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I thought of the other Euler's identity: https://en.wikipedia.org/wiki/Euler_characteristic https://en.wikipedia.org/wiki/Euler_characteristic ..which I think
by js8 5y ago
I thought of the other Euler's identity: https://en.wikipedia.org/wiki/Euler_characteristic https://en.wikipedia.org/wiki/Euler_characteristic
..which I think is beautiful too.
- gspr 5y agoI second your nomination of Euler's formula as the most beautiful mathematical statement! Another candidate in my mind is the generalized variant of Stokes' theorem (there's nothing wrong with the basic calculus variant, but the general variant is just so succinct): https://en.wikipedia.org/wiki/Generalized_Stokes_theorem https://en.wikipedia.org/wiki/Generalized_Stokes_theorem In addition to being pleasingly succinct and symmetric in its very statement, it couples shapes and functions on them in a beautiful way. One more with this pleasing connection is the Atiyah–Singer index theorem. However, it loses some points for requiring a bit too much setup for the statement. https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_theorem https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_th...
- MiguelVieira 5y agoA favorite of mine is the Gauss-Bonnet theorem which relates the Euler characteristic of a surface (i.e. its topology) to its Gaussian curvature (its differential geometry). https://en.wikipedia.org/wiki/Gauss–Bonnet_theorem https://en.wikipedia.org/wiki/Gauss–Bonnet_theorem