The hyperbolic triangle centroid. (English) Zbl 1099.51008

It is deduced that the centroid of a hyperbolic triangle in relativity velocity space is the velocity of the center of momentum of three massive objects with equal rest masses located in the vertices of the triangle. Employing “gyrovector space” technics, explicit formulas for the centroid are deduced in the Beltrami-Klein model as well as in the Poincaré ball model of hyperbolic geometry. The formulas are formally similar to those known for Euclidean geometry.


51P05 Classical or axiomatic geometry and physics
51M10 Hyperbolic and elliptic geometries (general) and generalizations
83A05 Special relativity
20N05 Loops, quasigroups
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