4 ms·
Indeed, a wonderful proof. It does, though, make one implicit assumption that if one stretches the fabric by the same amount, all holes in it stretch by the sam
by JanisErdmanis 11mo ago
Indeed, a wonderful proof. It does, though, make one implicit assumption that if one stretches the fabric by the same amount, all holes in it stretch by the same amount. In particular, it assumes that triangle stretching is size-independent. Perhaps there are fabrics where that is not true...
- lupire 11mo agoYou mean non-Euclidean fabric? https://www.johndcook.com/blog/2022/09/08/trig-hyperbolic-geometry/ https://www.johndcook.com/blog/2022/09/08/trig-hyperbolic-ge... https://math.hmc.edu/funfacts/spherical-pythagorean-theorem/ https://math.hmc.edu/funfacts/spherical-pythagorean-theorem/ https://en.wikipedia.org/wiki/Minkowski_distance https://en.wikipedia.org/wiki/Minkowski_distance
- JanisErdmanis 11mo agoThat is one possibility. Probably the only one, though.
- layer8 11mo agoThe Pythagorean theorem is only true in Euclidian space, where that “stretching” assumption is true. So you are right about there being assumptions, and indeed they are imposing limitations to the applicability of the theorem.