Adding Polygonal Numbers

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A polygonal number is a natural number such that
dots can be arrranged in an array shaped like a regular triangle, square, etc. In general, any
-gonal number is equal to the sum of the
-gonal number of the same rank and the triangular number of the previous rank. The diagram graphically illustrates how the addition works.
Contributed by: Enrique Zeleny (March 2011)
Based on a program by: Eric W. Weisstein
Open content licensed under CC BY-NC-SA
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"Adding Polygonal Numbers"
http://demonstrations.wolfram.com/AddingPolygonalNumbers/
Wolfram Demonstrations Project
Published: March 7 2011