Timeline for Efficient visibility blockers in Pólya's orchard problem
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4 at 2:11 | history | edited | GH from MO | CC BY-SA 4.0 |
edited body; edited title
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| Mar 31, 2017 at 21:55 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image links broken; now fixed.
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| Dec 27, 2013 at 6:38 | answer | added | Alexey Ustinov | timeline score: 5 | |
| Apr 28, 2011 at 10:01 | comment | added | Aaron Meyerowitz | more improvement And even that is not optimal. I think that squares of side $\frac23$ are. I added yet another picture. | |
| Apr 28, 2011 at 4:01 | comment | added | Aaron Meyerowitz | improvement This problem is kind of subtle. One could do this same cord construction allowing disks of different sizes at different points. Furthermore, the horizontal and vertical cords of length $\frac45$ can be replaced by segments of length $1$ going through the center of each circle. These are longer but also more central and the area turns out to be smaller. I added a picture of this to my answer below. | |
| Apr 26, 2011 at 7:35 | comment | added | Aaron Meyerowitz | I think that what you have is almost what the construction would give for those $12$ disks of radius $1/\sqrt{5}.$ By my calculations the outer (shorter) vertical and horizontal segments exactly meet the ones of slope $\pm 1.$ The inner (longer) horizontal and vertical lines for the circles with center at distance $2$ can be discarded, those circles don't block anything not already blocked. I put a picture below of what I think one gets. | |
| Apr 26, 2011 at 7:30 | answer | added | Aaron Meyerowitz | timeline score: 6 | |
| Apr 26, 2011 at 1:08 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Added figure illustrating DZ's chord construction.
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| Apr 25, 2011 at 14:24 | answer | added | Douglas Zare | timeline score: 12 | |
| Apr 25, 2011 at 13:09 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |