A property of the bidimensional sphere
Combinatorics
2011-11-08 v1
Abstract
It is natural to ask for a reasonable constant k having the property that any open set of area greater than k on a bidimensional sphere of area 1 always contains the vertices of a regular tetrahedron. We shall prove that it is sufficient to take k=3/4. In fact we shall prove a more general result. The interested reader will not have any problem in establishing that 3/4 is the best constant with this property.
Keywords
Cite
@article{arxiv.1111.1330,
title = {A property of the bidimensional sphere},
author = {Marius Cavachi},
journal= {arXiv preprint arXiv:1111.1330},
year = {2011}
}
Comments
4 pages