The equal tangents property

J. Jeronimo-Castro; G. Ruiz-Hernandez; S. Tabachnikov

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arXiv · 1205.0142

The equal tangents property

J. Jeronimo-Castro·G. Ruiz-Hernandez·S. Tabachnikov

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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.

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BibTeX RIS

J. Jeronimo-Castro, G. Ruiz-Hernandez, S. Tabachnikov. 2012-05-04. The equal tangents property. https://arxiv.org/abs/1205.0142

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