Timeline for Number of Reflections in a Circle between Two Points
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 14, 2019 at 23:54 | vote | accept | Argon | ||
| Apr 9, 2019 at 23:54 | answer | added | Noam D. Elkies | timeline score: 13 | |
| Apr 9, 2019 at 16:41 | comment | added | Luc Guyot | This problem was solved in 1992 (the keyword is "billard") and is well documented, see e.g. unige.ch/~gander/Preprints/Billiard.pdf (there is a nice optical experiment at the end of the paper with pictures of caustics). | |
| Apr 9, 2019 at 5:35 | answer | added | Ryan Budney | timeline score: 8 | |
| Apr 8, 2019 at 22:37 | comment | added | Richard | You seem right with $2,3,4,\infty$, that's very intuitive, by drawing a few pics. Also, you're right, vector calculus is probably not adapted to this. All this depends a bit on how much math/what type or math must your research paper contain. Guess you can (1) either take this for granted, (2) or draw a few pics explaining the possible cases, (3) or include some complete advanced math - which might be actually quite complicated - once you have answers here on MO. In any case, nice question! | |
| Apr 8, 2019 at 20:18 | comment | added | Ryan Budney | I imagine at best your result will only be true "generically". But like your central configuration there is probably a relatively low-dimensional algebraic variety of configurations that similarly break with your observation. This is a nice problem. Have to run now but will come back to it tonight if it's not already answered. | |
| Apr 8, 2019 at 20:05 | review | First posts | |||
| Apr 8, 2019 at 20:12 | |||||
| Apr 8, 2019 at 20:03 | history | asked | Argon | CC BY-SA 4.0 |