Timeline for Geometric probabilistic problem on triangles on a plane
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2020 at 16:50 | vote | accept | Penelope Benenati | ||
| Aug 4, 2020 at 16:50 | vote | accept | Penelope Benenati | ||
| Aug 4, 2020 at 16:50 | |||||
| Aug 4, 2020 at 16:50 | vote | accept | Penelope Benenati | ||
| Aug 4, 2020 at 16:50 | |||||
| Jul 31, 2020 at 14:17 | answer | added | fedja | timeline score: 3 | |
| Jul 30, 2020 at 22:46 | answer | added | user44143 | timeline score: 2 | |
| Jul 30, 2020 at 22:35 | comment | added | Penelope Benenati | I realized that I was wrong in the problem formulation at the beginning. The probability that the horizontal / vertical option is selected depends therefore on the two sizes of the triangle projection on the two axes. | |
| Jul 30, 2020 at 22:15 | history | edited | user44143 | CC BY-SA 4.0 |
removed non-standard and unnecessary use of capital A, B, C
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| Jul 30, 2020 at 21:26 | comment | added | fedja | Do you still choose the vertical option with probability $1/2$ and the horizontal option with probability $1/2$ or the mixture is different now? | |
| Jul 30, 2020 at 20:33 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
deleted 88 characters in body
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| Jul 30, 2020 at 20:15 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
deleted 170 characters in body
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| Jul 30, 2020 at 19:28 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
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| Jul 30, 2020 at 17:59 | history | undeleted | Penelope Benenati | ||
| Jul 30, 2020 at 17:58 | history | deleted | Penelope Benenati | via Vote | |
| Jul 30, 2020 at 17:08 | answer | added | Steven Stadnicki | timeline score: 1 | |
| Jul 30, 2020 at 16:57 | comment | added | Penelope Benenati | Matt, I will provide a "numerically calculated expectation for some scalene triangle" as soon as possible. | |
| Jul 30, 2020 at 16:51 | comment | added | Penelope Benenati | StevenStadnicki, Matt, I understand now the question. It is related to my research. I am developing a random algorithm, which would be very complicated to explain. In this algorithm, the use of random straight lines parallel to the cartesian axes reduces its time complexity, and that's why I am focusing on these two types of lines solely. | |
| Jul 30, 2020 at 16:46 | comment | added | Steven Stadnicki | Seconding what Matt F is saying — the question 'makes sense' in the sense that it's a quantity one can calculate for any given triangle easily enough, and probably for any orientation of the given triangle with some effort. But understanding why you're trying to maximize this quantity may help with giving more guidance and avoiding XY problems. | |
| Jul 30, 2020 at 16:45 | comment | added | user44143 | I understood all that, but by "how does this arise" and "what is the significance" I was trying to understand why this apparently awkward setup might also be interesting. | |
| Jul 30, 2020 at 16:43 | comment | added | Penelope Benenati | Matt, the randomization is only related to choice of the orientation of the straight line $L$ (either horizontal or vertical) and has nothing to do with the triangle $T$. One can think that a fair coin is tossed to decide if $T$ will be cut by a random horizontal or vertical straight line. About the uncut side length: almost surely the number of sides cut by the random straight line $L$ is equal to $2$, which implies that almost surely there will be one and only one uncut side of $T$. I am interesting in its maximum expected length. | |
| Jul 30, 2020 at 16:42 | comment | added | user44143 | Also, can you give an example with a numerically calculated expectation for some scalene triangle? It looks complicated no matter how you do it. | |
| Jul 30, 2020 at 16:27 | comment | added | user44143 | How does the randomization between horizontal and vertical cuts arise? And what is the significance of the uncut length? Both of those are different from typical geometric setups. | |
| Jul 30, 2020 at 16:03 | history | edited | Penelope Benenati | CC BY-SA 4.0 |
added 24 characters in body
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| Jul 30, 2020 at 15:54 | comment | added | Penelope Benenati | Thank you fedja. I am correcting the question. | |
| Jul 30, 2020 at 15:47 | comment | added | fedja | "What minimum expected length (as a function of a, b and c)" and "over all orientations of T on the plane and all possible choices of a, b and c" are incompatible. I assume the latter is just a typo (otherwise the story is trivial: put $a=b=c=0$), right? | |
| Jul 30, 2020 at 15:33 | history | asked | Penelope Benenati | CC BY-SA 4.0 |