Definition:Figurate Number

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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.