Timeline for Triangle area on surfaces of constant curvature
Current License: CC BY-SA 3.0
11 events
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| Nov 16, 2014 at 23:29 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
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| Aug 31, 2013 at 23:25 | comment | added | SashaKolpakov | There are some proofs by considering bigons (for spherical geometry) and subdivisions of an ideal triangle (in hyperbolic geometry). You may also consult J. Ratcliffe's book "Foundations of hyperbolic manifolds", some of the first chapters. However, the area of a bigon or ideal triangle is computed by "not very elementary" means there. I agree with Anton, all "elementary proofs" are cheating up to a certain extent. | |
| Aug 31, 2013 at 23:13 | history | edited | user9072 |
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| May 13, 2013 at 18:20 | vote | accept | Matthias Ludewig | ||
| May 13, 2013 at 18:20 | vote | accept | Matthias Ludewig | ||
| May 13, 2013 at 18:20 | |||||
| May 13, 2013 at 0:30 | comment | added | Igor Khavkine | For both cases, there are visual proofs, which can be considered elementary: mathoverflow.net/questions/8846/proofs-without-words/… and mathoverflow.net/questions/8846/proofs-without-words/… | |
| May 12, 2013 at 21:31 | comment | added | Misha | For $\kappa<0$ Gauss had a similar inclusion-exclusion proof: It is in his collected works (letter to Wolfgang/Farkas Bolyai). | |
| May 12, 2013 at 18:16 | answer | added | Anton Petrunin | timeline score: 7 | |
| May 12, 2013 at 12:39 | comment | added | S. Carnahan♦ | For $\kappa > 0$, I believe you can use inclusion-exclusion with 3 geodesics on a sphere. | |
| May 12, 2013 at 12:29 | answer | added | Alexandre Eremenko | timeline score: 11 | |
| May 12, 2013 at 10:44 | history | asked | Matthias Ludewig | CC BY-SA 3.0 |