Sets of constant width

Gulbank D. Chakerian

Vol. 19 (1966), No. 1, 13–21

DOI: 10.2140/pjm.1966.19.13

Abstract

A lower bound, better than those previously known, is given for the volume of a 3-dimensional body of constant width 1. Bounds are also given in the case of n-dimensional bodies of constant width 1, n ≧ 4. Short proofs of the known sharp bounds for such bodies in the Euclidean and Minkowskian planes are given using properties of mixed areas. An application is made to a measure of outer symmetry of sets of constant width in 2 and 3 dimensions.

Mathematical Subject Classification

Primary: 52.40

Milestones

Received: 29 September 1965

Published: 1 October 1966