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Polygonal Number

Polygonal Number

Figurate number that we can represent by a convex regular polygon or by a sequence that is partially superimposed on convex regular polygons.

If the convex regular polygon has c sides and if, on each side, there are n points arranged, vertices included, then we distinguish two kinds of polygonal numbers:

  1. Those that are represented on the perimeter of the polygon: pcn = c(n – 1)
  2. Those that are represented on the closed surface of the polygon: Pcn = (c  2)n2 (c  4)n2

Example

For triangular numbers :

  1. p3n = 3(n – 1)   et   p35 = 3(5 – 1) = 12
  2. Pcn = (c  2)n2 (c  4)n2   et   P3n = n(n+1)2  et  P35 = 5(5+1)2 = 15

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