Timeline for Threading pinholes in the wall of cylinder to pass through an internal coordinate
Current License: CC BY-SA 3.0
17 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 31, 2011 at 6:35 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
Writing/language edits.; Post Made Community Wiki
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| Oct 10, 2011 at 12:24 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
Deleted the vascular system example, which I feel is a bit forced.
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| Oct 3, 2011 at 17:24 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
added 148 characters in body
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| Oct 3, 2011 at 17:04 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
Provided a possible motivation for the problem
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| Oct 2, 2011 at 23:02 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
added 276 characters in body
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| Oct 2, 2011 at 20:37 | answer | added | Gerhard Paseman | timeline score: 2 | |
| Oct 2, 2011 at 17:11 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
Provided a Wolfram Mathworld site for 3D point-line distance
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| Oct 2, 2011 at 15:05 | comment | added | Joseph O'Rourke | As Noam suggests, this question seems interesting already in 2D. I've taken the liberty of posing a version (actually, two versions) separately. | |
| Oct 2, 2011 at 13:11 | comment | added | Joseph O'Rourke | I wonder if this problem is motivated by radiation therapy? | |
| Oct 2, 2011 at 9:42 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
added 51 characters in body
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| Oct 2, 2011 at 7:17 | history | edited | UltraBlue06 | CC BY-SA 3.0 |
added 452 characters in body; added 1 characters in body
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| Oct 2, 2011 at 5:12 | comment | added | Gerhard Paseman | Thinking some more, it seems to me that the largest distance needed will be at the top or at the bottom of the cylinder: I see this by looking at the graph on 2n vertices mentioned in another comment. If the original poster is willing to exclude such regions, he or she may find delta quite small even for small values of n. Gerhard "Ask Me About System Design" Paseman, 2011.10.01 | |
| Oct 2, 2011 at 4:59 | comment | added | Noam D. Elkies | Seems unlikely to have a closed-form solution. Even the 2-dimensional projection (find a diagonal of a regular $N$-gon nearest to a given interior point) leads to an exotic Diophantine problem (more-or-less finding the point $(x/N,y/N)$ nearest to a given transcendental curve). Where does this question arise, and what are typical sizes of $M$ and $N$?$$ $$A lower bound, and possibly a reasonable approximation, for the typical minimal distance is the radius of cylinders about each string the sum of whose volumes is within a constant factor of the volume of the cylinder. | |
| Oct 2, 2011 at 4:51 | comment | added | Gerhard Paseman | Since Joseph O'Rourke was kind enough to provide one picture of your problem, you might ask him for five more: one where the array is based on diamonds instead of a rectangular grid, one using a hexagonal array, and then copies of each of these with the lines given a thickness of delta/4, where delta is the largest distance between any point inside the cylinder and its nearest line. Hopefully he can compute delta for some reasonable spacing of the N vertical points in the three configurations. Gerhard "Ask Me About System Design" Paseman, 2011.10.01 | |
| Oct 2, 2011 at 1:42 | answer | added | Joseph O'Rourke | timeline score: 3 | |
| Oct 1, 2011 at 21:09 | history | asked | UltraBlue06 | CC BY-SA 3.0 |