Timeline for Expected area of a pentagon formed from a randomly broken stick [closed]
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Nov 26, 2017 at 0:40 | history | closed |
Jan-Christoph Schlage-Puchta Peter Humphries Mikhail Katz user6976 Jeremy Rouse |
Not suitable for this site | |
| Nov 19, 2017 at 3:03 | review | Close votes | |||
| Nov 26, 2017 at 0:40 | |||||
| Nov 15, 2017 at 3:01 | comment | added | fedja | I wonder why questions like that pop up with astonishing regularity? The answer is always the same: one can set up the integral (in this case the OP decided to go beyond quadrilaterals and thus challenge us with either implicit functions or parametric representations; as to myself, I prefer the latter) and evaluate it numerically. So, the answer is a long string of decimal digits that you can figure out up to any length you can memorize, given some cheap computer and minimal programming skills. No need to bother other people. Voting to close. | |
| Nov 14, 2017 at 17:50 | answer | added | Joseph O'Rourke | timeline score: 1 | |
| S Nov 14, 2017 at 16:36 | history | suggested | CommunityBot |
Propose better tags
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| Nov 14, 2017 at 15:08 | review | Suggested edits | |||
| S Nov 14, 2017 at 16:36 | |||||
| Nov 14, 2017 at 7:09 | comment | added | Fedor Petrov | I think, "cyclic" is a standard term for a convex polygon inscribed in the circle. It is not obvious at all, but there is unique cyclic $n$-gon with given length sides (each of which is less than the sum of the others) in a given order, and its area does not depend on the order of sides (this already is clear: permute the segments cut by the sides.) | |
| S Nov 14, 2017 at 6:54 | history | suggested | David G. Stork | CC BY-SA 3.0 |
Corrected the error in the number of breaks $n-1$ and the resulting number of sides $n$. Tightened the prose. Clarified the title to refer to area.
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| Nov 14, 2017 at 6:15 | comment | added | Martin Sleziak | The tag (discrete-mathematics) is deprecated - see the tag-info. So it might be better to choose some other suitable tags. | |
| Nov 14, 2017 at 4:55 | comment | added | Hugh Thomas | @PerAlexandersson: You mean 5 isosceles triangles. The fact that your interpretation makes the area well-defined (which it otherwise isn't) makes me think your interpretation of "cyclic" is the right one. | |
| Nov 14, 2017 at 2:25 | review | Close votes | |||
| Nov 14, 2017 at 12:22 | |||||
| Nov 14, 2017 at 0:52 | review | Suggested edits | |||
| S Nov 14, 2017 at 6:54 | |||||
| Nov 14, 2017 at 0:41 | comment | added | David G. Stork | In this context I believe "cyclic" pentagon means merely that there are no self-intersections. Moreover, under the conditions stated the pentagon need not be unique. | |
| Nov 13, 2017 at 22:17 | comment | added | Per Alexandersson | Cyclic pentagon means vertices on a circle, right? If that is the case, then the area is uniquely determined by the side lengths - draw the 5 lines from the circle center, and you get 5 equilaterial triangles, whose sum of areas is independent of how (the order) you glue together the pieces. | |
| Nov 13, 2017 at 21:08 | comment | added | Gerry Myerson | Is it not possible that the pieces form more than one pentagon? more than one cyclic pentagon? and do you allow self-crossing 5-gons, e.g., pentagrams? | |
| Nov 13, 2017 at 20:44 | comment | added | Fedor Petrov | Are there reasons to expect this value to be computable in 'elementary functions and standard constants'? | |
| Nov 13, 2017 at 19:18 | history | asked | John Smith | CC BY-SA 3.0 |