# Definition:Figurate Number

## Definition

A figurate number is loosely defined as a (natural) number corresponding to a set of objects which can be arranged in a geometric pattern (in an arbitrary number of dimensions, but usually $2$ or $3$).

## Also see

• Results about figurate numbers can be found here.

## Historical Note

Figurate numbers, that is:

triangular numbers
square numbers
pentagonal numbers
hexagonal numbers

and so on, were classified and investigated by the Pythagorean school in the $6$th century BCE. This was possibly the first time this had ever been done.