Filed under Geometry
Tagged as visual proofs
Reblogged this on nebusresearch and commented:
“Notes On Mathematics” here presents a lovely, visual proof of the Pythagorean Theorem, that bit about the squares of the lengths of two sides of a right triangle adding up to the square of the hypotenuse’s length. I find particularly lovely about this that it can be done without words or explanatory text, which one can’t often get away with.
I think anyone staring at the two pictures would come away convinced of the theorem, but might still ask whether this is actually a logically rigorous proof. One can draw pictures showing all sorts of things which look like they’re so but actually aren’t. I’m thinking here of that puzzle where a grid of 49 squares is cut apart into polygons and rearranged and what do you know but there’s one missing square.
Generally, appeals to “just look at the picture” are a touch suspicious, since that carries along a lot of assumptions about what we see versus what we think, and the eye is pretty much in a continuous state of being fooled about everything we think it sees. I exaggerate but not that much.
But the argument presented here could be written out entirely in prose, without appealing to the physical intuition of what ought to happen if we move triangular blocks around. If you look at that one long enough, or work it out, you might get the same grin of cheerful accomplishment that this pair of pictures provides.
I agree that visual proofs may be flawed sometimes. However as you say, it is not the case here because the whole argument may be written in prose (justified through rigid motions perhaps). Thanks for your comment.
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