Timeline for The number of triple intersections of lines
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 21 at 13:00 | comment | added | bob | @rus9384 Right in the double intersection case, for any two sets of lines every line in one set crosses every line in the other in the worst case which is O(n^2) from graph theory. Nice. | |
| Aug 21 at 1:41 | history | became hot network question | |||
| Aug 20 at 21:38 | comment | added | D.W.♦ | Is there any sense in which this requires answers from a computer science perspective? It seems like a matter of pure mathematics. | |
| Aug 20 at 21:27 | comment | added | Bader Abu Radi | @rus9384 Right, for the upper bound there is no need to have the parallel assumption. | |
| Aug 20 at 21:19 | comment | added | rus9384 | @BaderAbuRadi Though even if the lines are not parallel, there are $O(n^2)$ (double) intersections (also easily provable: at step $n$ there are $n-1$ lines on the plane, so a new line can only intersect at most $n-1$ lines) and since triple intersections are only a subset of intersections, the same upper bound follows for them. | |
| Aug 20 at 20:53 | history | edited | user150715 | CC BY-SA 4.0 |
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| Aug 20 at 20:47 | answer | added | Yves Daoust | timeline score: 4 | |
| Aug 20 at 20:27 | vote | accept | CommunityBot | ||
| Aug 20 at 18:28 | comment | added | user150715 | @BaderAbuRadi Yes, you consider each set consists of parallel lines for sake of simplicity. Note that almost two vertical lines sets creates quadrilateral which is rhombus, but horizontal lines through vertices of rhombus creates two triangles and four triple intersections. | |
| Aug 20 at 18:18 | comment | added | Bader Abu Radi | Can you add other assumptions? All we have is a picture. We cannot bound the number of triples from below by a quadratic if each set of lines follows an edge of a triangle, for example. If each set consists of parallel lines, then it is easy to show that there are at most quadratic number of triples. | |
| Aug 20 at 18:09 | answer | added | Bader Abu Radi | timeline score: 3 | |
| Aug 20 at 17:40 | history | asked | user150715 | CC BY-SA 4.0 |