- Generating the sides of a right triangle using all real numbers
Main Question or Discussion Point
Recently I created a spreadsheet that generates Phythagorean triples. Curious, instead of using only positive integers for the values of m and n, I found that as long as m>n, the sides 2mn, msq + nsq, msq - nsq, still form the sides of a right triangle even though m and n are non-whole numbers. I assume this is no big deal and that this is already known in the mathematical community. Does anyone know of a proof that Euclid's formula works for the set of all real numbers, not just for integer numbers?