SOLUTION: Does anyone know what Pythagorean triples are and a set of formulas that will generate an infinite number of them. I am so lost and can't figure this out for anything. can someon

Question 228349: Does anyone know what Pythagorean triples are and a set of formulas that will generate an infinite number of them. I am so lost and can't figure this out for anything. can someone explain this to me please.
Found 2 solutions by rfer, Theo:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
3 4 5
6 8 10
etc
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Check out the following hyperlink. It's the most direct and to the point reference I could find.

Pythagoren Triples

This set of formulas should do the trick.

Here's a copy of what's on that website.

There is a simple formula that gives all the Pythagorean triples.
Suppose that m and n are two positive integers, with m < n. Then n2 - m2, 2mn, and n2 + m2 is a Pythagorean triple.
Given any two numbers, m and n, with m < n, you can generate a set of pythagorean triples from it.

example:

3,4

first number is n^2 - m^2 = 16 - 9 = 7
second number is 2mn = 2*3*4 = 24
third number is n^2 + m^2 = 9 + 16 = 25

should be a reight triangle with f^2 + s^2 = t^2

7^2 = 49
24^2 = 576
25^2 = 625

49 + 576 = 625

seems to work.

try m = 1 and n = 2

f (first) = 2^2 - 1^2 = 4-1 = 3
s (second) = 2mn = 2*1*2 = 4
t (third) = 2^2 + 1^21 = 4+1 = 5

not too shabby.

try 5 and 7

f = 7^2 - 5^2 = 49 - 25 = 24
s = 2*5*7 = 10*7 = 70
t = 7^2 + 5^2 = 49 + 25 = 74
24^2 + 70^2 = 74^2 becomes:
576 + 4900 = 5476 becomes:
5476 = 5476

It works !!!!

A pythagorean triple is a set of integers that forms a right triangle.

This formula appears to work in all cases.

Here is a much more complicated explanation which winds up with the same formula stated above.

Pythagorean Triples Formuls and Examples

Here's a definition.

Definition of Pythagorean Triple

the derivtion gets pretty complicated, but the basic formula as stated in the first hyperlink holds.

You can find lots more info by doing a search on the web for "pythagorean triples"

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