I was surfing the internet recently, and found a reference to polygonal numbers. These are series such as the triangular numbers, pentagonal numbers and others, including the series of heptagonal ...

There is a long, beautiful history of thinking about numbers and shapes as two aspects of the same idea. Square numbers are often described using arithmetic: 1 = 1 x 1 = 1, 2 = 2 x 2 = 4, 3 = 3 x 3 = ...