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Being neither commutative nor associative, Einstein velocity addition ofrelativistically admissible velocities gives rise to gyrations. Gyrations, inturn, measure the extent to which Einstein addition deviates from commutativityand from associativity. Gyrations are geometric automorphisms abstracted fromthe relativistic mechanical effect known as Thomas precession.

Gyrations: The Missing Link Between Classical Mechanics with its  Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying  Hyperbolic Geometry