Timeline for 2-neighborhood of a simplex
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2013 at 21:48 | vote | accept | Thanh Vu | ||
| Dec 1, 2013 at 21:43 | comment | added | Thanh Vu | Sorry, I imagine the other side of the facet $a_1...a_{n-1}$. My thought was that is this possible to find such a simplex, whose all the points are either in $\Delta$ or in one of its reflection via the facets. (It is the $2$-neighborhood of $\Delta$ in the plane, but not in higher space I think). That caused me problems in understanding your argument. | |
| Dec 1, 2013 at 21:35 | comment | added | Ilya Bogdanov | I do not understand, sorry. The halfplane $H_{a_n}$ passes through $a_n$; for every point $b\in H_{a_n}$, the volume of $(a_1,\dots,a_{n-1},b)$ is the same, and IF $b\in H_{a_n}^-$ THEN this volume becomes larger, doesn't it? | |
| Dec 1, 2013 at 20:46 | comment | added | Thanh Vu | I meant it could happen that $b$ is on $H_{a_n}^-$, in this case, you cannot say much about the position of $b$ relative to the $2$-neighborhood of $\Delta$. | |
| Dec 1, 2013 at 20:36 | comment | added | Thanh Vu | No, this only true if all these remaining points lie on the same hyperplane as $a_n$. But certainly it might not be the case. Your proof only shows that the points lie in a slightly larger neighborhood, (maybe $2$-neighborhood of $2$-neighborhood.) | |
| Dec 1, 2013 at 20:32 | history | answered | Ilya Bogdanov | CC BY-SA 3.0 |