Category:Polygonal Numbers

If a number of physical objects (represented by circles, usually) can be arranged in a geometrical pattern corresponding to a regular polygon in certain ways, then the number of these objects is called a polygonal number.

They are as follows: and so on.
 * Triangular numbers
 * Square numbers
 * pentagonal numbers
 * hexagonal numbers

In the third dimension we also have pyramidal numbers.

These are a generalization of the two-dimensional case, and arise as sums of sequences of polygonal numbers.

They are as follows: and so on.
 * Tetrahedral numbers
 * Square-based pyramidal numbers