Timeline for A walk on a compact 2D surface embedded in 3-space that never returns home
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7, 2009 at 4:17 | comment | added | David Eppstein | Let f(x) map a starting angle to the difference in longitude (amount a curve wraps the long way around the torus) when the curve first returns to the same latitude (wraps once the short way around). Then f is two-to-one (if two curves return to the same latitude while wrapping the same amount the long way around the torus, they must go in opposite directions around the short way). So the set of x at which it is rational is countable. Ok, all of these qualitative descriptions are not a rigorous proof, but I think that's not needed to see that this example works. | |
| Nov 7, 2009 at 3:02 | comment | added | Aaron Mazel-Gee | Is it easy to prove this? Forgetting about the "embeddable in R^3" condition, I figured the easiest thing to do was work on the flat torus... | |
| Nov 6, 2009 at 18:07 | history | answered | David Eppstein | CC BY-SA 2.5 |