多边形数

多边形数是一种有形数，它涵盖了三角形数、正方形数等直到任意 r-边形数.

返回前 10 个三角形数.

In[1]:=

Table[PolygonalNumber[n], {n, 1, 10}]

Out[1]=

返回几个标准多边形的第十个 r-边形数.

In[2]:=

Table[PolygonalNumber[r, 10], {r, 3, 10}]

Out[2]=

多边形数计算在该类标准几何排列中间距相同的点的数目.

In[3]:=

points[0, r_] := {{0, 0}}; points[n_, r_] := Flatten[Subdivide[#1, #2, n] & @@@ Partition[CirclePoints[-Last[CirclePoints[n, r]], n, r], 2, 1, 1], 1]; points[ns_List, r_] := points[#, r] & /@ ns;

In[4]:=

polygonalNumberGraphics[r_, n_] := With[{ps = points[Range[0, n - 1], r]}, Graphics[{PointSize[Large], Point /@ ps, Line /@ ps, Opacity[0.2], RandomColor[], Polygon /@ ps}]]

In[5]:=

PolygonalNumber[3, 4] polygonalNumberGraphics[3, 4]

Out[5]=

Out[5]=

In[6]:=

PolygonalNumber[3, 6] polygonalNumberGraphics[3, 6]

Out[6]=

Out[6]=

In[7]:=

PolygonalNumber[6, 5] polygonalNumberGraphics[6, 5]

Out[7]=

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