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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.
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