Timeline for Cover of a n-simplex with balls
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2013 at 20:15 | vote | accept | Max | ||
| Aug 22, 2013 at 16:41 | comment | added | The Masked Avenger | Zeb's proof shows that for every vertex j, there is i with ij the diameter of a ball containing P (all j exists i). Is the (possibly) stronger statement (Exist j forall i) true? (Or even an intermediate, saying there are at least n-1?) | |
| Aug 22, 2013 at 16:36 | comment | added | The Masked Avenger | Draw a picture with P in the plane so dictated and vertex 1 on one side. If 1Pj is less than 90 degrees, j is on the same side as 1. If this is true for all j, P lies in a half space on the wrong side of a tangent plane to the (convex) simplex . | |
| Aug 22, 2013 at 12:37 | comment | added | Joseph O'Rourke | Can you please expand on the logic behind the last "so..."? Every vertex $j \neq 1$ is to one side of that hyperplane. How does this imply $p$ is outside? | |
| Aug 22, 2013 at 9:08 | comment | added | The Masked Avenger | So it seems the point is in at least n/2 of the balls. Can it be shown that it is in n-1 balls at least? | |
| Aug 22, 2013 at 8:54 | history | answered | zeb | CC BY-SA 3.0 |