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Volumes of Projections of unit Cubes
Author(s) -
McMullen Peter
Publication year - 1984
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/blms/16.3.278
Subject(s) - mathematics , unit cube , linear subspace , projection (relational algebra) , cube (algebra) , unit (ring theory) , volume (thermodynamics) , combinatorics , orthographic projection , geometry , algorithm , physics , mathematics education , quantum mechanics
Let Z andZ ¯be the images of a regular unit n ‐cube in E n under orthogonal projection on to orthogonal complementary subspaces of dimensions d and n — d respectively. It is shown that the d ‐volume of Z and the ( n — d )‐volume ofZ ¯are equal. This generalizes to a connexion between the volumes of strongly associated zonotopes.