Covering a Sphere with Four Random Circular Caps
Probability
2015-02-25 v1 Metric Geometry
Abstract
Let p(w) denote the probability that four random circular caps of angular radius 70deg<w<90deg cover the unit sphere S^2. An exact expression for p(w) is unknown. We give nontrivial lower bounds for p(w) when w>84deg; no improvement on the inequality p(w)>=0 for w<84deg is yet feasible. A dual problem involving randomly inscribed well-centered tetrahedra is also examined.
Cite
@article{arxiv.1502.06931,
title = {Covering a Sphere with Four Random Circular Caps},
author = {Steven R. Finch},
journal= {arXiv preprint arXiv:1502.06931},
year = {2015}
}
Comments
10 pages, 2 figures