PolygonalNumber

PolygonalNumber[n]

gives the n^(th) triangular number .

PolygonalNumber[r,n]

gives the n^(th) r-gonal number .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • PolygonalNumber[n] is generically defined as TemplateBox[{{n, +, 1}, 2}, Binomial].
  • PolygonalNumber[r,n] is generically defined as .
  • PolygonalNumber[r,n] can be interpreted as the number of points arranged in the form of n-1 polygons of r sides. For instance for r=3 and n=4:
  • PolygonalNumber automatically threads over lists.

Examples

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Basic Examples  (2)

Return the first 10 triangular numbers:

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Return the tenth r-gonal number of several regular polygons:

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Scope  (4)

Applications  (2)

Properties & Relations  (9)

Neat Examples  (1)

See Also

RegularPolygon  CirclePoints  Binomial  Power

Introduced in 2016
(10.4)