How do i explain how a set of whole numbers makes a pythagorean triple. I cant figure out how to explain this. All i can come up with is you take an odd number then square it and find the two numbers that can make that number.

Answer 1

If you are just testing if 3 numbers form a Pythagorean triple that is easy.
Assume the largest is the hypotenuse, (it has to be!)
and test
(smallest)^ + (middle one)^2 = largest^2

e.g. is 5, 12, 13 one of those?
is 13^2= 5^2 + 12^2 ?
is 169 = 25 + 144 ? YES, so you got one!

if you want to form them:
pick any two numbers, one even , one odd and call them m and n , so that m > n

so 2mn, m^2 - n^2, and m^2 + n^2 will always form a Pythagorean triple

e.g. let m = 5, n = 4
2mn = 40
m^2 - n^2 = 25 - 16 = 9
m^2 + n^2 = 25+16 = 41

is 41^2 = 40^2 + 9^2 ?? , YES