Timeline for Bijection from the plane to itself that sends circles to squares
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2017 at 5:31 | comment | added | JohnnyMo1 | @D.W. The problem in the original question asks about the existence or non-existence of a bijection which maps ANY circle to a square. | |
| Apr 14, 2017 at 2:38 | comment | added | D. W. | Wouldn't said bijection only map one of those circles to a square though? Or does a bijection from the plan to itself that maps one of the circles to a square automatically map all the others to a square as well? Would this depend on the nature of the bijection? | |
| Apr 11, 2017 at 6:34 | comment | added | user21820 | And this extends easily to prove that there is no bijection that maps every circle to some regular polygon. | |
| Apr 10, 2017 at 20:54 | comment | added | Gerhard Paseman | I wonder what a three or higher dimensional version would be like. Perhaps mapping nested spheres to various hypothetical shapes with square cross sections? Gerhard "Four Doesn't Suffice In 3D" Paseman, 2017.04.10. | |
| Apr 10, 2017 at 20:26 | comment | added | Nik Weaver | Well that is just lovely! | |
| Apr 10, 2017 at 19:36 | vote | accept | Tom Solberg | ||
| Apr 10, 2017 at 19:35 | history | answered | Will Brian | CC BY-SA 3.0 |