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