Adding Polygonal Numbers

number of sides n for polygon on the right

4

order k of n-gonal number

6

+

=

A polygonal number is a natural number

p

such that

p

dots can be arrranged in an array shaped like a regular triangle, square, etc. In general, any

n

-gonal number is equal to the sum of the

(n-1)

-gonal number of the same rank and the triangular number of the previous rank. The diagram graphically illustrates how the addition works.