Oğuzhan Demirel, The first sharp gyrotriangle inequality in Möbius
gyrovector space (D, Å, Ä),
Forum Geometricorum, 17 (2017) 439--447.
Abstract. In this paper we present two different inequalities (with their reverse inequalities) written in a common type by using classical vector addition “+” and classical multiplication “·” in Euclidean geometry and by using Möbius addition “oplus” and Möbius scalar multiplication “otimes” in Möbius gyrovector space (D, oplus, otimes). It is known that this Möbius gyrovector space form the algebraic setting for the Poincaré disc model of hyperbolic geometry, just as vector spaces form the algebraic setting for the standard model of Euclidean geometry.
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