Timeline for Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Nov 18, 2014 at 15:03 | vote | accept | Vesselin Dimitrov | ||
| Nov 18, 2014 at 12:55 | answer | added | Ilya Bogdanov | timeline score: 16 | |
| Nov 18, 2014 at 11:01 | comment | added | Ilya Bogdanov | @joro: You cannot get an example lying on a circle (or on any rectifiable curve), because the smallest pairwise distance between $n$ points on such curve is $O(1/n)$. | |
| Nov 18, 2014 at 9:44 | comment | added | joro | just an observation: taking $P_n=(10 \cos(n), 10 \sin(n) )$ gives a set of at 710 points and fails after that. Probably this has something to do with n \pmod \pi. | |
| Nov 18, 2014 at 3:08 | comment | added | Vesselin Dimitrov | @NoamD.Elkies: Actually I don't know the answer to this, and this could have been a part of the question. | |
| Nov 18, 2014 at 3:04 | comment | added | Noam D. Elkies | Is it known (or a known open problem) whether there exist $a,b \in {\mathbb R} / {\mathbb Z}$ such that $P_n = (\{na\},\{nb\})$ works (i.e. a vector $v=(a,b)$ in the 2-torus such that $nv$ is at distance $> C /\sqrt{n}$ from the origin for some $C>0$ and all positive integers $0$)? | |
| Nov 18, 2014 at 2:05 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
deleted 39 characters in body
|
| Nov 18, 2014 at 1:58 | history | asked | Vesselin Dimitrov | CC BY-SA 3.0 |