Timeline for What is the minimal number of lines needed to partition a simplex into cells of diameter at most $\epsilon$?
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| Nov 20, 2015 at 16:26 | comment | added | User123321 | Yes, the diameter in the Euclidean metric in the ambient space is what I mean. I was asking about the exact upper bound (in case the answer to this problem is already known), but a good upper bound on the maximum would be useful. In two dimensions, I believe it's not too difficult to compute an upper bound assuming the $r_\ell$ are such that the lines emanating from each vertex intersect the opposite edge in equally spaced points. But, I imagine there is a better choice of $\{r_\ell\}$, and I am not sure how to go about analyzing that. | |
| Nov 20, 2015 at 7:32 | comment | added | Sebastian Goette | Do you consider the diameter in the Euclidean metric induced from ambient space, where each edge has length $\sqrt 2$? And do you just want an upper bound on that minimum? Determining it on the nose might be tricky. | |
| Nov 20, 2015 at 5:07 | review | First posts | |||
| Nov 20, 2015 at 5:24 | |||||
| Nov 20, 2015 at 5:02 | history | asked | User123321 | CC BY-SA 3.0 |