The equal tangents property

Jesús Jerónimo-Castro, Gabriel Ruiz-Hernández, Sergei Tabachnikov

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Let M be a C2-smooth strictly convex closed surface in ℝ3 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 a Euclidean sphere. Moreover, we shall see that the situation in the Euclidean plane is very different.

Original languageEnglish (US)
Pages (from-to)447-453
Number of pages7
JournalAdvances in Geometry
Volume14
Issue number3
DOIs
StatePublished - Jul 1 2014

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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