The Joy of X: A Guided Tour of Mathematics, from One to Infinity

by Steven H. Strogatz

instead of adding just two odd numbers together, suppose we add all the consecutive odd numbers, starting from 1: 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 + 9 = 25. The sums above, remarkably, always turn out to be perfect squares.