English

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}
}

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4 pages