# RE: Is this a proof of Pythagorean Theorem?

• Nov 8th 2012, 09:59 PM
SC313
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!
• Nov 8th 2012, 11:09 PM
jakncoke
Re: Is this a proof of Pythagorean Theorem?
no, The Pythagorean thrm states the connection between the side lengths of right triangles and the algebraic equation $a^2 + b^2 = c^2$, 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 $a^2+b^2=c^2$. In order to prove the Pythagorean thrm for positive integer triples satisfying the algebraic equation $a^2 + b^2 = c^2$, 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 $a^2 + b^2 = c^2$
• Nov 8th 2012, 11:26 PM
SC313
Re: Is this a proof of Pythagorean Theorem?
Yes, but every side length of a triangle can be constructed using these equations, correct? They would, therefore, be "sides" in general.
• Nov 9th 2012, 12:15 AM
a tutor
Re: Is this a proof of Pythagorean Theorem?
No. Your 'proof' doesn't even mention right angles.
• Nov 9th 2012, 12:40 AM
jakncoke
Re: Is this a proof of Pythagorean Theorem?
Quote:

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 $a^2+b^2=c^2$. 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 $a^2+b^2=c^2$ nothing more.