(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 139837, 3173] NotebookOptionsPosition[ 132821, 3008] NotebookOutlinePosition[ 134589, 3060] CellTagsIndexPosition[ 134546, 3057] WindowTitle->TriangularSpiralPoints | Example Notebook WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", "\[NonBreakingSpace]", Cell["(4)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsection", TaggingRules->{}, CellID->462042388], Cell["Here are the points on the first four legs of the spiral:", "Text", TaggingRules->{}, CellChangeTimes->{{3.758294603410687*^9, 3.758294606202675*^9}, { 3.7583064174114933`*^9, 3.7583064332259207`*^9}, {3.758309373849429*^9, 3.758309376532813*^9}}, CellID->13078159], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "[", "4", "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.758294572868843*^9, 3.758294589685771*^9}, { 3.758306108060484*^9, 3.7583061083655787`*^9}, 3.7583089011954947`*^9, 3.759008912634474*^9}, CellLabel->"In[96]:=", CellID->443871870], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], ",", FractionBox[ SqrtBox["3"], "2"]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox["3", "2"]}], ",", RowBox[{"-", FractionBox[ SqrtBox["3"], "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], ",", RowBox[{"-", FractionBox[ SqrtBox["3"], "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", "2"], ",", RowBox[{"-", FractionBox[ SqrtBox["3"], "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["3", "2"], ",", RowBox[{"-", FractionBox[ SqrtBox["3"], "2"]}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["1", "2"], ",", FractionBox[ SqrtBox["3"], "2"]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", SqrtBox["3"]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox["1", "2"]}], ",", FractionBox[ RowBox[{"3", " ", SqrtBox["3"]}], "2"]}], "}"}]}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{3.758382083230144*^9, 3.7590089781808653`*^9, 3.760207003992275*^9}, CellLabel->"Out[96]=", CellID->225806864] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->1132819851], Cell["\<\ This shows the sequence of points in order for the first six sides:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.758294807060244*^9, 3.7582948264117727`*^9}, { 3.7584059047549057`*^9, 3.758405911363407*^9}}, CellID->697960947], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"s", "=", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "[", "6", "]"}]}], "}"}], ",", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Pink", ",", RowBox[{"PointSize", "[", ".03", "]"}], ",", RowBox[{"Point", "[", "s", "]"}]}], "}"}], ",", RowBox[{"Arrow", "@", RowBox[{"Partition", "[", RowBox[{"s", ",", "2", ",", "1"}], "]"}]}]}], "}"}], "]"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.7582946129978724`*^9, 3.758294769246249*^9}, 3.75830892474617*^9, {3.758309483842639*^9, 3.758309513117497*^9}, 3.759008914226666*^9}, CellLabel->"In[97]:=", CellID->1710216102], Cell[BoxData[ GraphicsBox[{ {RGBColor[1, 0.5, 0.5], PointSize[0.03], PointBox[NCache[{{0, 0}, { Rational[-1, 2], Rational[1, 2] 3^Rational[1, 2]}, {-1, 0}, { Rational[-3, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[-1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[3, 2], Rational[-1, 2] 3^Rational[1, 2]}, {1, 0}, { Rational[1, 2], Rational[1, 2] 3^Rational[1, 2]}, { 0, 3^Rational[1, 2]}, { Rational[-1, 2], Rational[3, 2] 3^Rational[1, 2]}, {-1, 3^ Rational[1, 2]}, { Rational[-3, 2], Rational[1, 2] 3^Rational[1, 2]}, {-2, 0}, { Rational[-5, 2], Rational[-1, 2] 3^Rational[1, 2]}, {-3, -3^Rational[1, 2]}, {-2, -3^ Rational[1, 2]}, {-1, -3^Rational[1, 2]}, {0, -3^Rational[1, 2]}, { 1, -3^Rational[1, 2]}, {2, -3^Rational[1, 2]}, { 3, -3^Rational[1, 2]}}, {{0, 0}, {-0.5, 0.8660254037844386}, {-1, 0}, {-1.5, -0.8660254037844386}, {-0.5, -0.8660254037844386}, { 0.5, -0.8660254037844386}, {1.5, -0.8660254037844386}, {1, 0}, {0.5, 0.8660254037844386}, {0, 1.7320508075688772`}, {-0.5, 2.598076211353316}, {-1, 1.7320508075688772`}, {-1.5, 0.8660254037844386}, {-2, 0}, {-2.5, -0.8660254037844386}, {-3, -1.7320508075688772`}, {-2, \ -1.7320508075688772`}, {-1, -1.7320508075688772`}, { 0, -1.7320508075688772`}, {1, -1.7320508075688772`}, { 2, -1.7320508075688772`}, {3, -1.7320508075688772`}}]]}, ArrowBox[NCache[{{{0, 0}, { Rational[-1, 2], Rational[1, 2] 3^Rational[1, 2]}}, {{ Rational[-1, 2], Rational[1, 2] 3^Rational[1, 2]}, {-1, 0}}, {{-1, 0}, {Rational[-3, 2], Rational[-1, 2] 3^Rational[1, 2]}}, {{ Rational[-3, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[-1, 2], Rational[-1, 2] 3^Rational[1, 2]}}, {{ Rational[-1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[1, 2], Rational[-1, 2] 3^Rational[1, 2]}}, {{ Rational[1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[3, 2], Rational[-1, 2] 3^Rational[1, 2]}}, {{ Rational[3, 2], Rational[-1, 2] 3^Rational[1, 2]}, {1, 0}}, {{1, 0}, { Rational[1, 2], Rational[1, 2] 3^Rational[1, 2]}}, {{ Rational[1, 2], Rational[1, 2] 3^Rational[1, 2]}, { 0, 3^Rational[1, 2]}}, {{0, 3^Rational[1, 2]}, { Rational[-1, 2], Rational[3, 2] 3^Rational[1, 2]}}, {{ Rational[-1, 2], Rational[3, 2] 3^Rational[1, 2]}, {-1, 3^ Rational[1, 2]}}, {{-1, 3^Rational[1, 2]}, { Rational[-3, 2], Rational[1, 2] 3^Rational[1, 2]}}, {{ Rational[-3, 2], Rational[1, 2] 3^Rational[1, 2]}, {-2, 0}}, {{-2, 0}, {Rational[-5, 2], Rational[-1, 2] 3^Rational[1, 2]}}, {{ Rational[-5, 2], Rational[-1, 2] 3^Rational[1, 2]}, {-3, -3^Rational[1, 2]}}, {{-3, -3^ Rational[1, 2]}, {-2, -3^Rational[1, 2]}}, {{-2, -3^ Rational[1, 2]}, {-1, -3^Rational[1, 2]}}, {{-1, -3^ Rational[1, 2]}, {0, -3^Rational[1, 2]}}, {{0, -3^Rational[1, 2]}, { 1, -3^Rational[1, 2]}}, {{1, -3^Rational[1, 2]}, { 2, -3^Rational[1, 2]}}, {{2, -3^Rational[1, 2]}, { 3, -3^Rational[1, 2]}}}, {{{0, 0}, {-0.5, 0.8660254037844386}}, {{-0.5, 0.8660254037844386}, {-1, 0}}, {{-1, 0}, {-1.5, -0.8660254037844386}}, {{-1.5, -0.8660254037844386}, {-0.5, \ -0.8660254037844386}}, {{-0.5, -0.8660254037844386}, { 0.5, -0.8660254037844386}}, {{0.5, -0.8660254037844386}, { 1.5, -0.8660254037844386}}, {{1.5, -0.8660254037844386}, {1, 0}}, {{1, 0}, {0.5, 0.8660254037844386}}, {{0.5, 0.8660254037844386}, { 0, 1.7320508075688772`}}, {{0, 1.7320508075688772`}, {-0.5, 2.598076211353316}}, {{-0.5, 2.598076211353316}, {-1, 1.7320508075688772`}}, {{-1, 1.7320508075688772`}, {-1.5, 0.8660254037844386}}, {{-1.5, 0.8660254037844386}, {-2, 0}}, {{-2, 0}, {-2.5, -0.8660254037844386}}, {{-2.5, -0.8660254037844386}, {-3, \ -1.7320508075688772`}}, {{-3, -1.7320508075688772`}, {-2, \ -1.7320508075688772`}}, {{-2, -1.7320508075688772`}, {-1, \ -1.7320508075688772`}}, {{-1, -1.7320508075688772`}, { 0, -1.7320508075688772`}}, {{0, -1.7320508075688772`}, { 1, -1.7320508075688772`}}, {{1, -1.7320508075688772`}, { 2, -1.7320508075688772`}}, {{2, -1.7320508075688772`}, { 3, -1.7320508075688772`}}}]]}]], "Output", TaggingRules->{}, CellChangeTimes->{{3.758309505709717*^9, 3.7583095147234383`*^9}, 3.758378333898365*^9, 3.7583820555797663`*^9, 3.759008981714727*^9, 3.76020701113999*^9}, CellLabel->"Out[97]=", CellID->421083182] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->1860705102], Cell["40 black sides with 20 red sides overlaid:", "Text", TaggingRules->{}, CellChangeTimes->{{3.7582948913614197`*^9, 3.7582948958539753`*^9}, { 3.758403960906299*^9, 3.758403962286571*^9}, {3.758405931354084*^9, 3.7584059436661863`*^9}}, CellID->1925797651], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"Line", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "[", "40", "]"}]}], ",", "Red", ",", RowBox[{"Line", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "[", "20", "]"}]}]}], "}"}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.758294852948044*^9, 3.758294882009931*^9}, { 3.7583061345745792`*^9, 3.7583061351011066`*^9}, {3.7583061709626017`*^9, 3.7583062164984818`*^9}, {3.758308720401732*^9, 3.758308724991219*^9}, { 3.7583095646285057`*^9, 3.7583095646303167`*^9}, {3.7590089161487226`*^9, 3.759008917946948*^9}}, CellLabel->"In[98]:=", CellID->509996249], Cell[BoxData[ GraphicsBox[{LineBox[CompressedData[" 1:eJxdmntcldWexhF3ikGxQUQQRGBzldsGTQnZvT/N1FS8a3aVMS0tm/RoXivx pKXmmJpp4+QZckzteqjQKQP3LzO7eYyOZVaWZOaQUpJXRMTR9TzMZ6/xn83X 9V7Wu9bze571rr2TJj46anJwUFDQTW2Dgq59/v9/zVeu/Tvif33o+Lr5O046 bcz/NvjRWlHc1nw2+rei3d/OcK3/VfJZnO/wfP9lwxecN8m4ToPTer32ON95 m/fD/x8urjB8yTnI/iy+uV/u4U9dcsHwKf8OtgezP5/xfBcuoPg4w+u79Ane /3rDIboK55ODdAM5is+7mYzms1VvkQ/h/s575HrDV5zd5PMG28s+MsazrdTy /hxzab2uG/13VrH/8Rwf3t8ZzvEp4/MbLOvgQ39CpR3H54+83l+FjYqQ1Ryf SrbXYPz9K3j+t+iv/xNe/xT6p/W8/2n0H+NXFuzD84TqePa/yXA4x/OSH5eL 0AdxfW3h8VMtbqsPk5vZn0fIDez/o+QQPu8MsovjM5OM8XPJYxaHyRwy9Bop 8yx2y9/Y3zY8/nlLjyGcj+PFVzhffo5HM+e3kuPVRD236vFP6qF1Pg5T//Wc D1z316pF5vgoiWG9RN9a8uzrToy0o97K2B5EPZ/g+U2cr228fhPH83GrHtpr Oft3luP/HPv/J+cL1/2z6gLn6wCfH/PbUVv1e85wJ/03jh+u11nfx/3JHfVd ch2v/6bF7XUruYb9f5lcTn3+B5nj73uB7KX+nyPHsF6WWRwiT5HDOL9PWBwl cyyOkRlk6CtaBlv6ipKBVr1HytkhGJ+LeD7Mi0b5UB+hIiUY35Os9985/seo n42cn53Uzx7O3xvUzznObx/qZynnv7gF+omjPiCXbtXQV5zEt4F++o67/7bB Od1kAfXzKtunUD8RPD8LD6TzeP1k1I/+zPvHYjx1DfsHPwrTiew//N6tk/h8 LdRPCPV1kXrAbTpXn6V+5mJ8/Keon/gSjO8Jw7G6i+P/q+E4/YPzU2u4q4Z7 Tf/IsRpicSdtY3GENuF5VKn/MxZf9TdyGf3nV3IQxtv/UytjfJ1vW4+n/9SQ hf7zmcVhspucSP18YHG0VFrcRd60OEG2kLsajpdUjkcXHt9SiPHqTD2/NSQw r6Llw8EY7wjq2XyU5/huZH8eG4b5CmW9LMV8OOHs/0nOdwjrK7IEemjD543H eMtZ6vnv1NNx6rkf9fY29fwN9ZhNP5xCvaJf7uoW87xJUg6B+z+trFo46waP DKWeL7N9EPU8iecnU8/7ef1E6rmQ90+gnjexf/HUcxj7fwP1XE+9wx8iVfn8 GJ8ozeD4YH0QrS+z3jtg/KF3SfBhvLpoNf0C64147UU/gb8n6EDqHfWUqDM5 v+Ak/ZLzD07Wyej//x3/ILkdrz/V4hjmaytH6SMWu/VRchjHZ4bFQTqTHMPx f4yM5saqOeQazi/9hH5/xVlAPks/fMLicFlIRn51lEUWd5anLI6TJRZ3k2fI WE8myTIybp8opzl+0GuibOf4cvzlaY4/5jNeWtdzqI8uUs48jMR4QqdB9cXR mH85RL9DPUbJ5/RD6C1S1lI/0KdbPqK+oOcwuUi/HYPxl1XU5z3Qr2RQv5Nw Y1Hq+1uMvzOe+j+O+XEaWR8n6Fd7WD+mub/Xh+unyDuX4G/37Prk8K2L0yS0 Bfn7PNsT6Ief8/zezGv4a5Jso39O5/0rMb/6E/vX6rdD2f99mG/dyeerpz9n sP5OMy+y6S+N9POQIoxfC/PiM9afi/XlGo7x5/xBlxU9fG7WVwz9L5T1MnpI 4Pwm6T/onxGsr4Yh0Af806PLqR/4a4rGU1+Y71R9q595PrJH37M4SXeTe7I/ +yzuogctjtZaiyP1BBn5HaZnLb66jibXQA/+EIy3lnM9EEnGAvuIE0/20p/T yC9iPsVrcagUkTF/EdLf4k4yzOJYGW9xV5lIPs56nGZxssy2OEXKyNCHR45x vE/z+EHM90bW+53QC98nEiW5KHD9ligHub7oyHr/EnnnT2C947C86kzW+0no xenJej8GvTgO6z2T9TyY9V7Keh7Let/Hei5lvU+h3g+y3l2sh3rWeznrJbgN 6r2Y9RQDw5J61vM9waj3nazHpcGo96Ws1ynXod7HsZ5hFwN9KeZ+GVJzBvV+ +pN/3tzxUqaMbkK9Z7F9wmXU+ySevxaG6t/I6//agno/2OonrPdw+kEc630V +9+L9R5cgufbxnqfxeffzno/zvHZzXofTz/4kvX+Qkng+1Oszqcf/IY80F3D MD94X7m6PhyJ+QtmvZuPpf18HViPXwzE/LtZ7/GDoY/OrN9M+kEC670//SCV 9e6lH2QbTtNdhdBnD8PpOpT1WGQ4Q78358eR07Te4hRtsThZ3UMDOVGTybOg V+1pcYwOsDiK7+Ot7NaHyHXQmz5ucZCuJNcYvTX4qUeMW5Cv+h1yqfGPU3xf iVMvCs45SI6BHqTO4nBpIq/AfEtYSSB3lgSL48RrcTfpR97Leh9jsUcesDhV 5lqcLsvJ0FOanKC/HOLxg4swfz/Tf16jv5zg9aOGYf7P0H++Lgrcr0iSzOHQ z3XQl4yB/pgviajD8X2rc80fCbJtEPSJhng5AP05o+g/r0J/zPsYqYP+ZDb9 Zy39ZSn9pyfrZwP952voT96g/8yivzzeBv4TxfpEPoTI9/SXPfSf11jfdfSf +az/WBf8ZzD9YaIL/tOF/jGuA/znBP3FnP3laN9Oc/8sufEk/Gf5Vz+uOzoj R7LOw38+ZvuUS/CfoE9x/s5L8J8+vH47+s9s3j+vBf7zNvs3vgX+U8/+L2qB /6TTn8bSf/bw+R+i/xTRn56k/1TQn9bQf9KgD9lC/3mJ/rST/pMKfch++k9k H8zfUehXW6APB4+TqBWjMf/Xsd7Nx6oSXzj9p64/9BNLf9gwCPry0H9Ke0N/ OfSTmYOhz970n49yod++9J+h9KchhjP1YF/oH3nVXUvpPxMMZ+mJMWZ8yJnq GhvI6ZpgcaoWWuzRURYn6TTyLuhfn7a4i5ZbHK07LY7Ur8nUr/5hsUtDMJ/a iHz0J5MbkId+5qkmmheOI844cgjyzuH6VRdDX7Lc4lDZTO4H/cguizvJIYtj 5bTFXSXsDvDLmH9JszhZxOIUucviNJllcYastLi7bCO/ZThTXMMwnx/w+NL+ mO9P6YdV9LtveP2YfOjlKP2wjn53iv0p7xPodx6pGAE9Ik890ncM9Ir3oWTU /dKh1dBrkly+DXrH/l2irLwd9TAPepBw+t0aw/FyB/3udehDhtPv9hiOkTPQ s/wIvch6+t15w1HSh34X3gZ+eAR6kYw28MMP6XdPBcMPn6df7AiGH06mn/wW DD/sTb+Jxwu3dKAfbWwHP/yBfhfcHn74Jv1s/43ww4X0O3N2/gTfSKOPPCk6 Aj9c/cjZi+NneWVBA/xwAtvfaIQfvsTz47Ch5v+O1/+4GX4YTb9sboYfjmb/ el6GH65i/6ddhh/+g8/3zxb44fXb8fx/tMAPB9Ivr6cfdoC+JI1+uJh+Sb3r FfrlffTD+fTL+fTDc/TLdfTDI/TL7+iHX9Mv/8dwkq4ZCX1gvzlZL46DftrS D83HS2N9EfSfe/tCf93oh3sGQJ859KtHekG/feiHc2+Hvm+nv/WlX95BP9zb G/UxmX44hH4503C21gxGfS0ynKNj6ZfPGc7V3831ksjZ2mJxdw3PC+QMTbQ4 TfMtTtF+FifraIsTdRI5weg7Xh+zOEaftjhK11vs1m3kYuhf37c4SD8nz0Xe +38gm9bakdV8P1G3+QLhlMP9OV2KwHNuhJ50j9Ffe+lmcbh4yUehP+lrcWcZ ZXGc3G9xN5lFngH9yBKLPbLO4lTZanG6vGdxpnxmcZZ8b3GOnCQvMpwtueMx /6t5/NP031Z//on++zav36sP9PVhq5/Tf79if/YNhz5/pj8/Xgz9/sn+jx8F fWN5lirT7wjc302Bz5SOqU4yf3jEfSvqJx/6kQysJxysD5JkEtYTMhJ6kkqs J2S34QQJpv8eNRwvr9F/8b7aRUbRf5OhN2kaQn8wHC2b6L8ToT95hf77V/rz PPrvJvpzCf1piSn4MEmif+01HCLn+sHf2hs9uuQz+u8gvPDLRvpjpAmoRmcG /XOt4QbnNvprttngqXVW0H/N2d7JvvOmf/ny4gH4c+npeds0r0B+OQF/DvKi /fI5+HM5z1+KF1D/Ql5/+SX48y7ev+YS/Pky+xfdDH8upn/f0wx/XkD/Hkl/ 3snnn0V/vsjxWd8Cfy6kf+9Evegc+vePLfDnR+jfQfTnevq3h/78MPQpA+jP J+jflfTnqdCnfEx/roE+5SD9eX9xoH979MXR0Bf2Z1I0/e7A/fE0+EbxfT7s j6XryWLoN4t+OL8/9F1sOFOdm6D/Evpn30Goj/sMZ+mmHNTPo/RbD/27zHCO bhbU32rDuZpK/95kOE+3jEb93gUB6Fr69f3XsMyrY98146t7efzDFufoIouz dL3FmfqmxVfX5xan6ncWe/SUxUl6HepDV5j6SNA4i7tovsXROtDiSL2XHIN6 0pkWu3QZ2Yv1jP8/yaXmC4Ba/3YyJviI8wW5xqxHLjg/k+uwHpELFofKDdCn Qr8R4rG4k9xscawMt7irTCYXQY+ywOJkWW1ximy1OE2qLc6QAxZ3l98szpYr FudKpx3gjddwoVeyyMNMe56MzYdeJvL4FubBbObFqOHQ23Jef8tt0OPfmBdN zIN32J9hBdDzXuZF/5HQ+/fsf70P9fAH8yJ9LOoFcZ0u9fcErse5Dxg1obo7 9CaHfKjHWwynyMbbAvcfPJKO9ZI8YDhZyrBekvnQo0zDeklWGk6UGOZBf+hT 9mC9JNOwHpHpzIO1zIt45kEV84LrFznGvChiHoSZB4oSN/2up+FIOV4NP8R+ qFuqWvPAvO+FyRrmwTjDITKFfvuKYZfcQj8+ixdw7ofkyTNG743OY/TzNPOF YINTyzxYHmfqwRnCPDD28Mk03w7T3x5y/iPkRdKcK+MyTvaQIb8gL3azfdhp 5MX9PP88NrT9LubJlxeRF6/w/p4m5MUK9m9OE/JiP/v/RRPywl2C51t1GXkx qnX/5DLyYi3z5Nhl5MVB5smNzIuYIoxvIfPiLubJRKy3uN+RJCtQj/oB82QH 1l96C9Y7Mp158SHzZAnzon8f7k8xLz5hnvydebF2BPS1h3mxAfrm+0GqCvTt QO9p+uJ9ge8DGWo+Kib6Yui3hTdD/1j/d9dV/VAf/ejP/XqifrDez9bigaiv afTzOOYJ1ve5+mIv1Oc6+n8n5sk4w15dczv3R40gvBrOPHnItOfrAOaJ2Y8t y1cX/f1J016gu01epZDz9bDFXj1PbmZ/3IWBnK3dLe6u/S3O0PssTtO5Fqfo GouT9Q2LE3UvuZHvF7UWx2iTxVEadXMguzWX3ID1mw6yOIi/J0nRWrw/+x8n m9ayCdXryIL3Y6eCnIgFhvM52Y33X35f1Mrh0kIO4fsF9U7uLAUWx8lQi7vJ A2QX9CxlFntkg8WpUmlxuuy3OFPqLM6S4D6BnCPxFufxfSFF/2rYKyMszpeH yCuv4cJ8WcN82sDjdzKfzP7l1fzacyf0eT+vHzUC+sX7eq5MGsD1EvtTWQz9 4/ubbHH1QH342f+to1A/WA92lwEO6ut3Pu/nd6D+sDzPlIiJqM846NP4aNDK SdUF5o90OVeI+sb7eZoU34r6N/V1Nb+uoH5lDvQrpVgPMo88Uov6lVegZ1mF 9aBUGU4SYT4dgL6lAetB+Yb5VY73eXGZfImXDOZTD8NdJIj5NNFwjByC/mW1 4WipYD4p82sp8+kU86uU+ZRg9O+WQubTBrP+ChM3/b3RcIjUjYX/jzP14ZJS 5kMlflDC7xvzxWO+0Gp0CpkvPxlucDYzfwrMhlyt42Y+mZPH/MWHeuspu9+9 Nl9H/HWXFl+3astN8vAPpt78y9k+3xjwBX82z+cPRP37ef1gU49tdTrvP8lw e41kvu01HKqV7H+GybtwfYP5hv2sCG3g85833FF7Mt/SmV9zmW/jDXfWKubb MsOxGuTH+CP/4rQ/8+2k4a66lPkWz/zax3xLN4+TqN2wfhNBvesW5tudhpM1 B+s3+QvqXyuZb88aTtE+WL/JZviBLsb6TaoNp+maW6Bf1Eu6CuqDw5mh76M+ nBD6ufk4/YAP7/NZ+k1P1E8R/X+YoL5GG87R2B6ov2nMi9ABqM8lhvP0yWzU L34/7NULN6G+7zZ+69XpDur/QdOer78Ngj+Y/a+r+TVxFPxjoWkv0N9z4C/P mvYCffUd+M96095DJzO//su099CkKjM/5AJ1LM7Xey326gLygDbo/79bnKP/ bfHV8bE4U89YnK4R1YGcqnkWe7TE4iR9mLzC1G+CLrO4i261OFo/tjhSfyHH YH2qbXYFsku7kb3mByyNfh+5FPsT/rvJ+IH2EWceuQb7D856cp1ZD7aV7RaH ygHyLKwP5U+LO0m4P5BjJcfirjKEjP2FRJlqcbI8Y3GKvGJxmnxkcYb8bHF3 uWJxtnTVQM6VPuR7mV93WpwvcywukBcs7iHvkvF9X4F8x7ycy+OvMC+fNu35 kloAPa/l9dfdBb1vMu1eOcq8rGB/cgeiXhaY9jyZ7+N68Qr6v5d5if2/HPGM QT3i9zHZslNQr9g/yZJNdwW+z2VJ+YOod/z+s7vx7aDmqdWF5o9M2dYDfoH6 z5At8APnXw2nSxX8QJYZTpNUrHdls+FUGci8xA+cU6QZ61353rBHKrDelXOG k2US89KN+pAY5mWW4UQ5nsv3BdSLKNa7spt5uoF52cg8ncW8zDV5GCPDmJeT DEdLBvNyg+EoCWZe1hiOlMM1yIt2ZoHhlh3My7nGQMNkEPPmmOEQ2c68HGE2 pFySzLyqwgaVPMc8G2Hqr9Fpno28y+h0jRucqczDIPMDkFrnIPPSnH1otu9W U1+9RMwG8BF/Rdn1lRf+pbf8L03IdiM= "]], {RGBColor[1, 0, 0], LineBox[CompressedData[" 1:eJxdlm1olWUYx8/0sB3bsZ3N43bcjnPzJYS0hCCtdniutDA2l2ARfvCTKSoh JiZmNpxopb2gZX0pihmRimlaS8o2nzsTfMFqITU/DDNIEV266THnpmfp8/+d 8GkwDr9zP/d1X/f/+l/Xc2rnL5uzcEgkEjl5+//O5///bg7e+fvD3zVr7vlX 9l/0CoJve3yt7q0bGnz2+du17hcGfMbfCWe132O/fyvg695uWHF6vHy8Iu33 9nGevu+q2xvwgPc7+Wx4ZPoDXUejdj3gy/5+1oeQzzH2RxXA6eMq8aOuifPv CTjmtmg/HHEfwknu+xms5WzbHviUzve+hbsDHvQOwf8EWGQnYOk51M5wPppb Pm5C+XtbyD+NPpzvzUafZu4fYPOwjPIptkL0ufTg1F/jc0rtXfRpZb1D+vtv s79T+fpHiH9Z+bluzr+i/KVf85CM7lPs5pJ/f8Al6DngK1ypW6T4LsfzS0I8 1L0A3ySfpXAP+S+DY9x3ORxFnxWw9IvayhDHbRUsv5bZ6hAn7BPyLeD5rSE/ xqjHubpB6uWjx03q24pe/fg578de/JCvRxf+76Yeinu2bV3wfNJS9Ev5jMa3 dnkpK8RvzaxH8PMF9vdTrx3E70fPV0P9UORayC+L/pvJv5d6KW5v23XqdZL7 q74jXN6/1wIe6d5BP8WrcN/pfHiE+xo+T/zdIS5y2+EO8t8Gt+DPj2D0z3wA T8H/m+EU/bIpxDFbD8epb1OIk7YqxClbDstf5VYf8lfSZob6vcyyDdLnhu6n urhkRv1RbNYofS/S73+j/1/452PqcwD/HKZ+X+Cfa9T3MfyzkfrX5eSfKvwh u4xpl7+qLF0g/zz+3PNP1k8eY2vwz07WF+OfUvbfrwu51cQfq/5xf3L+KOnp 3iM/zaO4m0/+mvcJt4D75fBPDH/dwA86pqI9i39elj7+ZfyTbpS+FwIe5Q6i /9mAq9wl6nMm4NGuZEqQHzzKxUI80hWEuNT16z7O4f+rIb493+Bm5s9ZOCK9 /dN5lr5eZ/555k8HbMyfYyGO2yG4Bv98H+Jyaw1xpe0OcbV9Do8OOG0T0KOS 53PTpFcFft7TcPf7qtx+qJfepfg5+GiZnLmXfFY+rXoV0y8bVQ+vhPwvUu8Y /VXWKD8UcN+09LYsfv4SP53Dz9Px2z78/Bt+nMQ8XIxflVeiPRfct9ZaZHD/ aGvb2peGj7NZ+PkW60/h5wXsH4uffyZ+DX6exvnV+PlT8kvj5zj5D8fP3fhd 86HMOe4vfZJuIvro90G520a/D5P+8rtVZ6RXpWtnXuj3Rto9zDzRfK92M/G7 +qnGraC+4lr3C/UXj3ULlf9/zy+CC4m/JMQp3q95TrqlIU64ZXAcfZaHOOJW wCn0Xwlrua9tFdxBfZknzPtBbw2cZR42hbjE1sJ6f42wdSGusPUhrrLXQjzG 3oD1e7LWNsE6vsauoJ/8WmPfoC/62+vor3qmLf97Tv1RaS28D8ukp3wa6a4r V/3tFPNO/Zi048xD+a3M3sc/8mfCfsRf8nPcbjBvn5X+tgV/zpN/bSL+XaCD zeHvTunvzcX/51Qfr4/+uMC8Okz/BMtPTMko/nj7akDzbd7BI10zNtxnxTm9 f7eyXs08PM7+qbyvNV9rbQfz80XOb1V93Wnyy8/bWeR/QvV2B7hfN/N5Iv13 hffFJOZLH/M89qj0y/G+OEb/Remv6GzpT/3ky70PZRL0V4r5V0y/PNNwd31r 3U/Mz1L6q6dB/tD8HOfexD+ar+NdGn+p3hPcnunB/dy/tsC//Q== "]]}}]], "Output", TaggingRules->{}, CellChangeTimes->{{3.758306187279694*^9, 3.758306217224358*^9}, { 3.7583087216780043`*^9, 3.758308726111217*^9}, 3.758309568919231*^9, 3.7583783392131*^9, 3.7583820956633863`*^9, 3.759008985449608*^9, 3.759009060173833*^9, 3.760207020400916*^9}, CellLabel->"Out[98]=", CellID->198811315] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->1213781700], Cell[TextData[{ "The number of points in the first ", Cell[BoxData[ StyleBox["n", "TI"]], "InlineFormula", FontFamily->"Source Sans Pro"], " sides are one more than the triangular numbers:" }], "Text", TaggingRules->{}, CellChangeTimes->{{3.758306755439684*^9, 3.75830678229506*^9}, { 3.758309576698048*^9, 3.7583096079518948`*^9}, {3.758378366482761*^9, 3.758378367265257*^9}, {3.758403972217086*^9, 3.758403985949888*^9}, { 3.768756043085307*^9, 3.768756049333294*^9}, {3.85402342660905*^9, 3.854023427447966*^9}}, CellID->2013137765], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Length", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "@", "#"}]}], "&"}], "/@", RowBox[{"Range", "[", RowBox[{"0", ",", "10"}], "]"}]}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.75830649989918*^9, 3.758306518662984*^9}, { 3.758306704517927*^9, 3.7583067078887453`*^9}, 3.7583095646352043`*^9, 3.759008919548439*^9}, CellLabel->"In[67]:=", CellID->744314247], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "2", ",", "4", ",", "7", ",", "11", ",", "16", ",", "22", ",", "29", ",", "37", ",", "46", ",", "56"}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{3.758306520814324*^9, 3.758306708756362*^9, 3.7583095821678762`*^9, 3.759009065126614*^9}, CellLabel->"Out[67]=", CellID->238967095] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"1", "+", RowBox[{ RowBox[{"1", "/", "2"}], "n", RowBox[{"(", RowBox[{"n", "+", "1"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "10"}], "}"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.75830666712463*^9, 3.758306688329217*^9}, { 3.758306720284157*^9, 3.7583067353839273`*^9}, {3.758309616258106*^9, 3.758309636911153*^9}}, CellLabel->"In[68]:=", CellID->1155380441], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "2", ",", "4", ",", "7", ",", "11", ",", "16", ",", "22", ",", "29", ",", "37", ",", "46", ",", "56"}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{ 3.758306690098545*^9, {3.758306726023838*^9, 3.758306736226756*^9}, { 3.758309622273615*^9, 3.758309641741866*^9}, 3.759009067258802*^9}, CellLabel->"Out[68]=", CellID->247600314] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Neat Examples", "\[NonBreakingSpace]", Cell["(2)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsection", TaggingRules->{}, CellID->540091361], Cell["\<\ This finds the coordinate pairs that are a prime distance along the square \ spiral:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.758306295846785*^9, 3.758306331221492*^9}, { 3.758306361349299*^9, 3.758306373619851*^9}, {3.75830727691092*^9, 3.7583073676611*^9}, {3.758307457319818*^9, 3.758307467215272*^9}, { 3.758308231526018*^9, 3.758308241381768*^9}, {3.758405984441292*^9, 3.758405985112544*^9}}, CellID->1039848554], Cell[BoxData[ RowBox[{ RowBox[{"UlamTriangularSpiralPoints", "[", "n_", "]"}], ":=", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "[", "n", "]"}], "[", RowBox[{"[", "\[IndentingNewLine]", RowBox[{"Select", "[", RowBox[{ RowBox[{"Range", "[", RowBox[{"1", "+", RowBox[{ RowBox[{"1", "/", "2"}], "n", RowBox[{"(", RowBox[{"n", "+", "1"}], ")"}]}]}], "]"}], ",", "PrimeQ"}], "]"}], "\[IndentingNewLine]", "]"}], "]"}]}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.758307394004264*^9, 3.758307430080327*^9}, { 3.758309564643347*^9, 3.758309564644534*^9}, 3.758378617290864*^9, 3.7583789354418373`*^9, {3.759008921222658*^9, 3.759008924005334*^9}}, CellLabel->"In[69]:=", CellID->914425330], Cell["The larger points correspond to the primes 2, 3, 5, 7, 11:", "Text", TaggingRules->{}, CellChangeTimes->{{3.758307624514155*^9, 3.758307664760827*^9}, { 3.758308151929039*^9, 3.758308154000259*^9}, {3.758378952128892*^9, 3.758378953453142*^9}}, CellID->1077324486], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"n", "=", "4"}], "}"}], ",", RowBox[{"Graphics", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"LightGray", ",", RowBox[{"Line", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True->GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "@", "n"}]}]}], "}"}], ",", RowBox[{"Point", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "@", "n"}]}], ",", RowBox[{"PointSize", "[", ".08", "]"}], ",", RowBox[{"Point", "@", RowBox[{"UlamTriangularSpiralPoints", "@", "n"}]}]}], "}"}], ",", RowBox[{"ImageSize", "\[Rule]", "100"}]}], "]"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.75830772123131*^9, 3.7583077253989677`*^9}, { 3.758307783767869*^9, 3.75830781817214*^9}, {3.7583080226757507`*^9, 3.7583080873792677`*^9}, {3.7583081610428534`*^9, 3.758308203597548*^9}, { 3.75830956464948*^9, 3.758309564651239*^9}, {3.758378646226054*^9, 3.758378646848001*^9}, {3.7583786820654078`*^9, 3.758378690022753*^9}, { 3.759008926268847*^9, 3.7590089286070833`*^9}}, CellLabel->"In[70]:=", CellID->1012815160], Cell[BoxData[ GraphicsBox[{ {GrayLevel[0.85], LineBox[NCache[{{0, 0}, { Rational[-1, 2], Rational[1, 2] 3^Rational[1, 2]}, {-1, 0}, { Rational[-3, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[-1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[3, 2], Rational[-1, 2] 3^Rational[1, 2]}, {1, 0}, { Rational[1, 2], Rational[1, 2] 3^Rational[1, 2]}, { 0, 3^Rational[1, 2]}, { Rational[-1, 2], Rational[3, 2] 3^Rational[1, 2]}}, {{0, 0}, {-0.5, 0.8660254037844386}, {-1, 0}, {-1.5, -0.8660254037844386}, {-0.5, -0.8660254037844386}, { 0.5, -0.8660254037844386}, {1.5, -0.8660254037844386}, {1, 0}, {0.5, 0.8660254037844386}, {0, 1.7320508075688772`}, {-0.5, 2.598076211353316}}]]}, PointBox[NCache[{{0, 0}, { Rational[-1, 2], Rational[1, 2] 3^Rational[1, 2]}, {-1, 0}, { Rational[-3, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[-1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[3, 2], Rational[-1, 2] 3^Rational[1, 2]}, {1, 0}, { Rational[1, 2], Rational[1, 2] 3^Rational[1, 2]}, { 0, 3^Rational[1, 2]}, { Rational[-1, 2], Rational[3, 2] 3^Rational[1, 2]}}, {{0, 0}, {-0.5, 0.8660254037844386}, {-1, 0}, {-1.5, -0.8660254037844386}, {-0.5, -0.8660254037844386}, { 0.5, -0.8660254037844386}, {1.5, -0.8660254037844386}, {1, 0}, {0.5, 0.8660254037844386}, {0, 1.7320508075688772`}, {-0.5, 2.598076211353316}}]], {PointSize[0.08], PointBox[NCache[{{Rational[-1, 2], Rational[1, 2] 3^Rational[1, 2]}, {-1, 0}, {Rational[-1, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[3, 2], Rational[-1, 2] 3^Rational[1, 2]}, { Rational[-1, 2], Rational[3, 2] 3^Rational[1, 2]}}, {{-0.5, 0.8660254037844386}, {-1, 0}, {-0.5, -0.8660254037844386}, { 1.5, -0.8660254037844386}, {-0.5, 2.598076211353316}}]]}}, ImageSize->100]], "Output", TaggingRules->{}, CellChangeTimes->{ 3.7583077269025803`*^9, {3.758307794978922*^9, 3.758307819182971*^9}, { 3.758308049748094*^9, 3.7583080881187963`*^9}, {3.758308163301917*^9, 3.758308204686307*^9}, 3.758309659980236*^9, 3.7583784014648123`*^9, { 3.7583786285564423`*^9, 3.7583786489083548`*^9}, {3.758378684230319*^9, 3.758378692598289*^9}, 3.758378943200592*^9, 3.759009072493442*^9}, CellLabel->"Out[70]=", CellID->76367517] }, Open ]], Cell["About 12% of the numbers up to 11326 are prime:", "Text", TaggingRules->{}, CellChangeTimes->{{3.7584049348365107`*^9, 3.758404949244348*^9}}, CellID->843341047], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"n", "=", "150"}], "}"}], ",", RowBox[{"1", "+", RowBox[{ RowBox[{"1", "/", "2"}], "n", RowBox[{"(", RowBox[{"n", "+", "1"}], ")"}]}]}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{ 3.7584048165566072`*^9, {3.7584048907708797`*^9, 3.758404901272431*^9}, { 3.7590090768232803`*^9, 3.759009086404874*^9}}, CellLabel->"In[71]:=", CellID->669943960], Cell[BoxData["11326"], "Output", TaggingRules->{}, CellChangeTimes->{ 3.758404818025424*^9, {3.75840489234787*^9, 3.758404902315119*^9}, 3.759009087594987*^9}, CellLabel->"Out[71]=", CellID->1731175762] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PrimePi", "@", "%"}]], "Input", TaggingRules->{}, CellLabel->"In[72]:=", CellID->991672100], Cell[BoxData["1369"], "Output", TaggingRules->{}, CellChangeTimes->{3.758404915618512*^9, 3.759009090194385*^9}, CellLabel->"Out[72]=", CellID->1332600328] }, Open ]], Cell["Here is a plot of the first 1369 primes:", "Text", TaggingRules->{}, CellChangeTimes->{{3.758307737030126*^9, 3.758307749085785*^9}, { 3.758308123305419*^9, 3.758308138992836*^9}, 3.7583792061403217`*^9, { 3.758404958900729*^9, 3.758404959908176*^9}, {3.7584051461015797`*^9, 3.7584051472610703`*^9}}, CellID->1606466798], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics", "@", RowBox[{"Point", "@", RowBox[{"UlamTriangularSpiralPoints", "@", "150"}]}]}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.758307753302867*^9, 3.7583077543096848`*^9}, { 3.758307831758318*^9, 3.75830795246375*^9}, 3.758307987633847*^9, { 3.758308096308929*^9, 3.7583081098521347`*^9}, 3.75830956465534*^9, { 3.758309687159231*^9, 3.758309750219214*^9}, {3.75837905458079*^9, 3.7583791090957003`*^9}, {3.758379139274301*^9, 3.758379148598527*^9}, { 3.7583791892321367`*^9, 3.758379190188808*^9}, {3.7584049638118677`*^9, 3.758404964812275*^9}, {3.758405233946012*^9, 3.758405260524021*^9}, 3.759008931279904*^9}, CellLabel->"In[73]:=", CellID->2071963721], Cell[BoxData[ GraphicsBox[PointBox[CompressedData[" 1:eJxVnHl8TdfXxjMSEQRBKBJEhERkkjm5K/PNIJKYYiyqZjXUXCQ1Na15KGoM WrRaNbZK4i5DTU3N1fAzRKuKGoKQOd571rPfz+foP/qVm3POXvvZaz177XO1 GTo+40MrCwuLvrYWFtqfVW+1/+6avk/JfDjzp/8Mlhbaf8Um+cOCw2vJn0Wm Hfi5qVo+X2r4TvEF9fsLQqK9b521Ifxemel3db066kLrhCvVdV/mfa8Y17Om W+p6NTW43rMuQZcdMhoSrl9qWqyuL/i2IY8Ac7G6/3jFNri/4WPFGI8jbVb3 eyGff27YI1yXKnBB0y7FpYK1ORefN5QIN+Nf8HO+pD6/VTHGYxfxpWIHYWea qLhcPt4AcWGniDB1/xx5Pidqjt/nler++Hxjdd1m+c/V/Vt2w/MXCTdnOx+J DxepeFQgXmyh4ndHcX25TiOakor5QHxsqCV+nxar+T17MC9rcr12FKnmb1jv D+KSOrsQ5r8F5ydjfvD7rTnhnXg78xiMRz13cd40xWVq/Fnv/LwNvVTP5yzc lAqVXlzV865W872yEuMZcOzMrZj57tRU6eG8et484bqcEtNt0W6DMz1W8fBQ 40N82/OeaPk5Byv9uuPzDH01odR3uBUNVfxEuB3dV8/fWq7XEvPp2iU/QM33 /WToJcdKxq/m141WQ+CmTYoPqfl9oObfChdCXHKiIxzlf9pyyyTMd6iwB9+U 67/HoerzbVPAk1X84xU7q3hXKMb6bkMdu+N6pJ7/Kq5vGKae/2Ey9Pe9Wi+T 8fvkU4P1sE89/0qlR/dQPH9n+bw7f5wEvUep500JRrzeF+7INr1ET3xM6SlX sV015mMC9MbRKv4OfcBbhTvRLsV/CLuTsy/0007pqToO+mlgCf3cxfXpgRX0 HqT0c6gM+tl4+faavyZ2pji1nt4q/czG/fm10k+Sen6DN+43XNiTE6Ogj+Vq vC6i5zaKXfkDxWqC+ZziIolnM0r3AU9Q+vryHe5APyvOFvYir0yMn9R4RwZh fWSr8c5U68HaBuM9f+ZKSOPKjmT7BuPdOq6kPHOyD7WownqJPIuf363B+Cci vhShxhvUFev7fTXezZ0x/sW4H/fH/fhSOebvruJQNT9HD4FThbtQD1+M57Rw RwpPh16eqfE26wV9Ir5tKScRehxgBT0ek/XrQe71sL7uSTx96c1LrC9bH3C7 Cuh1qeipC9VHvLlFKPS7AOuBjWHQ7w3h9pyG+xus1XzKH5eGRsyR//Fjlni7 cZWa31PB4DJLrL8yxcW4AA/GemHHKqzHKsU2ar7Xheq5AxUoXiHcmfaGY/08 VfE60gfxmSaXd6ORRsRnqBXW703cn+44Ij7fyHz407AyxKOxik9LiYcLX4C+ 6Druz2m4vmGsXN+breMxP1lq/P91xvxt1zDbjyPyZD1xvIy/PXfOBy+2gj7u KR7spHGRqS/WH0+uxvpONIGP1EAvxxXv1jDLhzolYH0hP3WgU/7Qe5rEtyl1 UvrOs4b+71zCep67TbvAXdO+bPuDpUOCaNhj6L+0cr7t8h1d6c0b6H/eyxm7 uIsfPalEvTin1kd9iUdb3oD1RskyXh8+5wn9z1Pj35SO9bhF2J9j9kPv5+R5 A3gViV7ZzRr6GA/9shEFlUsVQ06j8sNiwIfLoZeTiodJPPxp4s+4fq6wL71V 8QnE+iR/b+S/sZbID1kHkA+O2yA+Pmp8o+siPzyc+ra3x3/+dH4J4jXLdvnQ 91uF0MESxKfnNPz8icyPG/v0RTzGSnw8eII/8qOX3L8Lr+sIfzBVxed6BJ7v jXAg7z4l86XYh5f9Ci7E/HEfzCejwBaZniv2kPXThK6e1XMrcjkHtlfx2HBe z/70r+IIed4AMoVjfV1Q+WjGYKynRtA70uqqSfnDLbG+BnljfXxniXzUQq2v JzZYb6m9kF+qXmB9zRN9B1ILyT+NudkhrL9dFcg/Q9T6O1WJ9fdY/JwnHaxB /tmB/EgL5fk8+bNeWN/pav1FRWE95gt35S+9sB47yvMF8w3JB55shOHmKSlg oeWT8s8p3lON/DMuFfyn3N+X8ruD28n9u1JIBOL1pbAfPTMgH9WWC/ogXlun 5EfK/T1oixF+waEW4jNS5edw+QVH8pD8F0A2bshPZ2V+Q8j5FvK3/Vlw7HPE s7foP5imliN+oSqey2qQr2z8EC97eRBfjPPPaRHdtOfJDmaP3yUfMDiQ57/D fhx+Abxe8lVHTruo5/b8veIAW+iTkV84tyP0OR3+gX3+Q/27prigAnpdfAV8 oAb6PHhNz/7k+IeeQ8jtOvg/K6zfx7g/namNfLdBrdfxjbF+o9R6dbiG/Na1 wQaT9+pwmlWN9foA64NcJbzefL8r1utPaj2u6Yb8Za/iteoX5N8A4RAuPYH1 87HMbygbJN91URzAYzLA8FceXNlDz658sie4wBb5rwPWC+bJZ1p+D9RnblGN +rc7E7ykBvrb0k/PQWTdH7xd4hVKB1W8Lqr4PS7A83aQ9R9EvX9BvkQ9CaDX Qcjfo+T5O9N05CdaYI14Hx2L/HizDvJlsqofH/2O+Dqudv1oTfdImv8a9cKi FuJfIvWkOedWob4srUL9WP4Rrlcj4+vEucjf9FMN5oMTcf/Gqn5Y2yN/jhfu ysfd8bz7ZD7C+dPRcj3Fwfz0HfbjZWP07MO/Kh5qDX37Ynx8StZnC776Djfi OqgPXHwfet6teHMV6vMvGA+vlecPpR4ZyBcSb/P8PApAPvpM5Y/N0cgXP6v8 azdI+T1r5NMGKj8Mkni3pP8FIz+42iN/HM9HPt0VhHxhEL0YaFIJ8usSlS+C XyM/3FX5AvFvzy+hJ2otz9uZ5/ojX3wjz+PLhwciv4apfOrdHvXgsgXy6cdR 2D9Vq/zaWvyPr2I/LlBcIePxYvLWswfPVCyXu5SVfx3j5VpVyL9lqAdsrfTe 00/PERTuD96u4vnN+4hfa1lf3nQF+Z96435kTEI9cbdB/XqN+9NSG8T79gHk zzx7xPsHFd/FdRHvL6MRv0mRiPcymX+i8S8R76FSr8JoUwnqV4YJv/9BJeId 7Yv7pcnz+nObifCTczD/EofshvMinklAIjgsHvppKfGM5A3dsb5PqHz8RbH4 M55vC706vQAXP4I+CxTPknzbinrDz3FkNfS6/x3uREWKt6h8HP5Kz+Z1/A4b aE4JOPEt8o3xMPLJmLf4vNNA5M8mMrAA2t0W/quuPL8nDTiN/DtK5ZeFyn9O tUM+d/2iScMzhaEUEKtd8K7phx7vrV6/OZruXkG+SV9RmPeAo4ikvtTlrxx6 1M+yJXJ6g/wzXeUjL5Vvrqv8k1ON/FLC2O/ek/H4cLbKP5fl+YM53AP55TnG w25h8GuJFsg3z1Q9WCAcydcLkG/h/w3cXuWXCxaoD5vF//or9uP60Bv0z6Py 7bEfYT+VL/od0nMYrVS8SUMD0UdqPubK84VTIMbDjVS8PwzAfsAN+ZMWYn9K RmFf8u4Jv+pqifkwqf3BJzaIv4Wql//vj6+tQjw32aO+Hrvw5T9+fxP5PcR8 rFfzs7EC8Z+s5sNL9N+KN6r5PF2N+XD6FPWjt8r3ZWq/HfQW8zEB+x06KhzG 5zOgp7vCkVyt/LFMf5aBFyg/InaAorg+/AD6e+b5af0OB3Og4pYyAe35I8XB Fsj3CxWjQVpkWqMYfqHUsFnx2bdYXz8plvJgXl+nFUt6MK+nO+9wBNXH/kH1 P4ny1fxjux5JR5Uffan0YKf6my9Vvuut+q9gP/pK9aNw/470r6of4DbUQOV/ Kddvm9E48WMRJNtB837qU5XPDuPz/Jvynz+oetBC9beWCQfyF0bcf5pwKB9G vwvr/204r1T9mb7CBh4OP8/fyfiJrfogn30tP4/i/+B/ebnowVP1rwM4Gw1m k4timR6LERGNFR8W9qEDwXoOpnnvcDiNUZwiHEVHVP3xEA6jC13x/IUqvosz UP8wvwGUhH4D7VLx7qj2I7+jfpIvxkMj4L/ppvLzljWIfwtVj2fKeniP1qv4 B1ZiPvqp+j3wNebjqcxfFHld1Pi5oZ7oJYbCpR7Z8TLRSww9lvVp9hHq88ux /+JkNZ8nsD/j+imoTw8sUI+vq3p3RNiba1Q9RD/dnxejn0FroT/OCsR8Y35D eMow6HGkms/+aZhfyVeGaH5ULfmWh0l+DeaO73Ag13mHffhb5Gc+K/nag0e9 w26cqHhCLeSnRNQL3miJ/DaqQs9B1PEdjqBz5WDJvxxNiYo3I19QG5WvpZ9F RMNPIr/8JuMLontxyKcxwv7kq+qFn+QzL+qMfEzDlR/spfLbeplfV5qt8qkT /DF5q/q1cSzyS8UA9xejmsTT7Tqo5/1UfmXUS87BeMhVuAufQv2ndZLPzPu1 U2o/I9yV72H/QtLeMse7fyj89P0azM/x16gflzQ2RfP2mchHw6qxXum4+BfF QTyB9ezPdoqXK3+5Eft7Vg0zU4DiCcqvDoOf4o3y/H7klafnYFp+FJwqeo2m zCPgKI0phg6UYr5eyfxF0bejMF93ZHwh5LEd/uKm6Mm8n4EfoR1qP9n9hDof qcD8fKn2J3YZ2gXLTEUq/pPba+zAJX/mRlv1i6XrDVEP5jQZNCZ1VgwZaqFe TK6H+Xxkg/nZOwfzbWuD+SmcjP3ofjUfuXvwPPaq/nRti3rcSZ4/nGv1RT9Z +n3m+na3B/zGU5mvKE69DD1+UYWfn5kv91MczlnvcDA/n6fnQN6p2Kkc66kU +uSp1vADtefo2Z9Ms/UcQv/O0rOBGig+aon1FPQJGP2gWJpxGPMXK+svmpZ0 Qr5tq+b3ajLyP85TImmQB/Kvm8rXjeohvyxW/t86EPnIWIN8nGhAPXoo4+lC f/yEfDa4HPl4Rhjyb8Rj5NsUH+RHz0fIt5vF70ZTYxR8rhJ9xtMKZ+TTpVOR b7NrIT9+Dn1SsXzcPO4OeJ6zqv5Nt0B+DFD1L3Aznv8x9it8Zir2J/A7Bm7w AfZPtip/TgpDvfxR1pd5Pcr+N5gHVeL3/Y169uW68eA88bsduDQWXIQDNJMn 6j3qZc7KiIvYv3COGERHaqY4VvKNG1lH6dmDdhJ4mw3W6yqDnsPpTISeI2mM 4nRZz3EUEwbOUvM/z4j57qXmP92AemEjbKA9bTH/36l+htMg+Jld1Zjv3CSc b1RVof7aDES9LSnF/KeFY75jX6P+Hk5FvaNXqL/RH6Eezv4L8+9+CPWztRHz 31P6GQlkkvMTV+75AvqoUw/185o39LNJ6q877+qBet1d9i9+vGsv9Bcm4+/K PWKw35xnCb306QK9Sj/DIowntIK/SFB6CO+F8Y8VjuJ1Gehv/6WNPyuGk4Kx fjIlHrGcdAbry70C632bveQzxX6cUUfPPvyXHXid+PXmvB/5j0c2056nNW2z Bh+U8XWgE1bgm7bID5MswU+tkH/nVi/TcTQ1UrxAOJa2vUS+bm6J+jr2G+wP 96n6OtAd+a3SAvnExQn7rWrVv2qSgPzoX4X8vXci+kUjNP2b/fQl1CtaJ/Pb iRyXYH+RV4j66rjh7+Y/BcWRgzS4rCnXZdTZVq/iqedMS6m304f7poYsTqSh PyH/l2x/NnXBHiON6on8/6Q1Pu/SHvV4sKoH4+RAtTXfckI92OGA/D+/LurB G3vk/wmIF8WofmFsOOpxd1V/d17Cfq2uNp+GOF5Sa4HE6w9tvKY4XrsI+XS+ 6D2O718R/6g4mjMvg+3KoZ+Ci3qOYOM7HMR5v4OzlyM/OMKPIj8UbYhYDL/P Re+hXlucBpdJ/gukouN6DqeeDJ5ljXwfnq/nODqcB26rMcdRxykYzxFVL+of RD07KPkvgqbE9pX6HY56SIlT4LdSlB4uDVL+RfQQRJ+dRz3fWC76pv9Q/yhT zhu8qFTpYWQx9DG7Eean+CL0sXIg6v0BT8xnUzW/z+R8sCMPs8f+taIe5nPx AlwvSxt/to8532N+69igvjuNgD4XSX0MZKtT2E83kfkP45y2eP61ovdwDq8P fTeS2SCO7QP9Zyp9OJ3Hemmh/FnoNehFxm/Wy5x58Gs7lF5W2kE/cl5n/vnm NfK8iqP5+mpwYSn8wtSV4Oy5on/D0s/BaY5Y/2sW6tmTajB+9tD6M2Z/XWue ng20IxvsZIP5vTMH/FL0kEAlv0APS1U98GmH85MTIsAoWu2I/Cfz/TaMLPpj v+VYifqf+gHy/cIK1IN2gdivDPkP+d4wHvnd8yHyfbnK7/ULUP+nyP40lmIX adyAunyKfP9dubYAnxseif4TKbc58n+rYHx+rjPy/7Ip8ANPpH568Yp05P+V tsj3ph+Q/x/KeIP593Dk/wKpB6Hc1wP5P9IK+d+lNfwD/FAE926M8QZIvo/l +hNRL59UId9/E4H8Hy7xSOC+A6S+KY7lXv3A08UPhPDrnnr25bgMcPET+IWo NHCRHPA34wjUS3ZsjPrvawTn1MF6vxyt50hqr/iUDebvd9JzLJ2L1HMctXqH jdQ8HHxT1ks8ndyDetbTCr/fyBf+YLTSy/Cm8EddJH1F0tBS+K1VMv5giuoJ f5DxBH6gLcZLrUUfnWn1dey35/4LvbzyRT1v8Y/G7eiDn6CXZ9uhh/7Sr0oi XqE9jx1HKH1MkIamN69Pw/xPl3j4clI87ldoBz/QFvmS1klDKoCv/AT/eNgW fqBfB+jX2RZ6+TAW+s5U/d629aAHvC9HvGtZHxnvLeUHvHtj/azW1oMhlgtb SX5jD83/mPcHzi30HMyFzcBp4oc9OLMxOPsHrH/n+uDByIdUiHrGhfao/852 eo6gddZ6NlChFXisLfxBpqWeY8n57XodG8m5Cjxa0wMlUNFHqA95yj/s3Yd+ 3nCNKZaKdqFeHFH7QVqL/MiqH/3tV6gXedgP0Y+fot4eFv8TQgn/w/5Y9gfm +vHxVOTrAZIPA2i3teRP2vsGfqNxDurJrgeoJ/UaoB6k/YN6EnUZ+3N38dtN 6N5fu7dcvpRAk/+0En/RfEL4bjvrbnSzuxbPRvzLh/Ab09+DXxiyFPv/g86o L751cP1YiacfX5mLeuMs9SaY93+A5x1uCz9hlY/6Iu97mOvJrU3YX4bKejHw 2OpAqS9yPm3eP1rU7ifnZ7+KXoz8lzP83CPxB0ae8I+sD8VR/PVd8JVX8BdV t/UcxN/fBH8t68mTc7C+zL4D+ST4KviwD/wEXQB7i6CDqeC0nsPJ7Vc9R1La KXCzWsgvu06AL0h9SaBeY6GX9Uov0V9DH9lKH62c0C9uq/zGTiv1vkwV/Ea9 z6EPnwr4iyN3oI+qUuhjWhX6K4Uv4S/qbED/O1UaDu40xhn+r2wn/MQPIzC/ brHwm3We/FSVm5BMXm3gJzwb4/O5LTHf6b9BP/YOmO+XteBPTtWBn4idBv3l 1cJ8DxiK+Z9qg/nu/Q38z0tt/NmRfM1VjccK8/+wLvxGgfIPWybCX+yoRr7w LcT6+Uv5iVZPVfyUn1hVivXXT/xDAk9fpPrn5fh8yg6Jh+JoXr1dz1H8/TZw y5fIR7dywcH3kX8OrtOzGxesBU+QDXVzrvoSvFzON5vS4uV6bk1fLwOfxXqi J4vB9+shX7VcBH6pxc/sP3tm6dlIG2eB+0p8E+lEAOrREllfRmrhhf3ra1Wf zrdA/S1V/Y0Ue9SjVrL/DCJnRv3vdw/1Z8BE+JFjd1F/Fvqj3jy+ifpjMxN+ Yv+fqD+ZNdp+KY6aXod/mcvoR+R9A/9yXfb3RpovDftmZFFbW7+JNGRVldSr K9JP7kbBg2W98ZrTqFfunvAv6E8l0PUOGrvz2HLcL7AN6tn9Z9jvTnNAvZoc g3pWWQf1atcB1K+bGmYTP6iMkvokyzM7isvjUZ82vkX+0P467Y+9+YNqUK+W z4W/85CGZBLvGC/1U7GR94zTcywfGwVOK0b+uTJMzyF8Z4ie/fnxIHBuEfxN RT8wHUc+qpUJ5kjko9YZ4MEuGruRO+o5722gsQ/5ddOzHwWm6DmYohP1HE5J CeDC2shXvWP1HE39YvScQB9F6tlIkyLAu5T+HL6BH8q0wee9naE/vC8eRdrf Tji0PwLvMxMZb6KfUCwfCCP70fCfl+SAKIDqXoUfGb4eevpU6ee+i8YN6Kmc zyST41jo51UO/M9kP41debs1Pu8t/VBfPuoJPW+W/VFXDoMfpJf28DPp+6GX TqKfUD60E+tjjggmgld1wfOJ/CyiuX4n6Oc3pZcBj9Evm6L6HRP7Yb2Fyf4/ gU8mIB7nZD+QwA1/x/nZMm38WUm8dgTW86RS1LsVzlJfFZuv1xR8/xny07nG eg7nqHfYj79yBJ+9jXw1oz6YG1qKf0qsCw5uq42nA221Ay+1gx+KstJzNP1i qedY+tZCz0b6vCZDx8n0ogq8WdMLJ9HQF/BPx5SfGlqEfstCS/ilnIcpUu+8 tcc1RdHTQvgjOX81EE3dgnqRV4Z6GPYI9a8A+0M6+gL+oqoE/mnTAvRbUorh l27DX1LmH/BH3i1Q36ZfhT9KvYX9tPN5jV3p2Q70Vx7nwC+lPkV9NFbWSL3c 4581N6+oG9mMsxH/VDu/nc2T8DSiOfBPg8bDTx2eJPnf7J8nt386yuzPu6C+ 1vTFfr6qI+prRUM8j532fq15v57aHefT7pp+s/05qbbyW9qBsHm/vhj7VRpa F/V2/jOct6yuhfq6eifi0x/9LF5XLvGlRao+fm59R+plM02PJiP/vgL1csob 5LeXM6UeKE7gwYofy34lgiOn6DmEW0zWsy9fQT0x52GNXbgM/UxuKvu1QBo9 XM+R1HYYeFEd5BeL9/WcRLcG6jmZkhT/pvTVdjT278na+CmRsm9DX78pvSX1 xfiSlX9P+wp+IVmrlxRP03PQr5D1bNbfzoXod6wW/20g63/gX3JeQV+/1oX/ nvoYfutKJuar4BT0s20U/NXC2dBP8Y/lV3u2T6HsGfBf9pOgj1r9NANUZirO g346fQH9/OYLfRXIF0TacfowXO+Y9P/b85at0Od0b+in/TXoN6Ap9POx0lPL xtDPwHPwbyXiN4L5Qqn0P5VfM3A4/Cj1Fn9KvHcp/Lm7+Kt4Xv4S8dmm9NO7 Gv5rruSnZM7/FvGv0fRiSmaXLthPTXqNn4+9I/dXnMSXbus5jk/dBN+XeAby 99f07MeTr+rZhwuvgM/+AX+Wi/0NL5f+aUP2uQgO7oT8lnYe3LIJ/Nass3o2 75tO6zmEHBQvtUf+G3ZCz0k0Px9sEv+bQkd8UQ93S38pmYZ2RD6vVxv6vbMR 9bFU6kU07avXV+rfOPTP6fO12D/PEH8WSbOnoN6MkPUXQX/Mxn7bV/YzoTQ+ GecH9aR/GExneuB9iT/lCwZdKbkI/YOtsn/2o5GBqH8/Sn+pM3Ek+kUR8gWO DmS1AH7rhfiPduRdB/Wz67Uaqbf7xd+mUsGjCvFvlXJen0bzw7UEY8cd5P2Z NKqKgn+zV/V4YwT822YrXM9d+vd+/PWP6F+scUT95UjV/6iLevv1dtTftxKv WA79s6+cT/WX+hrH//yE86jGFchX8amor+NVPf3iDuL9dyn825sP4I83lODz lgaJh+JYHhUODpTztiBehXjxWHl/y5N7wQ9z4dfIZx+gH8Me/eHPbniBV3eG P1viqWcP+rcT+HxT+LPXHnoOp5/bgz+sC//l0k7PcdS5jZ4T6J6LnpPoeSuw i/JjoxuhH9fGEr8fPLSP+JMEpb+lW6G3Q9XQX9P9OL9aWQK9ZcSh33PnGfRV dQN+7IjoK4haD8J8BZzTuAttMkBPT05DXz9aLhC/fla+8NCM0q/B76dsgV87 uBJ6Oij5zZudj2D/cKs59HF/IvYbix3hxxocxv0dZH8TxVfqoT+ZJuOLYeeb 8Pd5GmbH8KwcGS/lqP5jQDbOpwYrvTisUe/zKL2M7I/3bRyV379TBP14ST+q G3vNwvo+oq0/Qzcu3i79EMVG3pWr5zjeu1nP0Xx4I3jyv/Brzuv1HMxn1+nZ jy+t0bMPeyi+JC/UNeeilXpuyMGKfYaK3yAj+jXs7Iv8V7YYvNgZ+c9ikZ6D yO5zPYfQ4BxwvAPy34T5eo4l13l6TqacOeALyv8NLsL52g5Vn10LUY8f26I+ czLehxD7afZ/Tfb2l/OUCjlPiCGbtai/38l+P4rmPkH9vfUa9XjrXPQXFks9 jqB7X6jvtzxDfR6yAf5oo+ZHsoJo63b1vvd91OuoXJy3tT4B/zfxAfphc/M1 dqcVo1FvD/dDvbb8xcbXbWN3WnMH9Tq5qPaZGZ+n0ycDNAE68LJWvz7/dXca ff4t6revqudHnVF/BzVAPX5f6nNXfoB4Uysb1NvMr+Ff+0v/MJpz5qH+fqVd jmN4zK/ojzWpRj0uykd/aIXmT0yJnLgc8Zz2GvpcEYj6e0iLjymVZ/+NenVN 9lepHFl7prZ/VtyNF9fSczJ72Oo5mh/UyH6bd0k/0cCXqvTsb15H4DR5AakD 33oNzl0j659PvwJn95OCZxqK9xl4bwDyZeAzPXvQ/KfgzBZSHyjzEdirHvzf 4ztgey3/cTeiUeiPfKTVZ+pGnf7BfmO90uPDTPTfHljC7xX+KPHkbRLPaFpz AvuLC5XQ28Vy+KH5L6Cv3g3h9wIeQ09PneDHF2v9VvP+omF/+L+eWjyy/KlV K8z3fe38PsuXum6F3uzyoLcPv4V/K/xRY1fa+jH8oH26xk3oV6W3s/Ox3yjJ Gv6/LS3S6WR3+MG4cfh8Fxf4vdLmOP+d8h70tu8y/GC5M/TWOQXPZyn7ixBO mYv1sMQB/o+GYP3sxHrkA8egt8+U3mb/iH7cv7IeE/izX6G/M0p/N5pjP9FB +mlJPH4l9Piv8ocfb4L/ri3+MIXLO6Ofu+sF9Np4pDyf4iS++6GejTximJ6j OOZ9cNrfb2U//NtAPYdzg3c4mNdifjhX6pMbf9wbTEuQPw09wYz9Gv2J/Rfv bSnxodoJ4Mz6yH/9Y/ScQB2i9JxMQZFga/F/afTgBvQ6VPx3dypqhnp9Ws7f jOT8IFD6BXOsUN8Ldks945VSz+JI+6NsHUfg+7WxdL9HP+k/NK1C/Xb8BOdJ F6S+EdEi+MWvZD8WSiVDUK+PPkT9dpiGfl9Cssbv0ST5PmB3qh6qTeBzwyVZ nxmUvRH+7tZyLV+l08JjqN97x8L/eWbA32XL+UsKLRF9evARI/oz6fKFay/2 Pon+nr0z/N6kDvCjMxvC73kcQH1vJfsR4rKN8H+3ZfyxPOAE6ntXC/Ez3CsT 9f2p9McTuOAE+nW9VP3O6QM/aFuKfJY7FPV9oJyXpLDXQ9T3cdLv7c5H5mM/ GSZ+II0dpD8Tw1OL4ReenNZzHOee0nMULz8OflKE/GjHeg7isjw9+/OEo+BC 8due7PYLeO885EsnnO+xDNfJFHH2ADhtFvzmrH1gJxf4yfvf6zmY1n2n53By /Bb8hfT/oujUDj3H0vSv9WykkVvBv2r6zTb7/PXg5krP2U2h3+G1kY8f2SDe 9rXgR8+X95Hz0DeW0HOeO/ynUc574im9Xm/x8/K+0NsYulUA/1ko/bJo+mQO 9NypEvrOWoj90CJ54TeSkv5Ev268nOcE0/dKz00eQN97QqCvIdr6N++H9udj v7FP9ocd6HQ69LlMvpDThtDPT6VmF6Dvn3/X6mUanRmksXk/0wPrI6Yv9D7p d/jZsFT41+gT0HeEq8YBHF+CfnW17HdCec4HeL7bjaH3kECsx9lyPh/J2/dC /5vfQl+P3SU+hmfi1+NFB5dWHc+/I+s9gb+7CL3PqYQ+O89Bv1HWf1Yi9/0c 562pyr8OnIj9z1pN34Y0npSI+TMovUc6oN4f1daLSxqHdZH6xVOfI3939dRz Ald3AD/RzpfM+/VercGF+civnzYH7/0E+bVZM7BHtDYST7oBP8RObaRe0fh6 eg6iq3XBX2j+3+w/fWvpOY7OWOs5gTyt9NyN+lQPFI7T6n9RGrlUgH01vbqa 89ZB+KFWyi8sTIM/2Kd9nlJojRH1apmcvyTRgBmqX2SF+328Cv5B2ndmP/Hl vQHiX/8R/xBD+dXwq10q4S9+sL0qfqLmMfzE2m3q+yW34BfcPkQ/8NkN+IWW j5Qf1d4PM/tV593wCwVynuJONlNQ/y+5wR9M2J60ufOIDFr4t1ZQykxWHy6Z ci+2B+28CX/qtw0//0j2B+35YPHxvhOOpdKOARp3ZKcxuN4J0bcnx+5Cv2qR B/zFtffhh78RPxHG99H/pe7iJyL54QSMp7X026LZcRX87Buch3PaRPhZvM8e x65b4C8Cq1Hfh11W/75NJfzEJPt8Oe/rXQE/sL/JWek/Hft//7AD81PrDfzD V154n2iNtn81pPKNIPiLO8r/zshHf2qmFNBUvrdc9peKu3GddziZ+y7Vs5Ev L9JzHCd+Di65hXwfMl/PIbzvU/DDXyTf8LlPwHRREp5pBb4fwc7xWkDc6NNJ YAd5X8+HysfrOZi+GqvncHo0GnzSDvn4l/7gxkrfx4vRf99XB/p+dg77r2m1 4U/cIuHPKm2h7+Vj0c87Lv3QRCr9dqicR1vL+3BGiliP/rx8X9sURy6nsD/r JX4wlnaUY37vid+LohGr4Sevi/8Kpac30H/MFD8cQv9swP7nL+180eyf85X+ H1+D3jeNg97c5YWzJrTtHvZbPg6ST2hz9Lf7e5SlU6C3jejd9bT3kKMHetCo ci0ejfivrdB7+lONW3D9u/j9NeM0bseXjmB/1llbwNl+/N5GrK9vO0g+4rgb WH8rtH+/wOyXo4zwz7bafiQ7nE1vJb5U3RT671Qi+w16Jf3naPa+gvP4/6yh f4dpyAffWCr9f4d+fHPx10a+chv6/1Lpv23dYRL/7uXIv0s6SP7gk0rfJw8h X83W/IupOx+Px37vThny95gC7Ic2a+tjSzqHlMp+gMOfYr08faHnZO5YrOdY rnyk5yju9S94usyXH8cVgYvlhUgP3nJbz26cj/MUtpAHuGvqUQh2XaPFvzX9 hn4157SX+NKNAj0byP88eKim38Fp5HtUx+Z83v2Iur6cB3Sj3p/iPC1Y+q8p NEneJ/HFv6/xNp5aXIdfNsr7SHEUcR9+Ixvvq9HDGXi/bV0Z/MfYNPS/rv4L v3EK53MUJ/4ignb9h/7qBjk/D6XvwuA3su7Ajyw1wW8kyPu9AdT7DPpb/ZZq 3I4G1Ue/tI78AxfvUYr0E9PporX4P4pfCb89sr22oJ4bPCRf9CBTRy2h2rGD fL+jB0XaaYJyYp8MTZ8ZtHOmFg9XftAZ16v9kcYePCgN/uXnERp78Xfn4V8+ 6AS/sjQE5/VdWsKf3Mf5C/WX/rbZ326C35oG/8auK+HHxV6Z/bfFyl4S3wXV yJf3TNLf5g7i55LYdyX8yVs5r0vhyyb038a8gT9J/w/zt/U18rHtRPj1b8S/ p3GP7vAr9d6A/86UfiPY7F9K+4BbPEH+7t9Dzwm8u7ueo7lBsp6juF0SOKAQ +TzZqOcQ/iwOPHIv8nlj9DvFl1k8OBmxKARcIO8rBNKILnqOpJ89wQ8aQ68X W+s5lf5uBX5VB/m8bkvwPOW/lzVH//FALfz8fw1xvrBG9u/dyXIp3leV97mz U6nbQuxv4uV9vWTaeT1K/GCgzJ+R/s2W+TL1rsJ6aDtH/XsleD+TChegv7pD 4h1FdfvhvCFF9i9hNB79cvr+DvQ/EP0hKpQvXHakIV/BTxfKF37b0BeX4Kd7 4R+A4nny/nJPutpYeyBnPpkO/facB/3+vRT6nzpDY3deNRr7zXXjod8vFuP6 sfIP1nTl6cHQb5l8QTKI8/ZjvQ2WBmMYx+7EejRIvIjf88J6PifxjuZ766Hv HhLvGN5ZB+v/R+mnx3LvKtnP0CeSPxK59k3o+0+l71ct+sp5xJQS+IvRFYj/ dulPdmePbPjvPlIf0zklHXpuLvFN5wdfKX+h6d8lgw/nS78IvCWNrx8BlzyG H2p5UM9RPHU3+KF2HpYVzLt26NmHL20D5/bR7tecrTaDnTsh/25bqmcD8SKw g3YexrH0cqGeE8hxvp6TyPtTPSdTcLaeU6n3bPAeyd/pdOIV/PhoLV+7ppP9 HvjxmtrI722fwL88scfvDzuuvn9pBz9T0hX+ZbX4j3j6q1q9H1AJf7KqlvhH mi/xjqGBTWdKPXYrgT/Z1B7vw5+9CX/SoC36dYclXkF0ZgT8SJn2DwyZ/fmI 8fAjD8/Bn7gcgj9+IPp2p54m+Amn/toDF5lOJR1s0G58Lxo7D347bRb6d/HS X+rCXp1wvjsuCP7aOAL++652npvdla+tgx/pqJ0fZQdy8R/wI/+0hf9YFws/ MsMF/uPSMfirTlp/iYmNT+BHVtrAbxQPg/+4KfuXeM7dIP6OaqQfmsDZ8+FH rldBX5G1gsWPtND0Z/bPaw/Bb48ogx6zMuA3yrX43k3jhEL4jatKv2tDsR/7 UOP3M/iTatRrlvczMji9jZwPcbactyVxejM9R3N6A7DFDuTbdCvFKRq7cLqF Yu2/7NMR6fJ9WzMf1P7CmdLLFfeDv04vVdwZ+Tn9hZ7DKf0ZOFvO46Ip/bGe jZR+X8+plH4HTHWRn9P/p+d0Sr8B/j8Wbu5f "]]]], "Output", TaggingRules->{}, CellChangeTimes->{3.758405261378477*^9, 3.759009094411817*^9}, CellLabel->"Out[73]=", CellID->1339982219] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->1081869047], Cell[TextData[{ "About 11% of the numbers up to 11326 are ", ButtonBox["lucky", BaseStyle->"Hyperlink", ButtonData->{ URL["https://en.wikipedia.org/wiki/Lucky_number"], None}, ButtonNote->"https://en.wikipedia.org/wiki/Lucky_number"], ":" }], "Text", TaggingRules->{}, CellChangeTimes->{{3.758380281559568*^9, 3.758380325918171*^9}, { 3.758404985811781*^9, 3.758404989811455*^9}, {3.758406016118944*^9, 3.7584060165356293`*^9}, {3.854023469462268*^9, 3.854023469463146*^9}}, CellID->1612587837], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ResourceFunction", "[", "\"\\"", "]"}], "@", "11326"}], "//", "Length"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.7583796714853697`*^9, 3.758379735561987*^9}, { 3.758380088569213*^9, 3.758380088766447*^9}, {3.758380318513714*^9, 3.7583803193748627`*^9}, 3.758404992920609*^9, {3.759503740314822*^9, 3.759503745687619*^9}}, CellLabel->"In[142]:=", CellID->981272946], Cell[BoxData["1248"], "Output", TaggingRules->{}, CellChangeTimes->{{3.758379681624024*^9, 3.7583797376296864`*^9}, 3.758380092896823*^9, 3.758380321230467*^9, 3.758404994528508*^9, 3.759009101895955*^9, 3.759503747595744*^9}, CellLabel->"Out[142]=", CellID->1764444338] }, Open ]], Cell["\<\ This finds the coordinate pairs that are at lucky number distances along the \ triangular spiral:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.758307737030126*^9, 3.758307749085785*^9}, { 3.758308123305419*^9, 3.758308138992836*^9}, {3.758375357599758*^9, 3.758375360055704*^9}, {3.758380032855719*^9, 3.758380033816297*^9}, { 3.75838023056177*^9, 3.7583802470647984`*^9}, {3.758380391566204*^9, 3.75838041562714*^9}, {3.758404231461878*^9, 3.7584042338851213`*^9}, 3.758406056321858*^9}, CellID->1940924303], Cell[BoxData[ RowBox[{ RowBox[{"LuckyTriangularSpiralPoints", "[", "n_", "]"}], ":=", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["TriangularSpiralPoints", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"1.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/TriangularSpiralPoints"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "TriangularSpiralPoints"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["TriangularSpiralPoints"], BoxID -> "TriangularSpiralPoints", Selectable->False], "[", "n", "]"}], "[", RowBox[{"[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ResourceFunction", "[", "\"\\"", "]"}], "[", RowBox[{"1", "+", RowBox[{ RowBox[{"1", "/", "2"}], "n", RowBox[{"(", RowBox[{"n", "+", "1"}], ")"}]}]}], "]"}], "\[IndentingNewLine]", "]"}], "]"}]}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.758374801067741*^9, 3.758374890744421*^9}, 3.758374922745802*^9, {3.7583797997804203`*^9, 3.758379800348208*^9}, { 3.758380111494788*^9, 3.758380116925457*^9}, {3.758380158183619*^9, 3.758380175827964*^9}, {3.758404242632964*^9, 3.758404254561058*^9}, 3.758405041439165*^9, {3.758405073650158*^9, 3.758405110325498*^9}, { 3.759008935826936*^9, 3.759008937409087*^9}, {3.759503757889477*^9, 3.7595037624783287`*^9}}, CellLabel->"In[143]:=", CellID->1279132408], Cell["\<\ Here are the first 1248 lucky numbers plotted along the triangular spiral:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.758307737030126*^9, 3.758307749085785*^9}, { 3.758308123305419*^9, 3.758308138992836*^9}, {3.758375357599758*^9, 3.758375360055704*^9}, {3.758380032855719*^9, 3.758380033816297*^9}, { 3.75838023056177*^9, 3.7583802470647984`*^9}, {3.758380344111113*^9, 3.758380351461541*^9}, {3.758405050553372*^9, 3.7584050517209597`*^9}, { 3.758406040926135*^9, 3.758406043086103*^9}}, CellID->838162591], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Graphics", "@", RowBox[{"Point", "@", RowBox[{"LuckyTriangularSpiralPoints", "@", "150"}]}]}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.758374960742985*^9, 3.758374972060505*^9}, { 3.758375030188692*^9, 3.75837506018578*^9}, {3.758375182688324*^9, 3.758375182973997*^9}, {3.758380128182886*^9, 3.7583801289972897`*^9}, { 3.758405054482452*^9, 3.758405055417062*^9}, 3.758405087733027*^9, 3.758405177483634*^9, 3.758405218589514*^9, {3.758405269213189*^9, 3.758405271825583*^9}, 3.7590089402398453`*^9}, CellLabel->"In[146]:=", CellID->711872390], Cell[BoxData[ GraphicsBox[PointBox[CompressedData[" 1:eJxdW3l8TWfXTSSICBJTYsxIIpLIPCd3JzezyESJOWYqSBWlTSVmVVOVFlVV VCnV1FwS2UrNVIlWVUlLzUMQEjJ9OXs97+93fO8fb7t67z3nefbez1pr73Pi OHxSxqgGJiYmpeYmJto/////TOX/y4qBOLymTvtfheG75My77+97UGwp/73U sAfYgO9VFp9TuJFgc56hvv9Yfl9nYMFVxS3xfcNK9f3zuH7x4pBor2snzQnf N+OH6nP83IbH4HM2V79/V2Hc34Lwz9vh1ep+WF+V4anAFup7TwvLBdvyT/J5 U76rPv9eYXW9iFUK2+E/0EcKWwm0o3cUPqjudwyYPlDx2ya4A5kJtuaRaj3/ ydc78GP1e/7ffnsE/WaVYcP5an8XFG4uuCVNTUE8rAVb0YM34lVhiDb2+ni7 wY7SBN8wjO07IjbJ0546qHwEq88Rv84c/0Y8rXmS4NZq/2WF7ymMeNrSnDew PS1Q+LUp6uHYnsK8Kc2cqa3K52mFN6v95aj1vBTchi1Csf7maj12SaiXdoK7 8M5oWS+PVOuvVThY7bcr9sN3BDvRNIUrBTtS/16IL/bnQL/3Qv35q/zd6ol8 mMj3G3MLby3ejhSo6qFBL+TvnsrX4RR8v7P83oVjeuL6U3A9jkO+FbbmtxVG PCOKdim8WMUvGtfnK4K7UFKoPr6O1C0V691givq+2gPru4sDSu9L/F3IRwL6 pPgXuX538q7Ffn5Unx9U6++SgvqMkp+7cXIw7jdUsCNnvyX54cOoNy5R2KIG 8Vb54ydyPRfaEIb6mYH8UYtg5HO74PaUivql2Q1Qr5+qethbifpY99vfn/37 jiddrsX5ttyLzz+U63fiF974fUtVD2lRqA8vwa48LhD3Hy24OydGIf+Id0bR A8SLc+R6rrQf+VWfd6Gsfrieg2BncjAqPjPF+vug3ijfFOfvfbX+WWbYj9Ph E9eMc7tSx9ao/yUTyl9lTvGmLmr9k2Lw+1eIF8cPxPU7qPWfCcf9R2gw35t7 75br83G13z/ewI5shvvzYqyHByo8ReLXiUYgfhwq93OnOwojPk60MBH5X6rO Q0fknwpNcR5Gq/oqb4j6aiv57kHOr1FPSxWeh/rkhDD8/gfBzrwuDdc3U/Ul /7gwPMJT/sWd86NRzzMF+zIHSX1ytTpPy4OBK7EernwDW7MH6pkdcMANJxW2 qAU/eYcCfyIfe1JBOOob8XYj+cfEkUXfqHisDML6WeqzNS2SfLvRnsbY/zmJ hw8drMH5icP1abLa7wG1/99RX5zWD/xgofaLYzQmIlX+xZufB2A9eWr/DzxR j58L9uMRKh6bVD3MKJT64ik1yG9iMfBB2a8XhTDwYA3m+dGPCm8X7E3u8TgP F1R97yHU4/QGOK8/o74oqzvq94+quQ2XbwmgkfdxPisUHlQNvu58Eec1TtXz j7G43hhZrw/vjsT9Tqn9dpDz6MYrTJHfOwqj/MYVhRmBc54jn3kKT6zFeb0U o8fdyTYWOEi+7kc3FS5T57mD2p+XKfa7pDf0prcZ9htUhPN6zgzn+8nxiyGt qrrREXOcb291fvtXYb+3/oercZ7vnsT3H8r9PThnAs5zoMqXmzf4qK+Kxwt3 6PdLwYG8/Zj8XmF/rngDe/OyX4CvmOF89zsBXCD1aM6bFHbDesj+FHDrWujf +DewF6WeBo6Q9fpTcTjqa6iKn5kf6k/Wa+JBvcNQv9fVeTmJeqXqpzj/c4Tv Ammr8IEtD/PG+Qiswvno2w/8gHw5c8swnJfXyCdPSYOekty/G6+LwPXT1XmI ioKeFgkO4FUeWN9mc/DBOdHb7pzzCPXSqRfwzhrUR5tU4Bq5XyC9ikN9JKr9 z1D7PSTYh65k4n5b1P6DjOCvSFPs/6sErHeR4K5k7QV+nNgA/JmG9dCWFhq2 IAsVn5gniFdfqedgyi3TcAveqD5/XoP4lKC+aZmKj7kvrv93LeITnI77e6v4 ZPuBP/sqvsg0YP2hsr4QjkvA/nuZor5Kz8l5VdibV58HXivr78I7fgX2fiDn 3VACPeazr1Ffd3Heebe2nrwAyr4MLOvLC6ass6ivHxT/tApCvcfj+jQc/EWO jXHefno6Yyv38KUJFjhvHyp+Ma3QLmDD9rMs91QMC6LtFTh/E6rxeYnUuwP3 m4jzeEHi15Vng+8oWM6PH3/gjvM3XJ2vRm5Yz7sSn2DelC71qbAv/5oBfFb0 zpo/fgsY9PVeUW/oHbevAR9tz9Tj7tSiP/ASyVcIjRkIXKXi43AUfNxb4hNI 7YbCP+XVIZ4LeoIv/1DxO56A9cvxz/elBfPhD35T8bwJfqCObTRsRT0aLh8+ tFMITTwHvrZe6TDxs9RIcpWGxoyzWnxR7LUynOJUvLLAB1Qr2J037Af/75f7 +3A+7k+tVDzNLHH/LxV/zQrBes8IDuKoZOznR6mvcJ71tuRH4VDer/Bw2ZAn V40HXi/5dKcnE/XYi7pMAk6tRTw+UfiEiu+8BJxnVzm/QXTPH+c5HueDPHuA vx7L/ZyohdLvf6VhbU3fRuM8nrXDeX1X/HIYifr1WxLxqfA9UfAL8NsNdX7d q3FeXX1wvb41OJ+h4BeS/NX58vIc3H+M1FcYnwvHetcIDuducYqfBEdyjvCb j8Lh/N0bOJg7ewKXN0Z9Dsd+UJ8X8op+V9hK/JA9HQYfs1kt+K3UR49D6KSv HkdQuB9wkOBw+nYQ6veS+r6PAXrxrdzQhwb5gq8Pm4EP2/cB3y9uKvxMq1R8 I3K13z8ptpH1RNHbN8F/LYVPIqi4CnzngvNDlyS+nmweAb3oIfHtwZvB1zQT /C37zreZEyF6W89306LQP60wQbw/8MN6h6n6S3gifKNwIG9+A/vzRYV/lvPl yLfLgC2aQm9zwFdcdg/8eFbhSFmfE819psde1Pw58BGp30jaoOq3oZyvcDp2 Bny5pA78sDoR56mp3L87DVJ+5G913k8rvhwi+e9MI/PBj/cVn0ar87+ov1Sw IeKTK4W3OYpuXAQfpCuceR988OL8qv98bxLlCL924qRG+P0/sl5vzld8UFcL PrAbBP/UX9brzz/HgR9Wgc94fCvww27BQbxN8W8zE8TfKgX8cB6Eyu7iN/04 2Ax6vk/hk9WoX/RXfuxbh/rcuVePDXRa4WS5n4HWKv4YUod4L7oEfZqt4h2o /LAL+Izme6KfdDBFvIsvwM/GCO5G/srvob/qQtem1fV1e+BHLSzBt32sejfP a0h00wvxXtG7w8q166PJ9y7ivVbhGeWId7CK/0vFv4vfw/XEv9bHOwd+ngaC /7lA+ek8FV/rkfCXJ7AffrQL/VwVwsHzs7H/5ireXlivwt7cV+EcE9TzUoVv 1YF/zyv8TOnR4zdwCNW+gcOoEdbP0s8WE3XW4zyi54qP5Pv1fLJM9WfAgcKz 9V1lEbAfTcD8iLAeV/oR+VfYkVoo/hV5q+/vJvwG/tgiuDHd6QF+uQnMveQ8 RtNPdeCb/32+U7Az1yh+Wi64G3+q7vetYF+eqfrfLxTfLFf98SjUI3up/hLz rCjG/M2fE9TnJ97AAfz5G9iH8xR2kHqw5SCF6TXW211hiZPJmIhWCpc2AL8+ CQbOkfr0oGKFByGw1FvhGMl/fT56g8/dwI90XvWfmGeG0spY+Ee000HIT9m4 iAMqPymp8J8LBXuTp/Kr50QfPMlH+X34f1saIH7JQBsxUDV8L/E1UqD49458 +C18rvw1zy+CH35Lvh7KlcqPw79HcpXqV2JUvPfu0/FBff1vqxF/yCNrcT7G vYFDOfEN7M3b4CeZZcBYafgI/pNLrXC+xymc0wh8201h8JUzNXkDd6dTr4HX iZ4EUOIbOIzuvdJjA21TWPiQoylRYWln6vVgUz7OuxF8QD6Kjx8rv/Sf4o/v BLvRl8ofOwl2oWaKz11kHtiOpim+KoM/NERf2RDdYEAMpZlD756tgF/E/KM7 L8T6CUJb7zPQL1Cl4qOBoeCnC4KD+HJX8Gk++ILja/vJ+i0UX50Ohf8u1OJv MPK8Oux3Vy3yufWI5J9PSv334A3FeuzKwQovV35sHfondniA8zJW4RxLnI+R qCcOFj9f378WAq+T/UVS+UHgFFOcF1b4T4FRVHkK+tFW5ev+9+DbfyUekeSQ CD27rvjRbRPy9Z3Kn18K9HGL8q+pP4PfJwv2pW3Qf/r3NfIZgvqk1X9puCnV thkyPiXXSBYZUp/FpYO6Ph3XJo6eycC/LVsofXGXfrMzd1R6fk7268oLF7ax OXEllO6ZI58FM+EXnGQ/fpz2M+6/tg7n4+TvyNdsWZ+Bl4zB/h5JvqI45Tf4 lTUaLo7m8RXwN7Eqn3fmyfV5UTXq49s5euzPQxW+0gznaVIe8EM5Xz0oFevj aWbQ5+IP9TiE7uTqsYFaKLxQ9mOky37gu7WK/w51RT+wTvgihPosgB9vrfjt cRz43LwW/LYM/QSR+KEu1CRF1w+Ef1m0SPxWPB2XgX5Z8TSFjwZo2IJnCx/E 0k/CJ9ZsIXwdQ+EW4LfxSbhevuzXiz86BL4bLvXoy9/C7xPmD8G8IQx8Cz4P 4dOuWO8GxYchqeDvCZKvaG4/AvzuKNjIMw6BH38QfYnhgUmidwobuS5Rj4kf JAAPqYJ++b2BA/hoHPBGc5yf8RHA6bL+aOoXrsexZAwD3ibny0h/ucEP7DTB 7z91AL9nCo6gFRX9MM9Q+Vo1GfOX72qRr9ZDEI+tsl5/2pCEfKVVQ4/27Yd+ J1RAj+4z4ru6HPnMuAS/oN2t4OjGosei/wkUE4v8lQhfxFGAI/LXR+XzQUfo Vclu6Fdv0QcX7pON/vAXC+RzqwF+orHEx5u3gk8oTOIRwL2NmA+1gv5yTifs b5PKZ+5sxOOl5I84dBz6mWzFj6sz0D+2qsF529VM+F1h4uFWwF1f4/z5WgIn y/49eLIF8GrRYxuOhj7wBS/o3Wxz4LG2OJ8bzYD3NIXe+Sp8tSHO4666ZYJn afmlaNq6H/zQzhT8mf0N+PI/0TeiL4LBJ5/Xgi9794d+1Ak/BJAz+IXOVYEf 6SX6ndXPwY/WS8Bnp59B7zbYYJ6RJfM0J9r6K/gveif4M3Mw+NK8ixagGwbv zY+nzduZQBOcwZfXWoNft1iBH+c2xfU2mUPvBlWAj8+AjzjhEdbzh/B/KDu4 Yf2fCn9G8PLB4E9X5UeK0qB37RRf/nQV8YnSllMcw3NmwS9f1vZfHMuffww+ m1uNfJdc0L4fwhZiqMP42Hk99mHvs8DWz6CXO87osTM7nAZ2uAW9tDsFXNYM ejjlGHCl8JEv3f1ZjyPpQjFwrvibOPIvBJZ5J8XQ53fA/74aZiPZjED/EQ69 p8Sp0L9jku8wOpgMfzD9CfJn9jn8xupH8CuNLiB/BZfgV5r/CX/isA75LLEf d7LT8zi69Tf0MGO0T0rI4kRa5aPhlrynMz7f3R35bfsHfn9dnsc58mKV79vy ALELT1+GfmyB5Nuf3R4ivzYNpL55OeoXz8/r8/lkHvrZEqWHy8ejX/9M8hvF 1/JQ39fU+cy6jnw7qXy/XYt4PdTq2xDDjT6TelbYyBNXARdIfFy4M+qds27g vPb9GBgPbK3oJfSd06xxPr0WALfW9lPvJ6/PBH5b5a+6AP5mvewvhhY6g48v Kn528wC/yPO4+n4huaaf8FFwDfh4ogH90JBK8G0r6AMNE//lSoZJ4MPU++Db D33Qbx2XhrUVPT0Mfh0jA5A6w3aZVyQKH184VFDkukhbbxLNlobEiZdN1c6H kUbagm9NFf+etwHfvnsWfG4ufieQv4a+UGQD8Kt9Z6y3QM3TTrtCP/ooveya oJ4nCP/E8tGfoZfhonfx3H+Q6LXCMfzWAD028rb+ehzF6ZnA019CL7/sDSx0 b70pIgTzRaZk+S+0pCewdSucR58EPfagefHAC5to2J9mxQIfM4feOpIeG2mq QY/j6J0I4KvCX3F0dCfyv1Hl/2UI/EIjwUbyckP+qyTf4TRqGPzGCeGjUJoR jXh+Ugm/NIDEb9Fg0dv6uMNP0H2Zj3WnRgPR3y2TF1psyViM/GfFQV+3mSP/ pZHQ10eF+LygA/Lto/Kf2Qj5nb0D+m4n+Q7mUTHoN1c3QH49O2B9mWqe6tRM Pc+ug55q/9Wh/9aixcr/5GZhvw+rkV+7qYjHOlUPeww4H9WiR3FsngR/WSj6 msCbhyC+K1/j/Np1Ev1QuF6vOwC7af1Kvf/NbAucdh96bNdajx34CvSMr2j9 S32/mGkOnK3tlxPIrnqt4LFaPjmWtv4DPmmpYYolGgz+Ha34uXQr+Ke50mdj U/AVw9/TtjXg59ZqPvnuEPBzYTX4+4dZmPcdeA29jv8L+mwlOJhsb6EftKiE fhvz0I+aiL/wot1rwO8J/4Df/7YF/07fJXxGbb6BHq8cCn5PHAM+r/7gtej1 f9+/utSnSzJtyTIVvp+l8Iom0OONNeI/aI859HjDLqwvQPUjZZ+Cjz9U+vp0 JuLTRcOGOHYyf1/iN0G7XXECt1wPvmwj+UvkaGfE/57obRyfvCl8ozDxhevA F8WfBPGOq3ocwFf+BN4sLyS58p7LwIOE3xwo+5wee1DZaWAv8SOhVPmLHkdS 2jFgWzkPRLlH9TiRLAqBPbR6oQTaXQZ/dt0U+nx6BfzYMRPUg8/TQPEnolf1 9eA4Ws1Da1APn78Hf7O1CvUQfQ56GHhL5bcF5gkl15DfNVeht+cLNNyJnB2h x9e+h56n39z+1W8X4mlWOvQ5qhTY3wV6PGb1zXb7gmKpwEnDrnzqMq7nIi9Y efKTJdDr1w2R7+iDqD9v4S8D30V9Y55Xr8cRkQNkHv22qoeP56P+B4jexvP0 j+G//FX+u3aAv23+Cvl/uE3qV+EYHvkNcEfNX9X3y1Zf6XEgh38JHHwL+n0W /oZJHqBXGgZhvsInhd+608PFwM+0/NX742tz9DiarGbrcRxlzwTur+H8RPrZ H/wj7yvkx9NkZ/DTUdV/resAfhus+L68pXofRvXLCWboL/C+VzSNjkD/5VwF /r/XB89fFrwC/4eMRv/ywVPo/8gh4PfD4k88ab4f9D7lT+i/Vzj63/KtGran HbPRLyd/BT/gLn4U+n/Xt7Co+lNtfylkelRbYFkxK1wyGnpxVfSyJ83sBn1o rvQi0BF+4NZjzHvtZeDty9W9sL5N0r8EsPdh8a/k2gT6MdIL+nUVfodvV0WJ Xjiofvl2FuI1vQrnf34s9GDza/iD5mmId6jSg4zL0Nc06Uci+Hfpxw0KB/G/ WcAbSjXcg58NAqYjoo/cKBNY0pH1Q0RLzEeZRR/tqHMGcIHMe3wpMBn4SmPk b4BRjxNpWjjwWA3nJ5H/PvDDQlU/G76Hnz+p6mf6Ovifu8ovnHSFHq5W9WTV HPFwU/U0vSH8E+bFUZLHnL27IrzL4AfuDUX8nf9CfQx7ifyM+hP+YN4B+Ll7 l4Uf6Zyql+4lqJ+ntei/f5ABoyOFzEH93HGWhtgQIM8Pe9GvFaiXMJk3p1Lu WPiJnsdRX8nSD7ix2StcL8ka9dFqHPxqnPTvYTzGCf5xbUP4hxcumC+8Z4r6 CLSEf5yq6uOdAdh/P5X/oRmoh8kV4I927YQfFY7nJnZ6bOR7bYBvPYY/cLQB Pvk3/MFH4Fd2eE/DZtwf81tmG9FDQ2JT4GAn8Ek7Cz3uQZ80Bl5qAX451UCP E+ij2gzBh5W/GF6Keex1M/DNsfWYf05rAH8RMw/60VzpycI/oB9Cz/V8FbPj LeHbsxXQi0NPwc/XND9c3/91+hDP06zK4R/+bjJP+uvp0u+5U8o18H3lGQ07 0flb0AcH1wai/8P3m/u4rEulnCDtho68cyT8wg4f6MV3HaE3JfKCYXfO+Bx6 0lLz0/X9/MbF0I+uNvAPSYgPeWv1UN//hX8EvxKj8Ud+IC9G/0TDNf6o7wfn PsY8IF+LX3445w7Bfm7I/qPY/5bEgypUv9d5HfSmTvmPd28ifrZKb859Av3Z pB0gQxJfdoT+uGq4OIk9v4UfmSr9RCLP/UDqVeEoLp8GfF9eQAvjHVP0OIgX vqvHAfxyMnDBamEY6oz5FWcmg19evw3cVvqPYLoyCvjjJvAby0focTRlD9fj WNqXpcc9KWkw8Bmpt560dDL064zoWSLtG4Z5R0/lV1pfhp/tif6a8j6Hns9/ hnqpWob59ewy0Vsasxr5ydXmB3l+NLcl8pk/Q9uvDVlODt9uYdaLyu/Xir90 8c+bXVjaiw7s1RJUYcg8gHrK/eyl+M3QImfzh+Fp5L5IW39LPuOD718NR72Z uU7p8mhcEhUEot4eXUd9mlujXlY0wPzoVlP4E8tHqJfCRvAn4ZvhT+V5Q329 9HyWLPuLw/nh7KVR4sd/rgM/9F/yFt4nrEU9vViKeZJXDeqpyUH4243Kz/St gd/vrOHieO5ocV3O7/va9gzJPGsP4j9Z60cMvXjzDZm3KJzMFgovlxdGbdgb 8zQu3aot0Ir4LLC8b5QfQDEn9DiErI4DL7UEH4z8WY/jqLwYOEDqI5mWfg89 +lzpk6Uj5sWvGkK/5q+EHsUrPepTFyX6UyR6FEfVLwOFfzFfjqXVZ0W/+ab4 1ygK2Qq+3i3zCT/KwPmgZfegTzMroUe2x6A3dvGYB58pht7EnIF+7JIXfG1p vvRnyXRwMfRlWjPgswb4kT6/4PvZYdCbuwZcLzxEw+7s+yH06zNr+A+OxPOA QPH34WzdDX6kkSX0J7gz9GioGfTnJvwcfSx6axSfYN34QNGv0q/FcfJo6NFN 6ceT+OUIxNMg/JvMoeWI9xfl8C8DI8WvKUz8Wwhw4D34l3nBehzGN4L02Ie/ 9gfOlvdLnLmJL/CVzfAzRXjfhwvkhcsWbKuw20DwzZ8ewCuFrz0oyh34dFvZ P9l0AR7VFPwz3kWP632esx7H0QIHPU6gMHtgo/I7Mz5BPcWq+vG42E/87zIT +JnU2X3hf1X9pA7DPGGFxCeCMmLV+98yrwyizuj/KUX6d38yTkV9ud9Dvb2F eNG/t1FveB5jpNYMv/OfqrezRai/iiaYhwRnabgVjfgM/tchSQyHoae835JG W9ai/ip/hf/JjEP9HVuA+VlBFOovuQGut0v6Sz92+wH3H94CfmeNL+Y1wc1R f87f43nFQak/Ax/piP36m6P+vnOG/y+UeBk5d6HMBymmBvV3/TD6CetK1N/1 UvhhPH/pxRfzoQfmov8pvNSI/Bx8Dj4q2yT6rHAUW6/TY+KxXwBP0frpPG92 +wz47nn4pfxVwBvC4JeW430bxgPCSgMtB7YTv+BMG9BP8mI78QOUuUiPQyhr oR6H0YEFwHFW4LecuXocS9NnA+/S6o9SKP8g+G6RFk/qRZwN/j2v9DCrFP15 S43/KIlM+sAPXJT5cTSZH8D85ZrMjwz09Wz4jT0Sv0g60kjmF3TsEfRxlj30 p/oO9NBmAJ4Pz70l8aKoDfBD5SO0+LSjf5Qe3hylxcecH80c/ddX7dOJIrT4 eLLl39C3JbbwRxuTcT2fNtA7d/A/fWsDf/SwRuZTNMMa+jdlOvT5U0voX8e/ MV/vIfMoI/f6C/o3oQ76FnKuj+hdVC30LcTFKPP2KuWPjrTBvKZEnm8k89WG Go5WOImnmetxDCeZ6LGRV9cJ3/PW/8Bvnav1OID7vtJjH35WAZx2Bvzm/gJY 3FPmwYiCp8AF8gdkDnT3sR670dxHwJnt4acy7+lxJEXfAfZopvzVbT1OJadr wNFSXym0/wDqaYuqr+0v4d8vanrKydR6GPyi/H1Vvd56s8SXpwl7xJCds8ST ksU/hVP2Kvip1trzhnp/Prsd3hc5JvUTQA3XwC/3+Q/11KkT5ncH9mgXdKGP nuyr3hDfkxJknudEq37EfM5k0XPxUybR23b1rkwnl06agFUWb4kCHr1b219b 7loIv3UmCX7qyB1cr4e9ibyvVtEOfj6oPervSXPc/5At6m/8R1jfh5pe5Afx NvgPWmKFeqNhmEd+K/6yvs/5C/V3pxp+acEv8Ofx1fBLn/wFP9VY/FMC/2Z2 Ut4XdH2F+pu0AvPDO1o9GVL56C3ko0SrT/s0jn9bzgdvfQo+azVWj5P4xig9 NvKhLD0mXjAEOE17gS0vkP/C+eX8/+C/UtOBs0LAXx1SgQs6gq/CEoEzm4Of LsXocSx9Fa3HcXQzSo+T6YMI4NeN4McSGmPesash9DNL3ufpzk7iR+Kp9hD0 c3IV9NJtDvTBXfphoh2J0I9Dd6GXVu9BH/++Bb3sXAQ9+vQm9NIlD/P+ulLo pbfZPOnXd8oL6d0poSn07NkP0MsB6ZgHadG4ZXemqETeh8mgU32gh3HnoY9L UqGHBxPw/ftafdX3/20PYH60tjP0Me0F5gPu1vBf6zyhj1ebQw+tt0Ifp4o/ rfc9ttjfhxKPaF7eDP4M7/PG8u1+4icMEbXQx839B4i/iK2G/6q9Ar3sJfFK 5JNLMK8bpfTywnTM94qeQy8H1cK/TZB+KJUPzoWehsn8PY2tZD5r5Gll4Mfq U3qcyAUn9NjIdkeBH5aCD2OKgdNy4c9yfwRe1AJ+qWyjHidT5no9TqEL64B/ twJ/vXLB/Oms8H8ver4a86YDqr7Om2K+NEjV1/GnybL/yDrhb1rev7/4i+US vxi6WIjnOf7iN4z07kT4s/kSz2h6bxrmlbmvUY9zluL5UON/UW97VH19X4p6 2xeFedOuKA3b0/n+mB/N26IltKx4r7yv2JsaDkI9RS6HHyvurWF3vhqPeqpx Qj1dnwF//2EnDQfyzom432B5HyiEk7rCD3o1hp/6xx5+f2Yj1FPPtXi+1dwM /upgtfQ7VCuCE8vZ+zCfTBH/FcuuBP/lJf4/gRvcRj2tV/Xz/CXi/VjVz0e5 qKdpT8BHY9yFTxVO5DXd9DiGP+2ix0b+xUWPiQc6AT+8LnrCxQ7AeIBeafge z9t5g4Wp8NeNVsBpc7UNdCZjS2C3aPDZVBvg1to8t76//NpKj0OoYVM9NtAX FsCLrMF3Po30OJUOVQ0WHKv5rdI0sn8N/GdD+K3sd9AvO8v8K5Fyx+H98FXi T+LJqbH041wk84hYenkIz0fSa6CnB6EX1E/mNUT7V0Bvfn8Ev/btWujrvzfh z4LhX2n9Deirxz+Ydx2/Bn11GYX3VTzk/RUvaj0B863N32jYjSx2Q1/dusG/ Tbf/5ckv29MoN6dM9DZ71JKp/8T0Jv/fJb68oiM+XzQU+nrLE37vYzfoa8lQ XN9P9DSc3XIx/1oq85koPlkCvZTn6RzDDmeHy37xvmosO3yFeZe831ivp22c B8v8r+9r1NeuNtDP9Zp+FifxM4dLEu9pMv9M5v6O8HNdn0NP2xnxvO2E9vmN NP5yEvQoogL89onE18jvPwafbVusx/H8apEex/A7C/XYyGsW6HEU35sHXH4N /s80H9guDv5t2zt67EG/5QBbyftD/pQ4UY+DaU22HofSkfHA823g70LG6bGR fhytx3HUbSTwj5qfq+8XHp/CPPYnLR/Uk7KnYB4boep3z0jUq5nMaxMoYi38 3jL4Z7I/hnp9qxr1uuUVnt/9I/GPojErUa/OFajft+wwj4XfC6MXtpinZV1D vf6yCf3DyD9Rr3td4c9ub9Di507zVH3G3NMMQYVhharHQC9z8X8Ox72GHdrd m5a/re23C5/ZhfnbojGozxdPjvTPOZxCnZzh744ux/0atkd9FteJ36VZ0o9F cMkM1GtVE/i73+/iefDexqjfK/2wv0kSLyPvWYJ59AN5Xh7DVu/hfdxuZqjv A+MRH5vXqNeQjqjfJXK+e/I/vpinhT+Cv3v0VM6vwvH89UPg6Vfr5PnguZvA ZeKXPXjWdeDScRq2YVs8L2Xrntr+e5DxN+CFXUykH837FfhYS/DbkhN6HEt3 julxHDV8A/ekL4r1OJl+OqzHKfSiEHh4E/Bj6kHgsfI8JJ3sS9B/5DSG3nd4 Plz0eqEZ9LrPavg/edxS7we1fyw8fCwiH+9T0N0Z0OcDVdDvXbOgzxYV0Gf/ TOjf9Bfwi9VD1ftEMj8xUOlNPK/bL34xnBZPwvOk+CvQ874n4N++vAS/6NEM /vD0WvjF8taYz037BH7x9ADo+yr5g4JWRPL3WRkU/a9G6I3Jfy/0ft12/EWN V1tNT3rLvi7YXSxykvfl+1C/KfADluMxj6noDv84tnqZ3P9X+QOLAN4zDX4g zBV+4OpurLeLJfQ+xhn7bWoGPS+9IfNMOlQNP3jkJd7vHSzPG5N4zZd4/vaH mp/89BLzFeNz+EHHBpdE7w1yvtPZsyX63/YP4Qfj5XlujML1/UyGHifynHQ9 juftqcD+Eu8wfjcO+ILMp2w5Fc/reIP8gVsLHhEGfFb260sGHz2OpP3dgW/L 84VY6tFVjxNovLMep1JFR+DnMi/OoIF2wPJ8gdNpQl/w5WfS76WS6VL4neNN 8XtXS8w/94nfSqZTj1C/8/E+F12Zh3ps+wp+8vU6+MW4SvjJfhnw94ulP4kg 13dQfzvkhf9QGlyL+bGVPK8LoZ6MfibzMw170rw2qL/Mj1B/65trfJpG3vIH dfaUL+/HpVPBA9Tj8D7oX7TVH0i+VOQt74/3IdNLGn+WFT8PBr7USjModnw0 Hd+PaKbhjty7DPXMuahPM5nXp5HHNNEzdm6C++/Q+KXej5p4wv8aJH7EHTww z5zQFPU5eAvOX4U874pm5zY4r03NUa9D/oM/ta+D/9R+Nf3fE0X9VP0lp2O+ 90jmz+ns3hr1+IM8b8jgY4OQz/L74NPafcL3Cidxxz16nMhdd+txPIf+qMfE +d8B39WeJ+f5c+FmPfbmCxuBL8jzDQeuXA/MafCn/muArdqAb68v1ONYqp4H PN8SfDnlfeD2GnbIoO/2gj9rG+Nzp4eYzzy0BN+OPKL+/sgC+l4egHnC4sbg 57iR0Pc+ZtD34FzoeW4D+NPybDxv9cf7KDSjk+gRlUg8o6mmE/R7ofa+VV4k TWoP/bYTva7PI/SIxv4BP3rjG+jr3DwtHi6U4AC/WCjPyzqRixHzmpzfNWxD JqOh59lzoN9puZgX7pmqYU+2fgT9nhAEf5kwBs/f3tX4MT+IrVrBLzQW/xnC MUtw/6Nav5Rv4IdV0PdGzaHn1nheSJObQs8PYF5KK8zhP8vgfyj6NfT51y5F 8nz1snZ+h6bx/rOYh32s1aN9Ojfugeffo7R4Dc3gD2qQLy5Hfabby7yB8++B L9Pb6XESp9vqcRynt9Jj4vRmwCaXwJfplnocxOkWCssfLLpyegOFk8Gn6fL3 UPV4Nfg0vVbhAVp8HSi9Uo/dKP2lwp7g2/TnwPlt4TfTH+qxkdLv6XEipd8E pqbg1/QrwP8H/rovRg== "]]]], "Output", TaggingRules->{}, CellChangeTimes->{ 3.758374979131558*^9, {3.75837503157605*^9, 3.7583750496884737`*^9}, { 3.7583751799436617`*^9, 3.758375203914423*^9}, 3.7583801317591457`*^9, 3.758380183124422*^9, {3.75840509073319*^9, 3.7584051155074167`*^9}, 3.758405179067046*^9, 3.758405220426038*^9, 3.758405272662887*^9, 3.759009108861803*^9, {3.7595037724721317`*^9, 3.7595037975451517`*^9}}, CellLabel->"Out[146]=", CellID->1631666198] }, Open ]] }, Open ]] }, Closed]] }, ClosingSaveDialog->False, WindowSize->Automatic, WindowMargins->Automatic, WindowTitle->"TriangularSpiralPoints | Example Notebook", Visible->False, FrontEndVersion->"13.0 for Mac OS X x86 (64-bit) (December 9, 2021)", StyleDefinitions->Notebook[{ Cell[ StyleData[ StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb", CharacterEncoding -> "UTF-8"]]], Cell[ StyleData[All, "Working"], Editable -> True, DockedCells -> {}], Cell[ StyleData["Notebook"], Editable -> True, DockedCells -> {}, ScrollingOptions -> {"VerticalScrollRange" -> Automatic}], Cell[ StyleData[ "Section", StyleDefinitions -> StyleData["PrimaryExamplesSection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData["Subsection", StyleDefinitions -> StyleData["ExampleSection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData[ "Subsubsection", StyleDefinitions -> StyleData["ExampleSubsection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData[ "Subsubsubsection", StyleDefinitions -> StyleData["ExampleSubsubsection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData["Text", StyleDefinitions -> StyleData["ExampleText"]], Editable -> True]}, Visible -> False, FrontEndVersion -> "13.0 for Mac OS X x86 (64-bit) (December 9, 2021)", StyleDefinitions -> "PrivateStylesheetFormatting.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[635, 23, 168, 7, 70, "Subsection",ExpressionUUID->"9855beea-657d-4372-9c7c-b800b12184bd", CellID->462042388], Cell[806, 32, 279, 5, 70, "Text",ExpressionUUID->"c3fa75c6-be05-407f-bae1-d67069e9b563", CellID->13078159], Cell[CellGroupData[{ Cell[1110, 41, 7344, 184, 70, "Input",ExpressionUUID->"50838c7c-ddde-4406-8a3c-bd084a944bcc", CellID->443871870], Cell[8457, 227, 1548, 61, 70, "Output",ExpressionUUID->"6fec04da-361c-434f-866c-969002c109d9", CellID->225806864] }, Open ]], Cell[CellGroupData[{ Cell[10042, 293, 145, 4, 70, "ExampleDelimiter",ExpressionUUID->"779b24b4-3877-4b1c-8a08-135e73a6f502", CellID->1132819851], Cell[10190, 299, 249, 6, 70, "Text",ExpressionUUID->"bf378e07-8b27-4494-89f9-f9aa58da5c68", CellID->697960947], Cell[CellGroupData[{ Cell[10464, 309, 8607, 211, 70, "Input",ExpressionUUID->"1444eaa3-b1ba-4aa3-bb76-bc53161d22e0", CellID->1710216102], Cell[19074, 522, 4687, 80, 70, "Output",ExpressionUUID->"35fad4f2-30b3-468c-a64c-693fa6cfa9cf", CellID->421083182] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[23810, 608, 145, 4, 70, "ExampleDelimiter",ExpressionUUID->"4213c50a-13a8-4fb3-9278-dd4c8f4bfa29", CellID->1860705102], Cell[23958, 614, 268, 5, 70, "Text",ExpressionUUID->"9e1cd7ae-9110-4991-8240-26c72d5a6fb7", CellID->1925797651], Cell[CellGroupData[{ Cell[24251, 623, 16359, 393, 70, "Input",ExpressionUUID->"f0073bea-f0fe-47ec-bc63-03386fc6e736", CellID->509996249], Cell[40613, 1018, 9390, 158, 70, "Output",ExpressionUUID->"a06875d2-ef40-4c9f-b4b1-7a21241c7cb6", CellID->198811315] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[50052, 1182, 145, 4, 70, "ExampleDelimiter",ExpressionUUID->"8bb16797-7d5a-40da-bb0e-9ab6d19f291a", CellID->1213781700], Cell[50200, 1188, 556, 13, 70, "Text",ExpressionUUID->"9d041ad0-9d54-4ffb-9c36-01cdaa163ed7", CellID->2013137765], Cell[CellGroupData[{ Cell[50781, 1205, 8070, 196, 70, "Input",ExpressionUUID->"fd7859d6-3573-4f3a-a373-1f794af7121b", CellID->744314247], Cell[58854, 1403, 353, 9, 70, "Output",ExpressionUUID->"4de6d9c4-d6f2-4f7f-87df-bb386fe3c22e", CellID->238967095] }, Open ]], Cell[CellGroupData[{ Cell[59244, 1417, 498, 15, 70, "Input",ExpressionUUID->"7322a9e6-dee0-4d89-a949-96efca3d0402", CellID->1155380441], Cell[59745, 1434, 403, 10, 70, "Output",ExpressionUUID->"cc31795d-40e8-4bc4-bcca-b0aad626de55", CellID->247600314] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[60209, 1451, 167, 7, 70, "Subsection",ExpressionUUID->"105c572a-512b-4603-b64b-01948029012c", CellID->540091361], Cell[60379, 1460, 453, 10, 70, "Text",ExpressionUUID->"86c51699-a36d-4d41-88c1-8c9a95e0a9c3", CellID->1039848554], Cell[60835, 1472, 8201, 200, 70, "Input",ExpressionUUID->"9e18d035-867c-4076-b670-df31fed378a9", CellID->914425330], Cell[69039, 1674, 278, 5, 70, "Text",ExpressionUUID->"668b78a7-d843-46a9-ada9-c656ba8e88dc", CellID->1077324486], Cell[CellGroupData[{ Cell[69342, 1683, 17846, 415, 70, "Input",ExpressionUUID->"700f78d5-fce1-4859-94be-757b7c2afbfc", CellID->1012815160], Cell[87191, 2100, 2528, 47, 70, "Output",ExpressionUUID->"e9c83fda-baef-4dd7-807e-990e147f352b", CellID->76367517] }, Open ]], Cell[89734, 2150, 170, 3, 70, "Text",ExpressionUUID->"ef537a26-5493-4679-a9fc-35fe9abc05bd", CellID->843341047], Cell[CellGroupData[{ Cell[89929, 2157, 469, 15, 70, "Input",ExpressionUUID->"d43cc2a8-3193-4e8f-821f-a57605c60f59", CellID->669943960], Cell[90401, 2174, 212, 6, 70, "Output",ExpressionUUID->"b6a021a6-eba9-4c7d-b972-a5acaa4c0bee", CellID->1731175762] }, Open ]], Cell[CellGroupData[{ Cell[90650, 2185, 118, 4, 70, "Input",ExpressionUUID->"5c098a3d-4453-42db-865d-a491089c9cda", CellID->991672100], Cell[90771, 2191, 159, 4, 70, "Output",ExpressionUUID->"19a81496-de5c-479e-977e-86d5ca5615b2", CellID->1332600328] }, Open ]], Cell[90945, 2198, 340, 6, 70, "Text",ExpressionUUID->"49606e22-fa60-4545-aca6-af4e5057c233", CellID->1606466798], Cell[CellGroupData[{ Cell[91310, 2208, 733, 14, 70, "Input",ExpressionUUID->"f41d9498-1165-4f9d-93e8-529fe584e76d", CellID->2071963721], Cell[92046, 2224, 15001, 249, 70, "Output",ExpressionUUID->"0c66c3c1-9235-4202-824e-df20ca0c4341", CellID->1339982219] }, Open ]], Cell[CellGroupData[{ Cell[107084, 2478, 145, 4, 70, "ExampleDelimiter",ExpressionUUID->"a8aa6597-6a69-423c-b53e-7cd6d9863643", CellID->1081869047], Cell[107232, 2484, 515, 13, 70, "Text",ExpressionUUID->"1562fd0f-671d-41ce-ab92-145301ee5b57", CellID->1612587837], Cell[CellGroupData[{ Cell[107772, 2501, 455, 11, 70, "Input",ExpressionUUID->"f4eea8bf-9c62-44cb-872c-9beb963752a7", CellID->981272946], Cell[108230, 2514, 282, 6, 70, "Output",ExpressionUUID->"137cff6d-8040-484a-882f-ddcaaa127f92", CellID->1764444338] }, Open ]], Cell[108527, 2523, 547, 11, 70, "Text",ExpressionUUID->"6e7a680c-3cc4-4a4a-b6f9-c4135cb53b99", CellID->1940924303], Cell[109077, 2536, 8435, 203, 70, "Input",ExpressionUUID->"c346b4d0-10ca-40cc-93e7-ce1b9b3dae89", CellID->1279132408], Cell[117515, 2741, 543, 10, 70, "Text",ExpressionUUID->"792aa4dd-c12b-432e-a6dc-37e855c710d4", CellID->838162591], Cell[CellGroupData[{ Cell[118083, 2755, 606, 12, 70, "Input",ExpressionUUID->"00687087-ed35-463f-ae14-a1c5f3b6da30", CellID->711872390], Cell[118692, 2769, 14089, 234, 70, "Output",ExpressionUUID->"8edafb42-e471-4a06-a579-df58674b3ccd", CellID->1631666198] }, Open ]] }, Open ]] }, Closed]] } ] *) (* End of internal cache information *)