Timeline for If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a nice proof of this?
Current License: CC BY-SA 4.0
24 events
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| Jan 6, 2023 at 15:23 | history | edited | Gerry Myerson |
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| Jan 6, 2023 at 8:15 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added a Wayback Machine link for the dead link
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| Dec 20, 2022 at 17:19 | answer | added | Zvonimir Sikic | timeline score: 4 | |
| Nov 27, 2021 at 6:46 | comment | added | kushal | Here's a nice argument: Let the length of the pieces be x, y, and 1-x-y. To form a triangle, each of x,y, and 1-x-y must be less than 1/2. A triangle is not formed iff the two cuts are on the same side of a midpoint. The probability that a given cut is on right side of the midpoint is 1/2, so the probability that both cuts are on the right side is simply 1/2 * 1/2 = 1/4. Imagine the two cuts as three cuts on a circle, where one of the cuts is to straighten it out. All three pieces have 1/4 probability of being longer than half. Hence, probability of triangle formation is: 1 - 3*1/4 = 1/4. | |
| Jul 14, 2016 at 20:25 | answer | added | Bill the Lizard | timeline score: 6 | |
| Feb 10, 2016 at 12:32 | comment | added | Ryan Oberoi | so here is the simple solution - divide a line into 6 parts of length 1/6 each. without loss of generality, the largest broken part will be greater than or equal to 1/3. So the largest part can lie in segments 3,4,5 or 6. Only 1 of these 4 portions will result in a triangle (since segments 4,5,6 will result in largest part being > 1/2). Ergo, 1/4 probability. | |
| Dec 30, 2015 at 20:36 | comment | added | aioobe | This problem was presented to me a couple of days ago. I just wrote a little blog post explaining my solution, which ends with a symmetry argument. | |
| Aug 27, 2013 at 11:45 | review | Close votes | |||
| Aug 27, 2013 at 14:13 | |||||
| Aug 27, 2013 at 11:24 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
replaced deprecated tag 'geometry'; shortened title because software complained that title was longer than 150 characters
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| Aug 27, 2013 at 11:10 | history | protected | Kim Morrison | ||
| Aug 27, 2013 at 10:56 | answer | added | Arash | timeline score: 6 | |
| Aug 27, 2013 at 10:52 | answer | added | Arash | timeline score: 4 | |
| Mar 22, 2013 at 18:21 | answer | added | Shaswata | timeline score: 4 | |
| Nov 2, 2011 at 16:10 | comment | added | Michael Lugo | This seems to be related to a recent math.stackexchange question: math.stackexchange.com/questions/72977/… | |
| Jun 4, 2011 at 14:26 | answer | added | Allen Hatcher | timeline score: 8 | |
| Jun 4, 2011 at 13:00 | answer | added | Christian Blatter | timeline score: 53 | |
| Jun 3, 2011 at 5:18 | answer | added | Peter Shor | timeline score: 66 | |
| Jun 3, 2011 at 0:12 | answer | added | Mort Schwartz | timeline score: -1 | |
| Jun 25, 2010 at 19:34 | answer | added | Michael Lugo | timeline score: 10 | |
| Oct 23, 2009 at 17:49 | vote | accept | Michael Lugo | ||
| Oct 23, 2009 at 3:57 | answer | added | Ilya Nikokoshev | timeline score: 12 | |
| Oct 23, 2009 at 2:59 | answer | added | Jason Dyer | timeline score: 21 | |
| Oct 23, 2009 at 2:43 | answer | added | Kevin P. Costello | timeline score: 123 | |
| Oct 23, 2009 at 2:28 | history | asked | Michael Lugo | CC BY-SA 2.5 |