• ← Multinomial
• → RogersTanimotoDissimilarity

PolygonalNumber

Polygonal number (WMA)

PolygonalNumber[n]

gives the n-th triangular number.

PolygonalNumber[r, n]

gives the n-th r-gonal number.

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

The sum of two consecutive Polygonal numbers is the square of the larger number:

• • Table[PolygonalNumber[n-1] + PolygonalNumber[n], {n, 10}]

PolygonalNumber[r, n] can be interpreted as the number of points arranged in the form of n-1 polygons of r sides.

List the tenth r-gonal number of regular polygons from 3 to 8:

• • Table[PolygonalNumber[r, 10], {r, 3, 8}]

See also Binomial, and RegularPolygon.