The equal tangents property
Metric Geometry
2012-05-07 v2
Abstract
Let M be a smooth strictly convex closed surface in space and denote by H the set of points x in the exterior of M such that all the tangent segments from x to M have equal lengths. In this note we prove that if H is either a closed surface containing M or a plane then M is an Euclidean sphere. Moreover, we shall see that the situation in the Euclidean plane is very different.
Keywords
Cite
@article{arxiv.1205.0142,
title = {The equal tangents property},
author = {J. Jeronimo-Castro and G. Ruiz-Hernandez and S. Tabachnikov},
journal= {arXiv preprint arXiv:1205.0142},
year = {2012}
}
Comments
a typo corrected