Simon spent the morning of December 5 pondering about how to test whether a number is a triangle number. “To test if something is a triangle number: double it, ask if it’s a multiple of its own square root. If that square root has a decimal, round it down”. This was his initial hypothesis, later discarded.
Another formula he came up with was if n is even, m is a triangle number. After we got back home, he quickly wrote some code to check it: