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- n. A type of vector for which addition is defined by a formula that satisfies the axioms for a gyrogroup.
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Similarly, this addition gives rise to gyrovector spaces that form the algebraic setting for the PoincarÃ© ball model of hyperbolic geometry.
In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative.
In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition.
The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky.