Vol. 29, No. 2, 1969

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A characteristic property of the sphere

Lajos Tamássy

Vol. 29 (1969), No. 2, 439–446
Abstract

It was proven by P. Funk that the only symmetrical star-shaped body, all of whose intersections with planes through its midpoint have surface area π, is the unit sphere. In this paper the same conclusion is deduced from a materially weaker hypothesis and an application of the result is given.

Mathematical Subject Classification
Primary: 53.75
Secondary: 52.00
Milestones
Received: 26 April 1968
Published: 1 May 1969
Authors
Lajos Tamássy