>>I got a call from a high school student who said she'd discovered two >>formulas that generate Pythagorean triples. She wanted to know where to >>look to find out if they're original. I'm sure I've read of famous people >>who've come up with such formulas, but I can't find anything on it. Can >>anyone suggest where to look? Thanks
In my geometry text, Geometry for Enjoyment & Challenge, McDougal, Littell, they give four ways to general sets of Pythagorean Triples.
The rule of Pythagoras gives the sides as (n2+1)/2 , (n2-1)/2, and n . [ Can't do exponents, read that as n squared] The rule of Euclid gives the sides as ( m+n)/2, the root of mn, and (m-n)/2 The Rule of Plato ( m is any even number) m2/4 + 1, m2/4 -1, and m. The Rule of Maseres ( m & n any two integers) m2 + n2, 2mn, and m2 - n2.