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Math Help - RE: Is this a proof of Pythagorean Theorem?

  1. #1
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    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!
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  2. #2
    Senior Member jakncoke's Avatar
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    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
    Last edited by jakncoke; November 8th 2012 at 10:14 PM.
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  3. #3
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    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.
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  4. #4
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    Re: Is this a proof of Pythagorean Theorem?

    No. Your 'proof' doesn't even mention right angles.
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  5. #5
    Senior Member jakncoke's Avatar
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    Re: Is this a proof of Pythagorean Theorem?

    Quote Originally Posted by SC313 View Post
    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.
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