# Accession Number:

## AD0646926

# Title:

## A GENERALIZATION OF THE MOTZKIN THEOREM,

# Descriptive Note:

# Corporate Author:

## PARKE MATHEMATICAL LABS INC CARLISLE MASS

# Personal Author(s):

# Report Date:

## 1966-11-01

# Pagination or Media Count:

## 32.0

# Abstract:

A figure A in the Euclidean plane is a compact set whose closed convex hull CA has a non empty interior a ball of support for A is a closed ball which has points of A on the boundary but not in the interior. For each figure A, let CA-A denote the convex deficiency of A and let S,q denote the skeletal pair of A where S is the set of centers of maximal balls of support for A and qx is the distance from x to A for xeS. The following statements are proved 1 Two figures have equal convex deficiencies if they have equal skeletal pairs. 2 Motzkins Theorem A figure is convex if its skeleton is empty. 3 A figure is uniquely determined by its closed convex hull and its skeletal pair. 4 A figure with empty interior is uniquely determined by its skeletal pair. Author

# Descriptors:

# Subject Categories:

- Anatomy and Physiology
- Operations Research
- Bionics