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On Hammer's X‐Ray Problem
Author(s) -
Gardner R. J.,
McMullen P.
Publication year - 1980
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-21.1.171
Subject(s) - hyperplane , diagonal , polygon (computer graphics) , regular polygon , combinatorics , mathematics , hammer , convex polygon , plane (geometry) , geometry , computer science , structural engineering , engineering , telecommunications , frame (networking)
Suppose that two distinct convex bodies in E″ have the same Steiner symmetrals in a number of hyperplanes whose normals lie in a plane. Then the directions of these normals are linearly equivalent to a subset of directions of diagonals of a regular polygon. In particular Steiner symmetrals in some four fixed hyperplanes will distinguish between distinct convex bodies.