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Title:

Dark clouds on spheres and totally non-spherical bodies of constant breadth

Document type:
Zeitschriftenaufsatz
Author(s):
Brandenberg, René; Larman, David
Abstract:
In this paper, we show that for any dimension $d \ge 3$ there exists a body of constant breadth $C$, such that its projection onto any 2-plane is non-spherical. We call such a body totally non-spherical. The circumradius of the projection of any totally non-spherical body $C$ of constant breadth onto any 2-plane is bigger than the half diameter of $C$. Showing the existence of such a body extends results of Eggleston [E] and Weissbach [W], who showed it in the case $d=3$.
Keywords:
radii, minimal projections, isoperimetric inequalities, dark clouds, constant breadth, constant width, non-spherical
Journal title:
Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry
Year:
2003
Journal issue:
44 / 2
Pages contribution:
531-538
Reviewed:
ja
Language:
en
TUM Institution:
Lehrstuhl für Angewandte Geometrie und Diskrete Mathematik
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