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ON THE DETERMINATION OF CONVEX BODIES BY PROJECTION FUNCTIONS

Published online by Cambridge University Press:  01 January 1997

PAUL GOODEY ,
ROLF SCHNEIDER  and
WOLFGANG WEIL
PAUL GOODEY
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA
ROLF SCHNEIDER
Affiliation:
Mathematisches Institut, Albert-Ludwigs-Universität, Albertstrasse 23b, D-79104 Freiburg i. Br., Germany
WOLFGANG WEIL
Affiliation:
Mathematisches Institut II, Universität Karlsruhe, Englerstrasse 2, D-76131 Karlsruhe, Germany
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Abstract

This work is an investigation of the extent to which convex bodies are determined by the sizes of their projections. It is shown, on the one hand, that there are non-congruent bodies for which all corresponding projections have the same size. On the other hand, it is proved that in the usual Baire category sense, most convex bodies are determined, up to translation or reflection, by the combination of their widths and brightnesses in all directions.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 1 , January 1997 , pp. 82 - 88
Copyright
© The London Mathematical Society 1997

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