Basic Examples

Get a diagram with a triangle with four levels:

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PolygonalDiagram
[3,4]
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First five polygonal numbers and its diagrams:

Table[PolygonalNumber[n],{n,5}]
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{1,3,6,10,15}
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GraphicsRowTable
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PolygonalDiagram
[3,n],{n,5}
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Options

"PlotLabel"

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PolygonalDiagram
[3,4,PlotLabelAutomatic]
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Applications

Add polygonal numbers:

With{k=6,n=5},TextStyleRowRow
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PolygonalDiagram
[3,k-1,ImageSize{150,150},PlotLabelAutomatic]/.Hue[_]Green,
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PolygonalDiagram
[n-1,k,PlotLabelAutomatic,ImageSize{150,150}]/.Hue[_]Red,"+",MapAt{Green,#1}&,
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PolygonalDiagram
[n,k,PlotLabelAutomatic,ImageSize{150,150}]/.Hue[_]Red,Flatten[Table[{1,3,i,2,j},{i,k},{j,i-1}],1],"=",18
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+=
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