Convex Bodies of Constant Width and Constant Brightness

Details Convex Bodies of Constant Width and Constant Brightness Convex Bodies of Constant Width and Constant Brightness

2003-06-30

arxiv.org/abs/math/0306437v1

Mathematics

Metric Geometry

20 pages

Scientific paper

In 1926 S. Nakajima (= A. Matsumura) showed that any convex body in $\R^3$
with constant width, constant brightness, and boundary of class $C^2$ is a
ball. We show that the regularity assumption on the boundary is unnecessary, so
that balls are the only convex bodies of constant width and brightness.

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