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THE n-SYMMETRY PLANES THEOREM OF A CONVEX BODY

DOI: 10.46573/2658-7459-2026-1-69-76

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Authors

Al.A. Shum, A.M. Vetoshkin

Abstract

The concept of a moment of the n-th order of a convex body relative to a given plane is considered. A plane is a plane of n-symmetry if the moments of the n-th order of the two sub-bodies into which the initial body is divided by this plane are the same. It is established that the moment of the n-th order of a convex body relative to the plane П, drawn parallel to a given plane, reaches the smallest value when the plane П is the plane of (n 1)-symmetry of this body.

Keywords

moment of n-th order, plane of n-symmetry, plane of half-mass, convex body, density function, mass, center of mass, center of half-mass, electric machine.