From: utzoo!decvax!harpo!floyd!vax135!lime!we13!otuxa!nwuxc!inuxc!burton Newsgroups: net.math Title: Math Discoveries as a child Article-I.D.: inuxc.265 Posted: Wed Jul 28 11:22:25 1982 Received: Mon Aug 2 05:29:12 1982 One of the neat discoveries I made in early high school was that the difference between any two consecutive perfect squares was always an odd number. When I showed this to my teacher, she encouraged me to prove it; it was an obvious proof, but it developed in me a taste for proving 'obvious' math relations. You can work the proof out for yourself, but one of the neat relations that pops out of it is that to get the next perfect square, you multiply the square root of the current perfect square by 2, add 1, then add it to the current perfect square; i.e., if n is the current perfect square, then n +2*sqrt(n) + 1 = next square in the series Again, nothing spectacular, but really neat for a junior high schooler! Doug Burton ihps3!inuxc!burton