English

Random Cyclic Quadrilaterals

History and Overview 2016-10-04 v1 Metric Geometry Probability

Abstract

The circumcircle of a planar convex polygon P is a circle C that passes through all vertices of P. If such a C exists, then P is said to be cyclic. Fix C to have unit radius. While any two angles of a uniform cyclic triangle are negatively correlated, any two sides are independent. In contrast, for a uniform cyclic quadrilateral, any two sides are negatively correlated, whereas any two adjacent angles are uncorrelated yet dependent.

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Cite

@article{arxiv.1610.00510,
  title  = {Random Cyclic Quadrilaterals},
  author = {Steven Finch},
  journal= {arXiv preprint arXiv:1610.00510},
  year   = {2016}
}

Comments

15 pages, 6 figures

R2 v1 2026-06-22T16:08:41.087Z