Scott: I think Andy Latto's proof is actually the best answer I've ever come up with to exactly this question. From this point of view, the essence of the Pythagorean theorem is that a right triangle can be cut into two pieces similar to itself, and the ratio of scales is just the ratio of sides of the original triangle. That dissection into similar pieces is an amazing observation about right triangles. --Michael On Mon, Feb 15, 2016 at 1:23 AM, Scott Kim <scottekim1@gmail.com> wrote:
So there are many cute proofs of the Pythagorean theorem. I'm convinced it's true, but despite that I've never seen a proof that gives me any intuition for WHY it is true. Why on Earth square the side lengths of a triangle? After all the theorem isn't true if space is slightly negatively or positively curved. I know square root of sum of squares shows up everywhere. Why?
On Sun, Feb 14, 2016 at 12:32 PM, Bill Gosper <billgosper@gmail.com> wrote:
On 2016-02-13 15:11, Gareth McCaughan wrote:
On 13/02/2016 18:38, Bill Gosper wrote:
gosper.org/Perigal.gif --rwg
Cute picture, but is proving that it actually proves Pythagoras any easier than just proving Pythagoras[?] Well, no. It's just a sketch of a pure-dissection proof that is a bit harder than the skewy ones sketched by gosper.org/Pythanim.gif, but more visually convincing. --rwg
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