The equal tangents property

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

doi:10.1515/advgeom-2013-0011

The equal tangents property

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

Research output: Contribution to journal › Article › peer-review

5 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 language	English (US)
Pages (from-to)	447-453
Number of pages	7
Journal	Advances in Geometry
Volume	14
Issue number	3
DOIs	https://doi.org/10.1515/advgeom-2013-0011
State	Published - Jul 1 2014

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1515/advgeom-2013-0011

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AU - Tabachnikov, Sergei

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N2 - 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.

AB - 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.

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ER -

The equal tangents property

Abstract

All Science Journal Classification (ASJC) codes

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