Asked by Payten
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.
Answers
Answered by
Reiny
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
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
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