On the Perimeter of a Triangle in a Minkowski Plane

Abstract

A Minkowski plane is a plane endowed with a norm that is not necessarily Euclidean. The Minkowski length of a curve in a Minkowski plane is defined in a manner analogous to the way it is defined in the Euclidean case. A circle of radius r in a Minkowski plane with norm I|| II is the locus of points X satisfying IX P II = r for a fixed center P. It is a convex curve that is symmetric with respect to its center. Golab's theorem shows that the Minkowski length of a circle of unit radius lies between 6 and 8 (see [2]). Let L denote the Minkowski length. We establish the following: