Thread: RE: Is this a proof of Pythagorean Theorem?

Hi,

Is this a legitimate proof of the Pythagorean theorem?

We know that Pythagorean triples a, b, c, such that a^2 +b^2 = c^2.

We know that that a = 2n+1, b= 2n(n+1), and c = 2n(n+1) + 1 for finding Pythagorean triples.

If you substitute these into the formula a^2 + b^2 = c^2, expand and collect like terms to show they are equal, would this be considered a proof?

Thanks!

no, The Pythagorean thrm states the connection between the side lengths of right triangles and the algebraic equation , namely that every right triangle has side lengths satisfying the equation. What you are doing is merely proving that a = 2n+1, b= 2n(n+1), and c = 2n(n+1) + 1 satisfies the algebraic equation . In order to prove the Pythagorean thrm for positive integer triples satisfying the algebraic equation , show me that you can use the positive numbers in the tuple (a,b,c) to construct a right triangle OR show that every right triangle has side lengths satisfying

Yes, but every side length of a triangle can be constructed using these equations, correct? They would, therefore, be "sides" in general.

No. Your 'proof' doesn't even mention right angles.

Originally Posted by SC313

Yes, but every side length of a triangle can be constructed using these equations, correct? They would, therefore, be "sides" in general.

You need to prove that every side length of a right triangle can be constructed using the equations. If you can do that then your proof would have shown the Pythagorean theorem for Pythagorean triples only. . Don't not be confused by the term "Pythagorean triples", they are only positive integer solutions to the equation . People use the "Pythagorean" prefix to "triples" to imply that these are using these triples in the context of representing the sides of a right triangle. If these a,b,c don't represent any object, then they are just triples, numbers, that satisfy nothing more.