Mathematical space used to study hyperbolic geometry
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A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry.[1] Ungar introduced the concept of gyrovectors that have addition based on gyrogroups instead of vectors which have addition based on groups. Ungar developed his concept as a tool for the formulation of special relativity as an alternative to the use of Lorentz transformations to represent compositions of velocities (also called boosts – "boosts" are aspects of relative velocities, and should not be conflated with "translations"). This is achieved by introducing "gyro operators"; two 3d velocity vectors are used to construct an operator, which acts on another 3d velocity.
^Abraham A. Ungar (2005), "Analytic Hyperbolic Geometry: Mathematical Foundations and Applications", Published by World Scientific, ISBN 981-256-457-8, ISBN 978-981-256-457-3
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