Cannonball problem

When cannonballs are stacked within a square frame, the number of balls is a square pyramidal number; Thomas Harriot gave a formula for this number around 1587, answering a question posed to him by Sir Walter Raleigh on their expedition to America.

It was not until 1918 that G. N. Watson found a proof for this fact, using elliptic functions.

The result has relevance to the bosonic string theory in 26 dimensions.

A triangular-pyramid version of the cannonball problem, which is to yield a perfect square from the Nth Tetrahedral number, would have N = 48.

[7][8] There are no numbers (other than the trivial solution 1) that are both tetrahedral and square pyramidal.