I was playing around with a calculator. I hit the pi button, then the square button twice, and saw 97.409091. I thought, hey, that looks like a repeating decimal! So I worked out that if it were a repeating decimal, 97.4090909090909..., it would be equal to 2143/22. Then I worked out how close sqrt(sqrt(2143/22)) would be to pi, and... wow!