# Plane of Support

## plane of support

[′plān əv sə′pȯrt] (mathematics)

Relative to a convex body in a three-dimensional space, a plane that contains at least one point of the body but is such that the half-space on one side of the plane contains no points of the body.

## Plane of Support

A plane of support relative to a set *M* at a point *A* in *M* is a plane passing through *A* such that *M* lies entirely on one side of the plane, or, more precisely, in one of the closed half spaces determined by the plane. The plane of support is very important in the study of the properties of convex bodies.