A characteristic property of the Euclidean disc |
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Authors: | Jesús Jerónimo-Castro Edgardo Roldán-Pensado |
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Institution: | 1.Instituto de Matemáticas,UNAM,Cd. de México,México;2.Facultad de Matemáticas,UAG,Acapulco,México;3.Instituto de Matemáticas,UNAM,Cuernavaca,México |
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Abstract: | In this paper the following is proved: Let K ⊂ $
\mathbb{E}^2
$
\mathbb{E}^2
be a smooth strictly convex body, and let L ⊂ $
\mathbb{E}^2
$
\mathbb{E}^2
be a line. Assume that for every point x ∈ L/K the two tangent segments from x to K have the same length, and the line joining the two contact points passes through a fixed
point in the plane. Then K is an Euclidean disc. |
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Keywords: | |
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