Timeline for How can simple physical "proofs" of mathematical facts be made rigorous?
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| Sep 16, 2010 at 3:18 | comment | added | Emerton | Dear jc, This is what I had in mind with my oblique comment at the end of my second-to-last paragraph. If you think about how the tank would hang, you can see that the pressure on the faces of length a and b is opposite to that on the face of length c, which is where the signs in the expression $c^2 - a^2 - b^2$ are coming from. | |
| Sep 16, 2010 at 3:02 | comment | added | j.c. | I wasn't able to understand the first solution until I found this more lengthy writeup cut-the-knot.org/pythagoras/MechanicalProofs.shtml and now I think the principle at work is the same as in the second solution - that is, the pressure of the water in the tank pushes differently on the different faces of the tank - the Pythagorean theorem is just Stokes theorem in this geometry. | |
| Sep 16, 2010 at 2:46 | comment | added | Qiaochu Yuan | Thanks for the answer; Stokes' theorem definitely seems like the "right" way to think about the second question. For the first question my vague conception is that the crux of the problem is its rotational symmetry and there is some unspoken assumption about this symmetry which powers the proof. If someone could point that assumption out for me, that would be enough of a resolution, I think. | |
| Sep 16, 2010 at 2:21 | history | answered | Emerton | CC BY-SA 2.5 |