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Document type:
Zeitschriftenaufsatz 
Author(s):
Brandenberg, R. and D. Larman 
Title:
Dark clouds on spheres and totally non-spherical bodies of constant breadth 
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