Figurate number

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean

Terminology

Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number".

In historical works about Greek mathematics the preferred term used to be figured number.

In a use going back to Jakob Bernoulli's Ars Conjectandi, the term figurate number is used for triangular numbers made up of successive integers, tetrahedral numbers made up of successive triangular numbers, etc. These turn out to be the binomial coefficients. In this usage the square numbers 4, 9, 16, 25 would not be considered figurate numbers when viewed as arranged in a square.