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- Document type:
- Zeitschriftenaufsatz
- Author(s):
- Brandenberg, René; Larman, David
- 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
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