Timeline for How many small dots can be drawn in a region such that no three are "collinear"?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2019 at 10:45 | comment | added | Joseph O'Rourke | Seems correct.${}$ | |
| Aug 27, 2019 at 3:14 | comment | added | Haoran Chen | @JosephO'Rourke If $r<(2\sqrt{(n-1)^2+n^2})^{-1}\approx (2n)^{-1}$, no line can cross ($2$ or more intersections) three collinear dots on $n\times n$ grids. Then there could be $0.75r^{-1}$ dots based on Hall et al. result? | |
| Aug 26, 2019 at 14:41 | comment | added | Joseph O'Rourke | Related: For exact no-three-in-a-line of points on a $n \times n$ grid, the best lower bound is $n(1.5 -o(n))$ and best upper bound is $2n$. Discussed by David Eppstein in Forbidden Configurations in Discrete Geometry. | |
| Aug 26, 2019 at 2:31 | answer | added | user44143 | timeline score: 4 | |
| Aug 26, 2019 at 1:30 | answer | added | Nate | timeline score: 2 | |
| Aug 26, 2019 at 0:53 | history | edited | user44143 |
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| Aug 25, 2019 at 15:19 | history | edited | LSpice | CC BY-SA 4.0 |
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| Aug 25, 2019 at 9:46 | history | asked | Haoran Chen | CC BY-SA 4.0 |