Figurate number

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

[5] The mathematical study of figurate numbers is said to have originated with Pythagoras, possibly based on Babylonian or Egyptian precursors.

Generating whichever class of figurate numbers the Pythagoreans studied using gnomons is also attributed to Pythagoras.

Unfortunately, there is no trustworthy source for these claims, because all surviving writings about the Pythagoreans[6] are from centuries later.

[7] Speusippus is the earliest source to expose the view that ten, as the fourth triangular number, was in fact the tetractys, supposed to be of great importance for Pythagoreanism.

Figurate numbers have played a significant role in modern recreational mathematics.

This gnomonic technique also provides a mathematical proof that the sum of the first n odd numbers is n2; the figure illustrates 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 82.