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On the Determination of Convex Bodies by Projection Functions
Author(s) -
Goodey Paul,
Schneider Rolf,
Weil Wolfgang
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396001968
Subject(s) - mathematics , regular polygon , projection (relational algebra) , translation (biology) , convex analysis , subderivative , reflection (computer programming) , mathematics subject classification , pure mathematics , geometry , convex optimization , algorithm , computer science , biochemistry , chemistry , messenger rna , gene , programming language
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. 1991 Mathematics Subject Classification 52A20.