Timeline for Is every elementary absolute geometry Euclidean or hyperbolic?
Current License: CC BY-SA 3.0
17 events
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| Sep 19, 2014 at 19:15 | vote | accept | Conifold | ||
| Sep 19, 2014 at 19:15 | history | edited | Conifold |
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| Sep 17, 2014 at 22:19 | comment | added | Will Jagy | Conifold, new answer from Marvin Greenberg. | |
| Sep 17, 2014 at 21:31 | answer | added | Marvin Greenberg | timeline score: 12 | |
| Sep 17, 2014 at 17:44 | history | edited | Conifold |
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| Sep 16, 2014 at 20:16 | history | edited | Conifold |
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| Sep 15, 2014 at 20:47 | history | edited | Conifold | CC BY-SA 3.0 |
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| Sep 15, 2014 at 19:30 | history | edited | Conifold | CC BY-SA 3.0 |
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| Sep 15, 2014 at 17:51 | history | edited | Conifold | CC BY-SA 3.0 |
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| Sep 15, 2014 at 17:50 | answer | added | Conifold | timeline score: 7 | |
| Sep 11, 2014 at 22:05 | comment | added | Conifold | @Will Jagy I read this paper when you linked it under your previous answer (thanks!), but for semi-elliptic plane it references an Appendix to Greenberg's book, of which the paper I linked is an expanded version, and Pejas's papers in German. I am still interested in lengths constructible by elementary means, which I realized is not the same as by ruler and compass w/o the line-circle axiom, and now I am not even sure that Euclidean or hyperbolic metric relations have to be satisfied! | |
| Sep 11, 2014 at 21:30 | history | edited | Conifold | CC BY-SA 3.0 |
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| Sep 11, 2014 at 21:17 | comment | added | Conifold | @Anton Petrunin Not quite. You can perform ruler and compass constructions as long as you do not rely on every line passing through interior of a circle intersecting the circle. Bolyai's construction and many others that Will Jagy uses in the Squaring paper for example rely on this, Greenberg calls it the line-circle axiom. It can not be proved without continuity, and it does not hold in the semi-elliptic plane. | |
| Sep 11, 2014 at 19:35 | comment | added | Will Jagy | for that matter, Marvin won a prize for this recent survey, which shows a fair amount of extra stuff that was added for his fourth edition , typing link again: maa.org/programs/maa-awards/writing-awards/… see if it works this time. Yup, good link. | |
| Sep 11, 2014 at 19:17 | comment | added | Will Jagy | Conifold, you might want to try Hartshorne's book on this as well. | |
| Sep 11, 2014 at 19:01 | comment | added | Anton Petrunin | Do I understand correctly that $({*})$ in Archimedean H-plane you can perform all ruler-and-compass construction? If yes then Bolyai's construction (mathoverflow.net/questions/45237) gives an other parallel line. This will do the job if the completion of your H-plane is Lobachevskian. So if $({*})$ is correct then the answer is "NO". | |
| Sep 11, 2014 at 18:32 | history | asked | Conifold | CC BY-SA 3.0 |