Current proofs of Pythagoras' theorem all do so through the comparison of areas of the triangles one way or another. I know of none that is able to prove the theorem using lines alone. As one of the few foundations of mathematics, the theorem holds a very important law, yet one which is too abstract for me to perceive. While the current proofs of the theorem do manage to prove it, they do not actually show why it is so, and do not explain the unique properties of lines, points and angles which give birth to this theorem. So I am wondering if there are any proofs which do not adopt the comparison of area. Otherwise, could anyone tell me why it is impossible to prove the theorem while not using area. What property of area calculation links it to the theorem and makes it the crucial key to proving it?
2007-11-24
17:32:55
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4 answers
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CVA
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