The equal tangents property

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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

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Tangent line
Closed
Euclidean plane
Strictly Convex
Set of points
Euclidean
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All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Jerónimo-Castro, Jesús ; Ruiz-Hernández, Gabriel ; Tabachnikov, Sergei. / The equal tangents property. In: Advances in Geometry. 2014 ; Vol. 14, No. 3. pp. 447-453.
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Jerónimo-Castro, J, Ruiz-Hernández, G & Tabachnikov, S 2014, 'The equal tangents property', Advances in Geometry, vol. 14, no. 3, pp. 447-453. https://doi.org/10.1515/advgeom-2013-0011

The equal tangents property. / Jerónimo-Castro, Jesús; Ruiz-Hernández, Gabriel; Tabachnikov, Sergei.

In: Advances in Geometry, Vol. 14, No. 3, 01.07.2014, p. 447-453.

Research output: Contribution to journalArticle

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Jerónimo-Castro J, Ruiz-Hernández G, Tabachnikov S. The equal tangents property. Advances in Geometry. 2014 Jul 1;14(3):447-453. https://doi.org/10.1515/advgeom-2013-0011