Timeline for Diameter of $n$-unit-vector closed scribble
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 24, 2014 at 8:32 | comment | added | Tom-Tom | @Lucia. You are right. Maybe I interpreted the question with the assumption that it cannot be that simple. | |
| Apr 24, 2014 at 3:19 | comment | added | Lucia | Indeed. Note that the problem asks about the diameter and not the perimeter. Hence my confusion about your answer. I agree that the diameter scales as $\sqrt{n}$. | |
| Apr 23, 2014 at 21:45 | comment | added | Tom-Tom | @Lucia. The segments of unit length create a shape in the plane, they can intersect each other eventually. Take a point $M$ very far away from the figure. All the points that you cannot reach from $M$ without crossing a segment form a bounded domain $\mathcal D$. The polyogon is the boundary of $\mathcal D$. By perimeter we mean the length of the polygon, which is made of segments of various lengths between 0 and 1. The size or diameter is, form instance, the maximum distance between two points inside $\mathcal D$ and it indeed scales as $\sqrt n$. | |
| Apr 23, 2014 at 14:40 | comment | added | Lucia | I am puzzled by this answer. I would have expected the diameter to behave like the maximum of partial sums of random vectors of unit length, which would be roughly $n^{1/2}$. Are you saying that the diameter in this case is substantially bigger, just because of the constraint that the end points have to match? Seems quite strange (and interesting of course). | |
| Apr 23, 2014 at 10:45 | vote | accept | Joseph O'Rourke | ||
| Apr 23, 2014 at 10:31 | review | First posts | |||
| Apr 23, 2014 at 10:35 | |||||
| Apr 23, 2014 at 10:12 | history | answered | Tom-Tom | CC BY-SA 3.0 |