The moments of the distance between two random points in a regular polygon
Abstract
In this paper, we derive formulas for the analytical calculation of the moments of the distance between two uniformly and independently distributed random points in an $n$-sided regular polygon. A number of closed form expressions is provided, e.g. the expected distances for $n = 3,4,5,6,8,10,12$, where the results for $n = 5,8,10,12$ are new to the best of the author's knowledge. Applying results of Voss, remarkably short formulas for the second and the fourth moments are derived.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2021
- DOI:
- 10.48550/arXiv.2101.03815
- arXiv:
- arXiv:2101.03815
- Bibcode:
- 2021arXiv210103815B
- Keywords:
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- Mathematics - Probability;
- 60D05;
- 52A22;
- 53C65
- E-Print:
- 22 pages,6 figures