Timeline for Can one "hear" the shape of a polygon via external reflections?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 25, 2018 at 3:36 | comment | added | Richard Montgomery | echoing Qfwfq -- the case of a convex polygon seems to lead to a fairly straightforward `yes'. First, you can measure angles at vertices via pencils of parallel lines. Similarly you can measure side lengths by rotating this pencil of rays until you get some total (180) reflection, and measuring the thickness of the fraction of totally reflected rays.... | |
| Apr 19, 2018 at 23:56 | comment | added | Joseph O'Rourke | @Qfwfq: For a convex polygon, each ray that returns at an angle determines the line containing one edge. Repeating, I believe the entire polygon is determined by intersecting those lines. | |
| Apr 19, 2018 at 21:56 | comment | added | StackOverthrow | If I understand what you're talking about, not only is it theoretically possible, it has a practical application. | |
| Apr 19, 2018 at 19:13 | comment | added | Qfwfq | I think it would be also interesting to consider a variant of the problem in which the polygon is assumed to be convex | |
| Apr 19, 2018 at 16:37 | answer | added | Newton fan 01 | timeline score: 3 | |
| Apr 19, 2018 at 14:22 | comment | added | Joseph O'Rourke | @JoelDavidHamkins: They die immediately, no reflection. | |
| Apr 19, 2018 at 13:15 | answer | added | Adam P. Goucher | timeline score: 34 | |
| Apr 19, 2018 at 13:04 | comment | added | Joel David Hamkins | What about light rays that hit corners? | |
| Apr 19, 2018 at 10:59 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |