### Abstract

Let M be a C^{2}-smooth strictly convex closed surface in ℝ^{3} 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 | |

State | Published - Jul 1 2014 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Cite this

*Advances in Geometry*,

*14*(3), 447-453. https://doi.org/10.1515/advgeom-2013-0011

}

*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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The equal tangents property

AU - Jerónimo-Castro, Jesús

AU - Ruiz-Hernández, Gabriel

AU - Tabachnikov, Sergei

PY - 2014/7/1

Y1 - 2014/7/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84925373760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925373760&partnerID=8YFLogxK

U2 - 10.1515/advgeom-2013-0011

DO - 10.1515/advgeom-2013-0011

M3 - Article

VL - 14

SP - 447

EP - 453

JO - Advances in Geometry

JF - Advances in Geometry

SN - 1615-715X

IS - 3

ER -