Also, the correct generalization to 3D should make the distance from the origin to (3,4,5) be cbrt(27+64+125) = 6. When you make a right-angled tetrahedron by slicing a corner off a cube, the area of the oblique face is sqrt(sum of squares of the areas of the three orthogonal faces). Why not cbrt-of-sum-of-cubes? Rich ------- Quoting Scott Kim <scottekim1@gmail.com>:
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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