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Pythagorean theorem based on cross product.

  1. Jan 30, 2014 #1
    I was developing a pythagorean theorem proof based on the cross product of two vectors..Below is my final solution...My problem is I had to get around using the distance/magnitude formula because that is using the pythagorean theorem to prove the pythagorean theorem. But after searching, it may be true that the cross product itself is a generalization of the pythagorean theorem. I'm asking anyone to look at this proof who is real saavy with Linear Algebra and vectors to let me know if cross-product can or cannot be used to prove the pythagorean theorem..My final solution to ascertain the distance of the orthogonal vector, was to use a number line and absolute value based on the standard conventions of the orthogonal vector itself. Thank you for any help?

    http://www.scribd.com/doc/202754816/3-d-Cross-Product-Proof-3-Vectors-Orthogonal-Solution [Broken]
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 30, 2014 #2


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    I think asserting the length of X to be [itex] \sqrt{A^2+B^2} [/itex] is fine. It's not immediately clear how you actually proved the pythagorean theorem though, since you haven't drawn any right triangles whose sides and hypotenuse have been calculated.

    The statement that |YxZ| = area of parallelogram is far from obvious to me given that you are restricting yourself to never using the pythagorean theorem.
  4. Feb 1, 2014 #3
  5. Feb 1, 2014 #4


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    The Pythagorean theorem is so fundamental that I would be very surprised if much of math in your proof did not depend on it. I don't know if you have seen the proof of his theorem, but it is very basic. He proved it before the number system was even a system. Fractions were not understood. He thought it was a religion.

    I can't resist recommending this for your Pythagorean entertainment: http://www.youtube.com/watch?v=X1E7I7_r3Cw
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