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Characterization of ellipsoids and polarity in convex sets
Author(s) -
Montejano Luis,
Morales Efren
Publication year - 2003
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014790
Subject(s) - mathematics , ellipsoid , polarity (international relations) , characterization (materials science) , regular polygon , combinatorics , pure mathematics , symmetry (geometry) , geometry , nanotechnology , materials science , genetics , physics , astronomy , cell , biology
By introducing the concept of polarity in convex sets, it is possible, in a natural way, to generalize several classic characterizations of ellipsoids, showing that all of them depend upon and are related to the concept of projective centre of symmetry. Using these ideas, it is also possible to develop new characterizations of ellipsoids and to propose new problems.