A perimeter-based angle measure in generalized Minkowski planes

Abstract

Defining and measuring angles in the Euclidean plane is a well-known topic and quite useful in elementary geometry. For general normed planes there exists a variety of different concepts. These can be of special types, e.g. also implying the preservation of special orthogonality types. But such concepts are no angle measures in the sense of measure theory since they are not additive. This led the author to define a new angle measure for normed planes that in fact is a measure in the sense of measure theory. In the present paper we extend this concept even more to generalized Minkowski planes or gauges, i.e., to planes in which the unit circle is an arbitrary convex set with the origin in its interior.