A characterization of the sphere

• Autores: W. Förg-Rob, R. Liedl
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 61, Nº. 3, 2001, págs. 201-204
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • This paper gives a "nice" characterization of the sphere: Taking into account the well-known secant's law that the product of the segments of a secant through a point P in the sphere is independent of the secant but depends only on the point P, one can derive -- roughly speaking -- the following theorem: If you run along a closed curve in the interior of a sphere with constant speed, at any point you can measure the distance to the sphere 'in front of' and 'behind' you. Then the integral over the distance 'in front of you' along the curve equals the integral over the distance 'behind you'. Moreover, and this is the more interesting fact, this property characterizes the sphere among closed convex domains.