Timeline for How many unit cylinders can touch a unit ball?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://page.mi.fu-berlin.de/ with https://page.mi.fu-berlin.de/
|
|
| Apr 8, 2014 at 9:26 | comment | added | Moritz Firsching | @MattF. : yes, but what if the lines are parallel? I think you need two polynomial inequalities. | |
| Apr 7, 2014 at 20:48 | comment | added | user44143 | Condition 4 has a nice geometric formulation as $(V_{ij}\cdot W_{ij})^2 \ge W_{ij}\cdot W_{ij}$, where $V_{ij}=(x_i,y_i,z_i)-(x_j,y_j,z_j)$, and $W_{ij}=(a_i,b_i,c_i)\times(a_j,b_j,c_j)$. | |
| Apr 7, 2014 at 19:32 | history | edited | Moritz Firsching | CC BY-SA 3.0 |
improved bound for r_7
|
| Apr 4, 2014 at 12:31 | history | edited | Moritz Firsching | CC BY-SA 3.0 |
lower bounds and k=7 pic
|
| Apr 4, 2014 at 1:55 | history | bounty ended | Wlodek Kuperberg | ||
| Apr 4, 2014 at 1:51 | comment | added | Wlodek Kuperberg | I doubt that I can get a better answer any time soon, therefore I am awarding the bounty to Moritz Firsching. Thank you, Moritz! | |
| Apr 4, 2014 at 1:49 | vote | accept | Wlodek Kuperberg | ||
| Apr 3, 2014 at 19:08 | history | edited | Moritz Firsching | CC BY-SA 3.0 |
changed pi to \pi..
|
| Apr 3, 2014 at 0:54 | comment | added | Wlodek Kuperberg | What a marvelous surprise! The configuration of $6$ cylinders with radius exceeding $1.04965$ is astounding! | |
| Apr 2, 2014 at 18:18 | history | edited | Moritz Firsching | CC BY-SA 3.0 |
added 2 characters in body
|
| Apr 2, 2014 at 18:00 | history | edited | Moritz Firsching | CC BY-SA 3.0 |
add discussion on varying radii
|
| Apr 2, 2014 at 0:58 | comment | added | Wlodek Kuperberg | Nice idea, fantastic graphics! | |
| Apr 1, 2014 at 14:36 | history | edited | Moritz Firsching | CC BY-SA 3.0 |
added picture
|
| Apr 1, 2014 at 11:43 | history | edited | Moritz Firsching | CC BY-SA 3.0 |
changed condition 3
|
| Apr 1, 2014 at 11:42 | comment | added | Moritz Firsching | @HenrikRüping you are right, I modified the condition.. | |
| Apr 1, 2014 at 8:31 | comment | added | HenrikRüping | Furthermore if we drop condition (4), we would just get a manifold (the 6-th power of the unit tangent bundle of the sphere $T^1(S^2)^6$). So in order to see that Figure (3) is an isolated point, one could compute the differentials of the polynomial functions appearing in (4) at that point. | |
| Apr 1, 2014 at 8:26 | comment | added | HenrikRüping | I do not understand, why you need condition (3). I would just normalize the tangent vector $(a_k,b_k,c_k)$ instead. | |
| Mar 31, 2014 at 23:20 | history | answered | Moritz Firsching | CC BY-SA 3.0 |