Geometric properties of a sine function extendable to arbitrary normed planes

V. Balestro, H. Martini and R. Teixeira, Geometric properties of a sine function extendable to arbitrary normed planes, Monatshefte für Mathematik 182(4), pp. 781-800, 2017. (arXiv link) (journal link)

Comments: In this paper we study a sine function which as a simple formulation in terms of the norm, and which agrees with the usual sine function in the Euclidean subcase. We study its properties and also use it to define a geometric constant to measure how far a plane is from being Radon. This constant can be also regarded as a modulus of asymmetry of supporting directions in the unit circle. Further on, we relate the sine function to angular measures in the sense of Brass, proving that they only can “agree” if the norm is Euclidean and if the angular measure is the standard one.