THEOREM ON THE CENTER OF n-SYMMETRY OF A CONVEX SPATIAL BODY

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Authors

Al.A. Shum, A.M. Vetoshkin

Abstract

The concept of the center of n-symmetry of a spatial body is considered. It is indicated that special cases of this general concept are the center of s-symmetry (the center of 0-symmetry) and the center of c-symmetry (the center of 1-symmetry). The following theorem is proved: in any convex region of space, it is possible to determine the density function so that the center of the n-symmetry of the resulting body will be located at any predetermined internal point of this body (special cases of this theorem corresponding to the values n = 0 and n = 1 were previously known).

Keywords

symmetry, c-symmetry, s-symmetry, n-symmetry, center of symmetry, density function, convex body, mass, center of mass, electric bus.