Classroom note: Compact, convex, and symmetric sets are discs

Abstract

Define the centre of a parallelogram to be the intersection of its diagonals. It was shown in an earlier paper that the intersection of arbitrarily many parallelograms with the same centre is the unit disc about that centre in a metric defined using ideas from Linear Algebra. In this note, it is shown that this characterizes compact, convex sets, which are symmetric about a point.

Notes

This paper is dedicated to the memory of Dr. Samuel R. Knox.

Additional information

Notes on contributors

Mark Lynch

This paper is dedicated to the memory of Dr. Samuel R. Knox.