { 3.44914423009375*^9, 3.44914447178125*^9}, {3.449145757015625*^9, 3.449145775171875*^9}, {3.449151213*^9, 3.44915121878125*^9}, { 3.4491513133125*^9, 3.449151314859375*^9}, 3.44915136978125*^9, { 3.449151406109375*^9, 3.449151414421875*^9}}, TextAlignment->Center], Cell[TextData[{ "Lun\[AAcute]rn\[IAcute] jednotka: 1 LU = 384 000 km (vzd\[AAcute]lenost Zem\ \:011b od M\:011bs\[IAcute]ce)\nPolom\:011br Zem\:011b: ", Cell[BoxData[ FormBox["R", TraditionalForm]], FormatType->"TraditionalForm"], "=0.0167 LU" }], "Text", CellChangeTimes->{3.44915137428125*^9}], Cell["Matematick\[AAcute] formulace \[UAcute]lohy:", "Text", CellChangeTimes->{3.44914577146875*^9}], Cell[TextData[{ "Poloha M\:011bs\[IAcute]ce v \[CHacek]ase ", Cell[BoxData[ FormBox["t", TraditionalForm]], FormatType->"TraditionalForm"], " je ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"M", RowBox[{"(", "t", ")"}]}], "=", RowBox[{"(", RowBox[{ RowBox[{"Cos", "(", RowBox[{"2", "\[Pi]", " ", RowBox[{"t", "/", "p"}]}], ")"}], ",", RowBox[{"Sin", "(", RowBox[{"2", "\[Pi]", " ", RowBox[{"t", "/", "p"}]}], ")"}]}], ")"}]}], TraditionalForm]], FormatType->"TraditionalForm"] }], "Text", CellDingbat->"\[FilledSmallCircle]", CellChangeTimes->{ 3.449145687078125*^9, {3.44914572515625*^9, 3.44914572734375*^9}, 3.449151199328125*^9}], Cell[TextData[{ "Po\[CHacek]\[AAcute]te\[CHacek]n\[IAcute] poloha astronauta je ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"X", RowBox[{"(", "0", ")"}]}], "=", RowBox[{"(", RowBox[{"R", ",", "0"}], ")"}]}], TraditionalForm]], FormatType->"TraditionalForm"] }], "Text", CellDingbat->"\[FilledSmallCircle]", CellChangeTimes->{3.449145687078125*^9, 3.4491457368125*^9}], Cell[TextData[{ "Rychlost labut\[IAcute] je rovna konstant\:011b ", Cell[BoxData[ FormBox["v", TraditionalForm]], FormatType->"TraditionalForm"], " (v jednotk\[AAcute]ch LU / den)" }], "Text", CellDingbat->"\[FilledSmallCircle]", CellChangeTimes->{ 3.449145687078125*^9, 3.4491457368125*^9, {3.4491555754375*^9, 3.449155632109375*^9}}], Cell[TextData[{ "Je-li ", Cell[BoxData[ FormBox[ RowBox[{"X", RowBox[{"(", "t", ")"}]}], TraditionalForm]], FormatType->"TraditionalForm"], " poloha astronauta v \[CHacek]ase ", Cell[BoxData[ FormBox["t", TraditionalForm]], FormatType->"TraditionalForm"], ", pak ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"X", "'"}], RowBox[{"(", "t", ")"}]}], TraditionalForm]], FormatType->"TraditionalForm"], " je vektor d\[EAcute]lky ", Cell[BoxData[ FormBox["v", TraditionalForm]], FormatType->"TraditionalForm"], " ve sm\:011bru ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"M", RowBox[{"(", "t", ")"}]}], "-", RowBox[{"X", RowBox[{"(", "t", ")"}]}]}], TraditionalForm]], FormatType->"TraditionalForm"] }], "Text", CellDingbat->"\[FilledSmallCircle]", CellChangeTimes->{3.449145687078125*^9, 3.449145742140625*^9, 3.44915153565625*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"t", ",", "v", ",", " ", "tmax", ",", " ", "dirQ", ",", RowBox[{"p", "=", "27.3"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", " ", RowBox[{"R", ",", RowBox[{"tmaxfound", "=", "\[Infinity]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"M", "[", RowBox[{"t_", "?", "NumericQ"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "t"}], "p"], "]"}], ",", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "t"}], "p"], "]"}]}], "}"}]}], ";", "\[IndentingNewLine]", " ", RowBox[{"p", "=", "27.3"}], ";", RowBox[{"R", "=", "0.0167"}], ";", "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{ RowBox[{ RowBox[{"sol", "=", RowBox[{ RowBox[{"X", "[", "t", "]"}], " ", "/.", " ", RowBox[{"First", "@", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["X", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", FractionBox[ RowBox[{"v", " ", RowBox[{"(", RowBox[{ RowBox[{"M", "[", "t", "]"}], "-", RowBox[{"X", "[", "t", "]"}]}], ")"}]}], RowBox[{"Norm", "[", RowBox[{ RowBox[{"M", "[", "t", "]"}], "-", RowBox[{"X", "[", "t", "]"}]}], "]"}]]}], ",", RowBox[{ RowBox[{"X", "[", "0", "]"}], "==", RowBox[{"{", RowBox[{"R", ",", "0"}], "}"}]}]}], "}"}], ",", RowBox[{"X", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "tmax"}], "}"}], ",", RowBox[{"Method", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"\"\\"", "\[RuleDelayed]", RowBox[{ RowBox[{"Norm", "[", RowBox[{ RowBox[{"M", "[", "t", "]"}], "-", RowBox[{"X", "[", "t", "]"}]}], "]"}], "-", "0.01"}]}], ",", RowBox[{"\"\\"", "\[RuleDelayed]", RowBox[{"Throw", "[", RowBox[{ RowBox[{"tmaxfound", "=", "t"}], ",", "\"\\""}], "]"}]}]}], "}"}]}]}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"LastPoint", "=", RowBox[{"sol", " ", "/.", " ", RowBox[{"t", " ", "\[Rule]", RowBox[{"If", "[", RowBox[{ RowBox[{"NumericQ", "[", " ", "tmaxfound", "]"}], ",", " ", "tmaxfound", ",", " ", "tmax"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"newtmax", "=", RowBox[{"Min", "[", RowBox[{"tmaxfound", ",", " ", "tmax"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ParametricPlot", "[", RowBox[{"sol", ",", " ", RowBox[{"{", RowBox[{"t", ",", " ", "0", ",", " ", "newtmax"}], "}"}], ",", " ", RowBox[{"PlotStyle", " ", "\[Rule]", " ", RowBox[{"Thickness", "[", "0.004", "]"}]}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"Thickness", "[", "0.004", "]"}], ",", RowBox[{"Circle", "[", "]"}], ",", RowBox[{"(*", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"v", "<", RowBox[{"2", RowBox[{"\[Pi]", "/", "p"}]}]}], ",", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Thickness", "[", "00.003", "]"}], ",", "Dashed", ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", FractionBox[ RowBox[{"v", " ", "p"}], RowBox[{"2", " ", "\[Pi]"}]]}], "]"}]}], "}"}], ",", " ", RowBox[{"{", "}"}]}], "]"}], ","}], "*)"}], "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "R"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"PointSize", "[", "0.03", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Darker", "[", "Green", "]"}], ",", " ", RowBox[{"Point", "[", RowBox[{"M", "[", "newtmax", "]"}], "]"}]}], "}"}], ",", " ", RowBox[{"PointSize", "[", "0.02", "]"}], ",", RowBox[{"Point", "[", "LastPoint", "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"dirQ", " ", "&&", " ", RowBox[{ RowBox[{"Norm", "[", RowBox[{"LastPoint", "-", RowBox[{"M", "[", "newtmax", "]"}]}], "]"}], ">", " ", "0.015"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Thickness", "[", "0.001", "]"}], ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"LastPoint", ",", RowBox[{"M", "[", "newtmax", "]"}]}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", "Blue", ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"LastPoint", ",", RowBox[{"LastPoint", " ", "+", " ", RowBox[{"v", " ", RowBox[{"Normalize", "[", RowBox[{"(", RowBox[{ RowBox[{"M", "[", "newtmax", "]"}], "-", "LastPoint"}], ")"}], "]"}]}]}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", " ", RowBox[{"{", RowBox[{"0.85", ",", "0.8"}], "}"}]}], "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"0.07", ",", RowBox[{"-", "0.07"}]}], "}"}]}], "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"M", "[", "newtmax", "]"}], "1.12"}]}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameTicks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",", " ", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",", " ", RowBox[{"{", "}"}]}], "}"}]}], "}"}]}], ",", " ", RowBox[{"BaseStyle", "\[Rule]", "12"}], ",", RowBox[{"Axes", "\[Rule]", "False"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", "400"}], ",", " ", RowBox[{"PlotRange", "\[Rule]", " ", "1.25"}], ",", RowBox[{"ImagePadding", "\[Rule]", "15"}]}], "]"}]}]}], "]"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "v", ",", " ", "0.15", ",", " ", "\"\\""}], "}"}], ",", "0.01", ",", "0.3", ",", " ", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "tmax", ",", " ", "0.1", ",", " ", "\"\\""}], "}"}], ",", " ", "0.1", ",", " ", "100", ",", " ", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "dirQ", ",", " ", "True", ",", " ", "\"\\""}], "}"}], ",", " ", RowBox[{"{", RowBox[{"True", ",", " ", "False"}], "}"}]}], "}"}], ",", " ", RowBox[{"TrackedSymbols", "\[Rule]", "Manipulate"}]}], "]"}]}], "]"}]], "Input", CellChangeTimes->{ 3.35696210375764*^9, {3.447079193847231*^9, 3.447079372858618*^9}, { 3.4470794636744547`*^9, 3.447079469269176*^9}, {3.4470795349106913`*^9, 3.4470795390629387`*^9}, {3.447079641404047*^9, 3.4470796791108294`*^9}, { 3.44707972555199*^9, 3.447079730513205*^9}, {3.4470934315481367`*^9, 3.4470934348148212`*^9}, {3.44709359105888*^9, 3.44709359835594*^9}, { 3.447093910010538*^9, 3.447093946464732*^9}, {3.449125536359375*^9, 3.44912554*^9}, {3.4491439454375*^9, 3.449143945875*^9}, { 3.44914449028125*^9, 3.449144566046875*^9}, 3.449144617578125*^9, { 3.4491449561875*^9, 3.449144966*^9}, {3.449145087890625*^9, 3.449145164453125*^9}, {3.449145252671875*^9, 3.44914525765625*^9}, { 3.449145298671875*^9, 3.4491453003125*^9}, {3.44914533565625*^9, 3.449145340984375*^9}, {3.44914541603125*^9, 3.449145437421875*^9}}, FontSize->18], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`dirQ$115201$$ = True, $CellContext`tmax$115201$$ = 0.1, $CellContext`v$115201$$ = 0.15, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`v$115201$$], 0.15, "flying speed of swans [LU/day]"}, 0.01, 0.3}, {{ Hold[$CellContext`tmax$115201$$], 0.1, "flight time [days]"}, 0.1, 100}, {{ Hold[$CellContext`dirQ$115201$$], True, "swan velocity vector"}, { True, False}}}, Typeset`size$$ = {400., {197., 203.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`v$115201$115202$$ = 0, $CellContext`tmax$115201$115203$$ = 0, $CellContext`dirQ$115201$115204$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`dirQ$115201$$ = True, $CellContext`tmax$115201$$ = 0.1, $CellContext`v$115201$$ = 0.15}, "ControllerVariables" :> { Hold[$CellContext`v$115201$$, $CellContext`v$115201$115202$$, 0], Hold[$CellContext`tmax$115201$$, $CellContext`tmax$115201$115203$$, 0], Hold[$CellContext`dirQ$115201$$, $CellContext`dirQ$115201$115204$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`R$, $CellContext`tmaxfound$ = Infinity}, $CellContext`M[ PatternTest[ Pattern[$CellContext`t$, Blank[]], NumericQ]] := { Cos[(2 Pi) ($CellContext`t$/$CellContext`p$115201)], Sin[(2 Pi) ($CellContext`t$/$CellContext`p$115201)]}; \ $CellContext`p$115201 = 27.3; $CellContext`R$ = 0.0167; Show[$CellContext`sol = ReplaceAll[ $CellContext`X[$CellContext`t$115201], First[ NDSolve[{ Derivative[ 1][$CellContext`X][$CellContext`t$115201] == \ $CellContext`v$115201$$ (($CellContext`M[$CellContext`t$115201] - \ $CellContext`X[$CellContext`t$115201])/ Norm[$CellContext`M[$CellContext`t$115201] - \ $CellContext`X[$CellContext`t$115201]]), $CellContext`X[ 0] == {$CellContext`R$, 0}}, $CellContext`X[$CellContext`t$115201], {$CellContext`t$115201, 0, $CellContext`tmax$115201$$}, Method -> { "EventLocator", "Event" :> Norm[$CellContext`M[$CellContext`t$115201] - \ $CellContext`X[$CellContext`t$115201]] - 0.01, "EventAction" :> Throw[$CellContext`tmaxfound$ = $CellContext`t$115201, "StopIntegration"]}]]]; $CellContext`LastPoint = ReplaceAll[$CellContext`sol, $CellContext`t$115201 -> If[ NumericQ[$CellContext`tmaxfound$], $CellContext`tmaxfound$, \ $CellContext`tmax$115201$$]]; $CellContext`newtmax = Min[$CellContext`tmaxfound$, $CellContext`tmax$115201$$]; ParametricPlot[$CellContext`sol, {$CellContext`t$115201, 0, $CellContext`newtmax}, PlotStyle -> Thickness[0.004]], Graphics[{ Thickness[0.004], Circle[], {Blue, Disk[{0, 0}, $CellContext`R$]}, { PointSize[0.03], { Darker[Green], Point[ $CellContext`M[$CellContext`newtmax]]}, PointSize[0.02], Point[$CellContext`LastPoint]}, If[ And[$CellContext`dirQ$115201$$, Norm[$CellContext`LastPoint - \ $CellContext`M[$CellContext`newtmax]] > 0.015], {{ Thickness[0.001], Line[{$CellContext`LastPoint, $CellContext`M[$CellContext`newtmax]}]}, Blue, Arrow[{$CellContext`LastPoint, $CellContext`LastPoint + \ $CellContext`v$115201$$ Normalize[$CellContext`M[$CellContext`newtmax] - \ $CellContext`LastPoint]}]}, {}], Text["Moon orbit", {0.85, 0.8}], Text["Earth", {0.07, -0.07}], Text["Moon", $CellContext`M[$CellContext`newtmax] 1.12]}], Frame -> True, FrameTicks -> {{{-1, 0, 1}, {}}, {{-1, 0, 1}, {}}}, BaseStyle -> 12, Axes -> False, ImageSize -> 400, PlotRange -> 1.25, ImagePadding -> 15]], "Specifications" :> {{{$CellContext`v$115201$$, 0.15, "flying speed of swans [LU/day]"}, 0.01, 0.3, Appearance -> "Labeled"}, {{$CellContext`tmax$115201$$, 0.1, "flight time [days]"}, 0.1, 100, Appearance -> "Labeled"}, {{$CellContext`dirQ$115201$$, True, "swan velocity vector"}, {True, False}}}, "Options" :> {TrackedSymbols -> Manipulate}, "DefaultOptions" :> {}], ImageSizeCache->{453., {272., 281.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.449145177125*^9, {3.449145258140625*^9, 3.449145291203125*^9}, 3.4491453421875*^9, {3.449145403546875*^9, 3.44914543834375*^9}, 3.449145471515625*^9, 3.4491458195*^9}] }, {2}]], Cell[TextData[{ StyleBox[ButtonBox["Flying to the Moon", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FlyingToTheMoon/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FlyingToTheMoon/"], FontSize->14], StyleBox[" ze str\[AAcute]nek ", FontSize->14], StyleBox[ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontSize->14], StyleBox["\[ParagraphSeparator]", FontSize->14], StyleBox[ButtonBox["http://demonstrations.wolfram.com/FlyingToTheMoon/", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FlyingToTheMoon/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FlyingToTheMoon/"], FontSize->14], StyleBox[ButtonBox["\n", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/FibonacciRabbits/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FibonacciRabbits/"], FontSize->14], StyleBox["Autor: ", FontSize->14], StyleBox[ButtonBox["Stan Wagon, Macalester College", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Stan+Wagon%2C+\ Macalester+College"], None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Stan+Wagon%2C+\ Macalester+College"], FontSize->14] }], "Text", CellChangeTimes->{ 3.448955826234375*^9, {3.448955858875*^9, 3.448955869140625*^9}, { 3.44906364003125*^9, 3.449063671734375*^9}, {3.44912559846875*^9, 3.449125632328125*^9}}], Cell[BoxData[ RowBox[{"384000", "*", RowBox[{"0.25", "/", "24"}]}]], "Input", CellChangeTimes->{{3.449145585125*^9, 3.44914561128125*^9}}] }, Open ]] }, Open ]] }, ScreenStyleEnvironment->"SlideShow", WindowSize->{1272, 683}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, DockedCells->FEPrivate`If[ FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], FEPrivate`Join[{ Cell[ BoxData[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztXXdYFNfaz3O/f+79vudek3vTLKBIEaQpTRC7BgtqLCTWGxNjYsFookE0 NoxRY6oFuyIiWJCO9N4WWHrZpSy7VKkiBo2iy+5+Z/fsHg4zO7NLUZJ4fs/I Mztz5j3v+87u+zvnPe+Meuu3L1v/P6+99poJ+Gf+t9dek+8LBwiBIHvu/Byd ManLXMoSE+ExkQoZX+8W641rHWPUaDZZav+BZOoa6ZRVkhkftXrdrC3lg60h JuGh667nVjNkJjbd4ywfjhzbcP7iQFUiICAgIHiVkHfVO0dHL0tnDFd/XNGH q/g3bgrz84VFRVmnznAMrGRjDCSjxz6xmCFx3iFZtl/ickC6ZK/U6YtnS7Y/ c/6s23Zpt8V73aaOz8wdn+pbto4yqI2NG2qDCAgICAj+HIBTHn5GRrGhMV9H r0hXr1hnbKGuQaGlQ6G9U5TJTJ7ZFJneaNnoMd0GZl1rjos3X+7efEn8uafk k1OSlUfFi78RO30htl/5fOK8p2ZTmnXHNxlbVWVzh9osAgICAoI/ByANVVVU 5DpMKRs1pnS0fumYcTwDywIjh6IJixMcVrWNt5HTkL5Bt/7YR9OXi9yv1+7y urfLu/1rryfbLnR/7iledUQ8b7vYcUXn+Ol1uhZ1EycLCwuH2iwCAgICgj8B 0AIQ2C9Yv0E4ckyNvmmh8YSs2U6chUvTlq9JcFnDc5pR9t4M/rw5/IULeDMd M9Z9lrTVLWXLDs7Wr3O3uhVt3sn79Ev+2k2lLmvy5r+fY2JXZjO9qrh4qC0j ICAgIPijQ4RB/vGAR72OUaHlpIqzhxsCL9QHXq4N9q4L8mryP9d051xT4IWm oEtNARca75yvC79eG+Fbd9e3/q5vQ4TvvfDrjaE+94KuNgRfFvmdips8jZ+W wd51VXl5bkCgIENDMwICAgKCvyoA9VSroOShbw7UjbXJ/+KzxqCrLSHhTZFJ dbEZnRFRv4eGPQqP7IyK64yN74yL7wwP74iOackrbCkobs0taOXmt3FyHyRx QPv6oIi68IhSz3NRK9bnht2tEgjwHiv4/JykpOgTJyI/3cBdubru7Pnq0tIh sp7g1YUgNFTg4zPUWhAQvLpA0x9IQDUKyJlIKCxfuqbOYm7RQbfG8KC2pLzG tIKWhHTeuXPtsUlPsoseZxU+zsp/xC14lMF9lJjSmc7pKK1oLxO2lQjasoub knKqYzKqIlOrEzOrwuJDxtpfe2fMRSs7/wWLvZe5/DR/wS7HyTuNx/365lvh 7wxvWLuuLi1tqD1B8CoCcBDvtdfAxtfRAfsvqJcMMs0n+OsiIiLC1dX12LFj PB6vfxJwGgIEVKuAqKKi6OB3FaZzBDPW5Xnsro2+W59e0JKc2ZGUGjppcqrD NN4V7/a84of5JR25RR25hR0cLjjVEZ/Qnpp2PzWtOT6pNjqxKiy2PCymMjaJ Fxrx7bsjdg1745dhbx/4xz+//Pv/nvjXsKi33m4Zrts9fkLzZa/B9QkBQZ9Q sXFj+cqVciYaNqwqOXnQ5efl5Z09e3bQxRIQ/EEARlmBgYF79uzx8tI2mPMz OKnXrqVcv56flFReVARmPVUCQSWPV87llsbF8QKDC095Zi9akW04JcveJXOB a46He/XdoObY5N/iku9ncFPmL7ynY1ww0iB5xWp+cFhTblFrTmEzh9uSmtma kNwaGdUYGlIXHCgM8C+/daPI93pxSFDW7ZtfvPPumRHjfN/R8X9nROUYPamh kUxPr9vSuj787gv1DwGBlgBkBJiozNFx0CUTGiJ4FeDn5weYSMvGIj6//nYQ d8VHZ/QND41491drK087uyAb23Rru6yJtlwbB96kqeWWtgJzxxqrWS02Mwr3 bK2/49MWGduWlH4vIztunnOVgUW1qW2Fnmmq/vikbV/yI2JqOTm1yZy6+OS6 qJi64BBRQED5rZulfr55167mBfjzbt3Ot5xeZ+oonjhdamYvNZkg0x/XbTmh PibmhbpF4OMzWDn/qvx8ubQXlrQhGHKAeRDMzg36OhGhIYJXAWBO5Orq2tf8 c11ymuiLr/JMLTMMxsUYjeNaTOh0mCab5CiznCgzMpTpj5YZjJWNG5/n7iq6 ff1eVEJdQpowNSNyrnOpkWWpmS3PzK7c1DZ/jEnkRLuUI9/zoxOq4lMFEdGV AcEVN2+X+PkW+Hhnel3m3bnTGp0iXXdIsnibZOpKqe08qYmtxNT6XkiI9qoC FoAhAmxgHx3nDxumNnTAkS3awEd0Cgx38UEv5SOA8pJdu9CRyiNHUEegJTiF LoH7PNXbk4AaFH3o0nCxcjlmZnjX8ryQykCYKULKI6PAcRAzgQJgQ8wIdvg6 OmiNA16LhKMYW3n6NHIpaAPtApeUL1gAdYZaIT/TL4S9QK1AG+hAIAfYCCRA reiug5pQtIJqg66VvjUzg47quQoY6OMD+gI74CDdh7gyFFA0x/0DRIFNfit7 X4hucS85DI6ie4YJ7DQEfrkRERG91ODxduzYAY6jI3CcCY6Av2Afbwwkg+Og PUzLA1EeHh6uCoCdhIQE1MWvv/4KW1IyJyzC1Z6CCwGoTWBgIPgI/lLsojTT pke6KyjScOADb2AR9BiwEe8XmA+9ARqDffAX6QncBVwHrwLHQfCER6CLgBzQ HuyjxQ7cz3gX4MJjx45BlcAOCsJ085F1LB2xeADvCBiFOxyZCQAkI53BFw/I RzayZMyABNwK+LXRaAjlFOgOfKR8hbSEKC1d9MmGBxNtH9o6dE6Z0WUzWapn IBujIzMykppPlJnZZbtvLb95XRQZL4hNKk9MCXCal2ZokWlmw1Fsmea2mSZW EToGd2bNST3pWRoaURYUzPP1LfT25l65zLl0oTImqS456/mus5JPjkmct0om L5WZTW07ea5PSqLwjkd4nJvwOI/CNdjB9+HZftAQCqTgYE/MHDANocVxxDuU xkq+UwRtxA7gI+iazr9IMcgIqH2PFTBiq4RDw6EhUCCQIFQ3KaBcqKQShflw XynEzAxpRXEd1EpOKL3dBfrq4XeFXWBDCoB+oWKwjVofQquZMmm45koOGjZM LlNHB9Ec/XZQRjVMjqJ7hgkaaYgSw8EPGQYE/COIIaAZ+Iv/0mEEAx/BKRQe QeQJVADswJYo4oGD4AjORCzCmU5B3sEVUBvf8GZ069T2qJbOcGmBGFC4hhwE nYCirlDF5iCoIquRfHAKhGV0FZAAgjxkJXgEXIWPBCh+RqaBO4u6QFeBg2rN R72zdMTkAdgRZB8AyGKoJXAFOILMhF82aD4kengKXM7iW9wKXDiLIZRTSI7a XjRCJBLVnvR8OnWWxH6a2G6m2Hy6ZKy+TE9XamErnfQex8211Ne7IjyaFxFb Eh3nPXvOTT3jAGPLO9gWaGJ5W8/44sjRN5a5ZF64WOzrV3DFK/X8uTy/myVx KRXxaR37Lki2npKs2C+dtqZr6QZh78ptjUDhC//V49yEIgPiJkowR9G+rzSE ekFkAQLmoNAQOgsb95RsqRbKkTTUEYh7yo5UjSm0AjlLnkJUNaDwFFSbfhZ2 B3coYZ8S6nGTYaeAjCinqOarpk6UflF71BdMfiodrnACOAKjvVquofifAlxz 5cxFNaVCrI2bD52P98XuKHYSROgTDcHoAQe38AgMWagBDDVwnxIH6DMd1AUe HHAJLMKZTlGCMIj8au1ioiGWHjXSkNpTFIEwigpVY3VICugjlA+ZC51il0Pv HX0Et5WyGgI+wnvNEr1ZOmLyAL0jaAK9JfInaAAu0Vi6BhrAoQt+EE6c4bXa 0xAwBE5y+10vV1NT0xAdI35vocx8Sre9i3juFrGVg1RXR2ppn+a2pcDnSmnQ 3cKQiILwyDMzZv48Su+0vvGp3hs44qlv/PNw3eO6erfWr088eTL70qXcsOiC qITSmKR7Hhefu52RfHxEOuPj5tt9SMdBKH/vivhPCXrKpJAqPleePo0HMSEt edJnGqLNWQYrKYd6h2fxMIhsRNLoasCZCOJfJU8NG8ZkCN4AJzgmrZgk99gY GorP1yDUzrmQKIpWTCQCnYCSXXBmh5uGQHc4Dlxz+BVCk+KeSZ8qq6nMkSqm PD1jA1ZH0X2uFn2iIRhG0A8c5tvxgAlTHzD5g8cBekumLpAEFuEsp2CncELB MvRVSxzs5vSDhugCUUuW+AlYnn5HoNvV9shEQ/RMFwz+7L2zdMTkAXpHTAsx cKoFbdSmbg1OSClfG3hT4OVa0hCkM8j1THlFjaiurq6trW1MSeuetkhq94Fk +Tf3N53onDpfNtaQ47al9Oa1irsxpZExJVFx52fNPqVrcM5wvNrtvJHpWX2T X94aecnCMvG7wwXR8fyk9PL4tFqPC4/czkjXH5HM21yf3OdnKGBwoyymKJdO 0GRHwTtqIxse+vqRlFPS34IFMGQNIg3BnCGM0vBaFAahObBreDlaWFEu4igI F8VAOv9SKACnD7QPJFM2IX3m1Xt6ghslXxtSjQ2UzsEsQh+RKGHvCRQTDSHe AUaBLtAMV22JCIuHe5kcGopmeXTfImWA5tCTymkjq6Nw+WrvL4T2NASnQjCL whRLhQxxgJ62QpkrcBzP9gtV6X0W4RpPwaEvy7hXrQR2c/pBQ/SVC5hAU3sJ e0cwgAOB9FkAEw3R5WhDgiwdMXlA7XFKwEfrO8hGmKnDQR+lwPtI7xGNMbSk IXgjgEXgKqYJskZAGgJzoubgMKn1YsnSPR2up0p2nm6fPDvX3VUQ4Fcdm1QZ l1yekHzDaV6YoXmkmbWazdQ6wnhCtIVV1jLn9N2uCefPlscnizg51enZdR7n H7if7t70o2zu9par/n3SDUUhtAOPwzAiXxZX7MDB84ugIbhIzcNqHgaLhpRU oojSMPbK47lCCAzUyikPNgGEjIxvKHnF671iTqcAHpaYogjpkYanxWCVAk0y Pi3FV/DRpmZyiuaSmFZ06sQ9A3vBN7VVCihHCtkBMhe6cfiFeDkE2np8q1AM X0iCN5HFURT5TNCehuiJr77SEB1CBhrShmtYTtFlUvByaIh+vN80JMRKHXDv 0UUNkIZYOuorDaGDcLUIr5FQ+2WgC2FKq8JVNnZD8FOgPaIttdlCjRCJRDUq gP0n63ZIF2x/4npC4Ha26Kufcr/5QhToVx+fIkpKr0zJCJo3P8PQgmtum22m 2FQ7WSbW3PFWJU6zit03JZ79pTAyuja3qCY9q5bDrePkNHx74b7bSfHG49LF X4udNtRmq0kdMEGZrVIELjxhguI/mhYJBy8ph6JTL00U8wh8jX6ANIR0AztQ FM6V4KByXoBRiRBVj/v4KCeJlBo2VV9q5kdw/K9ITFHK8HpmHD4+TLxDqdnD c3HQFnAthXfoBQ94JZ583Ye5/AC5VO7z3ik1HPQRgnwapeIFiuZKmYr7SMko 4glSlKBjd5Sw90IhE7SkITQVEmI/cO2TcpTKLngWDnQp8QdKAO0HkpQDYUeb 2RA+FAeNB5iUw6XBS6DV/UjKsSSsgGQgFmarKDIpH/uXlGPpqH80BJ1ASYXR 6x7VjhxcFZMmeo+Q19gNwU+hry76dtFlsgO9QgHS0MN9x6VzPn/+2Y+NOz0L 913IOexeH3SjKTGtPjVTmJYZNde5zMCy3NS23NRG8de23MS63Hhi9RRHkeva TM/jKX5+uf53mnLym3MLmzNzmrLzmji5Tfs9H+4+I/74kGSJm8x+RdfSTTV5 BVqq1ysJphqyKlNYihiCNxisEgVY2QWPgFiKD9dhSKSklWDcQzFWOVNADMg8 WkbrIDgNoQkRZUlIrgler06pYeu9Yo56RykyPGbCs6g+nBJdlVUBZmZKpyku lPsEy7z1kC+WklJTaNebaNRWKSDJOPAjOPVTgN8CNEhAHEq5EJdJKSbEaQip LSdlVkeh7liYVEsaYqo96FOJAmXtGw50XWklCoiwBlKiwM5E9NkZDE3sJQrs BQ84oBC4JKF2xZ8lfjIt3+NHWPyMPmosUUDUQAnOTB31j4bU1sZTdENJM7oQ bWhIrSHID5AH0USsT69TgMDf5CN/m1yloOv9jyWz1ks+PvJw55nyPWdzj+1r DLvdnpjakp5dz8mOn+dcrW9RPd5GvplYVxtNqJ9o27h2SdEvHlkB/qVhEcVh d0uDQ1q4+fdzi9oz8zpyCjoyczu2He3c9pN4nYdk/hbptLUyc6dn81fXJado oyF9mAp++2hHiC3uw/ZaFmzDJ0eUz4Mo6njxbBXKfcHROAzmeME2bIxioLIS WCVN/tHMDAlheUUMsg6nISE2IcKDHqxwpmiCFnRQaTFavOjRR0cH5bgQK6G1 NiQN+RB9xC9U2qXqpWdZ6sgR+QM1K1fKdVA1BgEfTvHQ0zqwjFzIUIkntwtK UNRsCxVUqEy1oQemsFIHBDQDRXM3pUDFFJIyXQVdyO0FXwygmMo58JTa0Qvk LxZHoXU0egU4gjY0hE+FhL3jHlOFMyzTRXMEdBVcEYCn0HNDrqpC7sEt2GZZ IWJKo7EXbMMlCfqzJ0zShLSCbWis2ksoE09U/wwLtgGQHLzymcnPQk0F2zsU wAuzoaOYOhL2l4agOej+wpuO13jDXtRSvDZJOSZDmOgYTQm1B+XVpk3B4RLz Gd3TVkpWHOjaerLB3bPghwMtkYG/JSQ9SM9uzs5NmK+kIZHRxBozq6YlcysO 78i84cNPSL6XlnEvLr4kNLwoOLiVW9CWU3ifk9uRV/woq+Dxp/t+X7VL+sEe yexPpPbLpDaLZTYLxI7zqry8NWqI103BsTSMJHjQoER7cBZ/YkXt46t4ETge glBMQ2tP8mdFe69T9KSnsKE46hE+HYk+sj9XgsIdVAzFUjQhoozSKasb8qCN TVjwDfgKVSmgSI7P8oSKxB3uKDRrQwmrXnadPt3LLqzqTK1/8Ae7cOail89R 1rwQxeNLTiyvHqXogxKDeDEGquvAO8JNpnAZZdbD5Cg0BEIlEHT1tKEhGChQ PKeEULXPe8IjCCj6oZYocMFQP1iPr+K6wSVpcJa+9s1CHGrFwnkNCKFQT+2l CbGlFkhhrljBNt6MMqpHDxmBWA31R4pBaoC3g+5nbR5fhTcCPjPrij1KTPEA 3pFwAGtDoF9Y5A+LH5CNUDdKLzi0KVFgMgRPTuLfcHqmVCNwGqrl8Z/OXSIx myK2X/h8weautYfuu/5c9P3+1siAR3HxD1Mz7mflRM53Lh5rxjOxEs6eLnD7 jHv1XEF4pCghpTktozklpSk2tvJueEFQUHN6dktmXms6tz2n6GFWwf3/7nm8 dPvTmRu6HVaJrRdLzGdLLabLLGdKJ0xt3/xlDSeTST16YS0Kvzw886MqpcOv VfsyH41JOYqEHk1UKzKMqioa4OvjkMKY2kOggjeKRUIsXNMnAjDA4sJ71b9t 3Ag1wSuK4doNntPDzdRsF94Xg11QDt4F/sgqTJohTdRm4egaMjXGQbmJFOqh DwbotxId6aU83ck0R+GiKF8ABI00BDkIpwD2qNvXZkzBrX8YXN0Gt9NB7/fF yVSLftNQv6GxYJsFg+sWxEQPP/28e7zVM3OHbus5YkeXZ4u2ta7en394T1PY rYfR0Q/iE9tSUv3nOCVbTCj5fFXOmR/ygoOFsQn1iUnC2PjqmNjGmJjau3cr Q0Jy7vjfi0u6l8Spi0tv4uS1cwoebvjuscuurtmfPrVdKLZ4T2LuJB0/VWZs JzOeJH9SyXJK20cbqgODhBUVFN3QyBYdQUkh/CDLEjYFfaKhl4CelwaoFiPQ KWQ7ngViB+XRKnqt9csHvZxMbcwfCChrVWi9RllF0PsZ25cPjTQERpj4VEio 9Q+c5YU5lC4IDQ0EWvp54Hj5NKTx8VUWvAhXV2zcLB5rLDaxemxo0TbOttl8 Vp3DysIFm7MPudcGXGsJCWoJC2uMiAxZOC/tm23ZftfKgsOEkVGCiKiy8IjS sPDCkJDioKDSO3cKb91Mu36tKiRSEJtWGZVSk5zdmpLzdN13Txdu67JZJjZ9 76nt3IdrtzzYe7j1hGfLxSvNV661el7o2Pvtgx27m05Rf614il6lpzLm4JVa 9GZMUEtDlFK0lww8TUQZbOOntKESuEZPf6eExveevVAAAoLrWRSt2NOVfZJP yf7hXw+1dX0vExppyJX2Ji7tf+DalCQNIQ3Ra9sG0qk20l7QzAX3M1q+H3S8 fBoSanqZj8YLB64AhIjHa3XdLh6l1zVKr11Hv1HXQDTWtGb8ZJ7V/Jx5GzkH vxb4Xay+4Su6dav61i3Ozz8WXvctvu1f4u8vCAgUBAYW37qVfv168rVrYMu4 ejXzypXYC+dLfG/zwxL4QbG1iZltabnPluwQO6zsdNnUeupiTXYOoyqCKsoB EGHQ0rayiSLPQzkIV8O1CWsUGkIpIxCmhmrADF/dqXyjWu8JgnyJSnWqf+/3 1vK9Zy8ZUKvBcjhcBcM3+GgtPEt5WevLh0YaokyFhIM9/B4SGqK/jLR/L71k ksbk0peQQBsSGqK/mkDtwf6B5dWmLBhEVzf53nruOKtzlF7NOLOaibaVVrZC m0k8Q9N8HeNsI/u0mavjN3/Gu+lVfsOv3P92xR1/fsCdquBgUWxcbSa3Pr+o LqegIT2zNia+MiiIc8Mv9qpXrNeVqCuXMq/5VIbHC6OSH1TV1kXEPp+8+vfl m0T8skHReSCAMR9P36F6hiEcML840O39IwAuu7yc/zgDkdRQ/T8dQ/4fPQxi vBK+xAxV//AHV48dg3unXjQGxdWi4mKB5/nwj9cH7tmTHxhUmZMjKCkRlpYK i4srk5MLz5xNfn9VmPX84ElTOD//IORmN1VWtolEbXX1bU3N91va2lsVW3PL g8bmjsam+w2NrbUNzVXCmoqKSj6/qozfJqp+9OBhe01N8axlT0xmNt64Myi2 ExD8uTDkNERA8IdFVWlpEZdLP44qFspzc8Ns5/jpG9wwNoqYM6dw3cYS96NZ e49x9hzJ3Hck99BxsHEPHM13P8jf8U32VveUDV8lfOYWu37nTecl+6c6Rs9b kL9kdan17DaL6Y8MrOvDyH+0SvAqAtYGD7UWBAR/MiAmCpjl9Mub/z45YozA dq5k44nn+7ybvrsuOOIjOHpN+IOv6Mfrwh98ag9d/H37MeHGw/lr92Ws+zZ9 1cGi5bt8jO02vvF6pZFZnfGEJkPz+7oGNX43h9osAgICAoI/E8rS0o6OHO7x +ptn39HvmuwiWbZXsun0E7eLD/Z6tRz0bvDwrj10tcbjSsO+i+0bj7as+7Z6 xYHyNYf5y3bxnT6vmvxhpJ55/CjdyrGGVXpG9Tp6Fd8dHWqDCAgICAj+PBAI kn788cib7+7/v9dTdMdJHN6XzNkgWbZb8slPkq1nn3198fHuK527L993v/Rg 57nfPj32ePV3vy37pn353ntzNtZMcqk0nV5mZJU1Wi911Oji0XplI3XLFi0V VlEL4QgICAgICNSiSiDITUw8NFLH45+vPzOxlk6cKZm0WDJtjWzWZtnifdI1 30s2/Nq98WT3phPP133/fOWhrkV7njq5ds5c/8hycfPUJTV2s/ijDXOGj4ob PjJ+pA5nhG6OoXGFuqUoAgICAgICtcgIDV3/93+kDB8pNZkgHW8nM50msXPu ctny++aDzz50k87cIlm0W7LIXeK8s9tp29MpH/9us/ypyezWo7+IioqFYAsK Llm5OmXM2MC33ol8e0TcuyNzvTW/QY6AgICAgADiyv59B//1L5m+vsxgnNTM utP1q7pU5ZPLovKKhx4nZXYrpFP+K53yUbfd8qcWzl2G03775AuKEF5sbMJS lytv/Mf/P29HOi8ieTkCAgICAm1QJRBstbYSDB8p09Pres+pITqG3qbzKw+Z zWLpxLkSG+cnxtO6jB3r45PUSuNcunRGR/fCsDdq1ckhICAgICCgICs5+ei/ /y3T0ev48isRwzvuqotKxLOWyl+UbT7tmZH9o8WrhAIBk8Di5OTjxkZx06eT CREBAQEBgUb8vGVz24jRTZ7n2Js13wyQjbeXmTmKDa3aftXw/kwel/uzpYXo 0uXBU5OAgICA4C+IHA7n0tvD205d0Kbx74s/lBlNkBpb18TFa2zMz8uLcd1a nZM7YB0JCAgICP6yuPT1zta9h7Vs3HLJS2Zs02ntWFFYqE378sLCCkJDBAQE BAQMyMrI4B//Rfv2osrKbodZ9xcseXEqERAQEBC8OqgoLu5rFcGTlRu4HwzZ /25JQEBAQPBHw/8DCp03+A== "], {{0, 0}, {557, 41}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {557, 41}, PlotRange -> {{0, 557}, {0, 41}}]], "DockedCell", Background -> GrayLevel[0.866682], CellFrame -> {{0, 0}, {0, 4}}, CellFrameColor -> RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> {{0, 0}, {-3, 0}}, CellFrameMargins -> 0, ContextMenu -> None, ComponentwiseContextMenu -> {}], Cell[ BoxData[ GridBox[{{ GraphicsBox[ RasterBox[CompressedData[" 1:eJztWl1Ik1EYFrqNEoLMbHPmNkRrEhJERj93ra4cJvbDRIsyMk1pc03tTL1w aD+LfkQIJBkR/dBFdtHFDLywCykqoqgLIYRu6jbb8me933e+HT/P2fZN+sZ0 vg9n43zfec973nPe57zvOWNFDS2OhnU5OTlG+LyBj1S/ikAgEAgEAoFAIBAI xEpFMBh8jUgPYG0z7d7MAOYedm/Bko4Ca5tp92YGSCokle5AUiGpdAeSCkml O0RS/R1tjEajUIHvyIhdehPyLNZjrVSAgT5CK1Tmf32e+/qcdYEy+/4+vKTd oQJN89PjojbaHcrCzE8qn0RGfIxrEjcF0SomD49hYqDDUUSGKtUKWRMYz42L pFJDg1RPamGdlRWGuuDi2Yl+WHkoiy72W6jjgFeSm/wWKEAScCvtCxWpSzxt 1FPU9dJ76Lt8UnEmcVMQrWImUQE6nKJB7sgUKpb4LcpEtHiFpEpEKim2TI8n IhXv4pAHXCAJEAPIq7d5JFAOYYEGKHEstTbQAJKSx+XH5ZKKE+CmIFq1ZC/E SBVXoboJyMliKZKKgyapwLlK1ohHKgpYYfGRbnNpg4c8dP3prtckFQ0gUm5K miKpVZxnRZP4KcSziiU1bjhOobpJ2TtIqnhITipYZ7byydJfoDzMpT9ZWMo1 EHbgBBLyhOWzlmakUtKQnB/VuUYkFbWNjZXIJHEKnFVL0t+IXSQVU4iRKkUk JxVzhJI7hirpDpXOGzJ5eFLFvMNORxAlaJZhmtmZStQGAvSQA/FECSksH/kt VLMyokw5qHDOFU3ipiBaxZmtTSo8U2lBI1LF/BWNXZ0Y1LckLo9IqQdYIWdA 9T0uvPT2J2qjrUr2lGMRSzrq4eiIVIxFGC5bMZO4KYhWcWYnSn8gv3j7k+vJ GbVaSNXt9fo6O/XVib9Tpa+sClLdvtB0q+WSvjqRVGucVA/q6p9V1+irE0m1 xkk1cuLk2O49+upEUq1xUg1X14yZraSrS0ed+H+q9GFV/J+qx25/u9U40Nqa aUMQ2YMrFRWf8g0vDh9JvUvgYjPR+8KIyA5AyiNeb1Pe5ql840xxSV97eyq9 Hp1y3nE602waYoXC19GRqInIGHC57lY53Lm53/O2RQ3Fr6qqNXUG609/LLX1 ulOiHyL74D/XeLPxvPiexHDtsuulyexbv2GqwLRgNP8xl/W7XAQE1IUQ1nHw zNl5o2XYoc09RLbC5/E8te26V9+gfskY5SPkuss1abLc2Ljpm9E8Z7FFt++c POroJoQWn1wotQAPj9XMFZp/m6y9bndGpoNYCZBikbNuoqBwsPY4IxIrQJu+ trYf5pLRfOOXotJw6d7Zsv0LtkOPzzb1ENKjolagueVD5YGodUfEZH2372Cm p4X4X/wDFcRtOg== "], {{0, 0}, {199, 30}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {199, 30}, PlotRange -> {{0, 199}, {0, 30}}], ButtonBox[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztlDFuhFAMRJHS5w45Re6RI+wFcoOUtNtR0lJSUlNSUtNS0m9JXjTKaPQh UfpgCeT1n2+Px15ebu9vt6eqqp55Xnm+/I/L/p+1bbtt277vvJumIcKbnwWs 73vBsHVdE1bXNQ55Ho8HMOEd3L9tWRZ+6tRBrrjEMAwigHO/37M6SII40zRB Q7QLkpQWjKOu63RqGHHVIoOYYAR16oucinYGxUo2jqMIzPNMnpQRPF2nMkeS cCBDXsm7ZNZp6oZRS3wsIBFNIYM2iY8gYmJA8imqawHcOAKqio4KSp4O7Qjp K1nOUygasaG2hoKSaud3krkArggZzyhhTohP3Uz7E0mNu9g98oj26exOSTon fRUtn8IUJL+W80gyuz6OW3mgrSXXEv5dSaRTaRz9KQpY/knxtVomKdFQxvFT JZFR6pFBJWT5tbEvR9+H3F6S+GOSMC+DTHtrHYyh32Qu855cdhn2CUundjY= "], {{0, 0}, {55, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {55, 14}, PlotRange -> {{0, 55}, {0, 14}}], ButtonData -> { URL["http://store.wolfram.com/view/app/playerpro/"], None}, ButtonNote -> "http://store.wolfram.com/view/app/playerpro/"], GraphicsBox[ RasterBox[{{{132, 132, 132}, {156, 155, 155}}, {{138, 137, 137}, { 171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{ 138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, { 171, 169, 169}}, {{135, 135, 135}, {167, 166, 166}}}, {{0, 0}, {2, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {2, 14}, PlotRange -> {{0, 2}, {0, 14}}], ButtonBox[ GraphicsBox[ RasterBox[CompressedData[" 1:eJztlSGSg2AMhTuzfu+wB1qzR+gF9gbIWhwSW4lEV1ZWYyvxSPZb3vAmDdDq zpCZdvKH5CUvfwhfx9+f48fhcPjk983vXy922eU9paqqcRx9HGcZhiE+PZ1O KHVd24KOgt0WFKLQ27ZdJrper0JGcS5CVqs6n89yRpGl73tZBK6kkvv97kCe ChOlLEvbVW2kiYPoxKcYRdwWld00jS2EcFSFMYXCqbOcBJzL5aJcxK7SFEFB GQFn8AWupPUkMRfIJEK53W5d1z2hGVP7yohVbfanWoxAJQTfeywbT1+xK9mi GQGTj8FT0uRAN3Tdjl3SlNANP5WoabIIRP+x52ojLEgXs8fxs7+R1cCXNFH6 SVJhKZwx0+BxBZ7nraGNpBSrEFlA1khgRDcCRg1navIWTeVKPVmliaeaL+c4 tCmcknRHfjtWaS6HNtYmC1wYjGJ+6eKjJcficWgVssz1nGbabFtD682gZaIO MHXqkq/vyW3GFaQXliNuOhbz9lOHU3a6SrhWkCmnXC9pUoPBt1aQpquYrtJt 0f6Pazkd497W1MkSlxierkrrN254iz8oHqS0ByzxGzfOHx2yq9plYSl8l13e Xf4ArlmHrg== "], {{0, 0}, {77, 14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {77, 14}, PlotRange -> {{0, 77}, {0, 14}}], ButtonData -> { URL[ "http://www.wolfram.com/solutions/interactivedeployment/\ licensingterms.html"], None}, ButtonNote -> "http://www.wolfram.com/solutions/interactivedeployment/\ licensingterms.html"]}}, ColumnsEqual -> False, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}]], "DockedCell", Background -> GrayLevel[0.494118], CellFrame -> {{0, 0}, {4, 0}}, CellFrameColor -> RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> 0, CellFrameMargins -> {{0, 0}, {0, -1}}, ContextMenu -> None, ComponentwiseContextMenu -> {}, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ NotebookLocate[#2]}]& ), Appearance -> None, ButtonFrame -> None, Evaluator -> None, Method -> "Queued"}]}, FEPrivate`If[ FEPrivate`SameQ[ FrontEnd`CurrentValue[ FrontEnd`EvaluationNotebook[], ScreenStyleEnvironment], "SlideShow"], { Inherited}, {}]], Inherited], ShowSelection->True, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (November 10, 2008)", StyleDefinitions->Notebook[{ Cell[ StyleData[ StyleDefinitions -> FrontEnd`FileName[{"Creative"}, "PastelColor.nb", CharacterEncoding -> "WindowsEastEurope"]]], Cell[ StyleData["Hyperlink"], MenuPosition -> 10000, FontColor -> RGBColor[0., 0., 1.]]}, Visible -> False, FrontEndVersion -> "7.0 for Microsoft Windows (32-bit) (November 10, 2008)", StyleDefinitions -> "PrivateStylesheetFormatting.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "SlideShowHeader"->{ Cell[567, 22, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[1756, 55, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[69613, 1734, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[142102, 3335, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"]} } *) (*CellTagsIndex CellTagsIndex->{ {"SlideShowHeader", 228860, 4996} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[634, 25, 659, 13, 237, "Title"], Cell[1296, 40, 423, 10, 189, "Subtitle"] }, Open ]], Cell[CellGroupData[{ Cell[1756, 55, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[1845, 60, 307, 4, 130, "Section"], Cell[CellGroupData[{ Cell[2177, 68, 238, 3, 63, "Subsection"], Cell[2418, 73, 664, 12, 112, "Text"], Cell[CellGroupData[{ Cell[3107, 89, 15361, 334, 922, "Input", CellID->876584969], Cell[18471, 425, 10695, 203, 573, "Output"] }, {2}]], Cell[29178, 631, 1344, 36, 78, "Text"], Cell[30525, 669, 949, 36, 48, "Text"], Cell[31477, 707, 483, 14, 120, "Input"], Cell[31963, 723, 280, 7, 61, "Input"], Cell[32246, 732, 250, 7, 47, "Text"], Cell[32499, 741, 242, 6, 61, "Input"], Cell[32744, 749, 357, 9, 61, "Input"], Cell[33104, 760, 385, 7, 61, "Input"], Cell[33492, 769, 411, 8, 61, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[33940, 782, 129, 1, 49, "Subsection"], Cell[34072, 785, 362, 10, 48, "Text"], Cell[34437, 797, 3662, 105, 352, "Input"], Cell[38102, 904, 297, 5, 61, "Input"], Cell[38402, 911, 296, 5, 61, "Input"], Cell[38701, 918, 317, 5, 61, "Input"], Cell[39021, 925, 363, 6, 61, "Input"], Cell[39387, 933, 316, 5, 61, "Input"], Cell[39706, 940, 1236, 47, 81, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[40979, 992, 109, 1, 49, "Subsection"], Cell[41091, 995, 311, 9, 47, "Text"], Cell[41405, 1006, 296, 8, 61, "Input"], Cell[41704, 1016, 315, 9, 47, "Text"], Cell[42022, 1027, 322, 9, 61, "Input"], Cell[42347, 1038, 291, 8, 47, "Text"], Cell[42641, 1048, 345, 9, 61, "Input"], Cell[42989, 1059, 622, 20, 82, "Text"], Cell[CellGroupData[{ Cell[43636, 1083, 3811, 83, 222, "Input", CellID->1496021318], Cell[47450, 1168, 3069, 58, 547, "Output"] }, {2}]], Cell[50531, 1229, 1664, 48, 78, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[52232, 1282, 173, 2, 49, "Subsection"], Cell[52408, 1286, 199, 4, 47, "Text"], Cell[52610, 1292, 242, 6, 61, "Input"], Cell[52855, 1300, 209, 7, 47, "Text"], Cell[53067, 1309, 439, 11, 61, "Input"], Cell[53509, 1322, 435, 7, 61, "Input"], Cell[53947, 1331, 166, 3, 61, "Input"], Cell[54116, 1336, 387, 13, 48, "Text"], Cell[54506, 1351, 767, 18, 61, "Input"], Cell[55276, 1371, 209, 4, 61, "Input"], Cell[55488, 1377, 558, 12, 79, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[56083, 1394, 157, 2, 49, "Subsection"], Cell[56243, 1398, 224, 6, 48, "Text"], Cell[CellGroupData[{ Cell[56492, 1408, 5896, 155, 546, "Input", CellID->14096020], Cell[62391, 1565, 5472, 114, 541, "Output"] }, {2}]], Cell[67875, 1682, 1677, 45, 78, "Text"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[69613, 1734, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[69702, 1739, 215, 3, 130, "Section"], Cell[CellGroupData[{ Cell[69942, 1746, 125, 1, 63, "Subsection"], Cell[70070, 1749, 31186, 521, 342, "Text"], Cell[101259, 2272, 990, 22, 145, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[102286, 2299, 115, 1, 49, "Subsection"], Cell[102404, 2302, 726, 17, 112, "Text"], Cell[103133, 2321, 2783, 70, 236, "Input"], Cell[105919, 2393, 215, 5, 49, "Text"], Cell[106137, 2400, 680, 19, 61, "Input"], Cell[106820, 2421, 299, 7, 49, "Text"], Cell[107122, 2430, 238, 6, 49, "Text"], Cell[107363, 2438, 675, 19, 61, "Input"], Cell[108041, 2459, 287, 7, 49, "Text"], Cell[108331, 2468, 660, 18, 61, "Input"], Cell[108994, 2488, 339, 7, 49, "Text"], Cell[109336, 2497, 977, 24, 61, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[110350, 2526, 126, 1, 49, "Subsection"], Cell[110479, 2529, 650, 12, 113, "Text"], Cell[CellGroupData[{ Cell[111154, 2545, 17690, 469, 1512, "Input"], Cell[128847, 3016, 11748, 269, 479, "Output"] }, {2}]], Cell[140607, 3288, 1434, 40, 78, "Text"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[142102, 3335, 64, 1, 4, "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[142191, 3340, 111, 1, 130, "Section"], Cell[142305, 3343, 468, 9, 80, "Text"], Cell[142776, 3354, 702, 13, 112, "Text"], Cell[143481, 3369, 29861, 495, 360, "Text"], Cell[173345, 3866, 225, 7, 48, "Text"], Cell[173573, 3875, 17283, 291, 361, "Text"], Cell[190859, 4168, 303, 8, 80, "Text"], Cell[191165, 4178, 101, 1, 47, "Text"], Cell[191269, 4181, 722, 24, 48, "Text"], Cell[191994, 4207, 398, 12, 47, "Text"], Cell[192395, 4221, 350, 10, 48, "Text"], Cell[192748, 4233, 902, 34, 48, "Text"], Cell[CellGroupData[{ Cell[193675, 4271, 10668, 246, 1087, "Input"], Cell[204346, 4519, 5722, 118, 593, "Output"] }, {2}]], Cell[210080, 4640, 1645, 44, 78, "Text"], Cell[211728, 4686, 143, 3, 61, "Input"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *) (* NotebookSignature kupDnSpYfgPCWDK9#YVOEmN2 *)