Proper Velocity Space Model and Proper Velocity Addition
A proper velocity space model of hyperbolic geometry is given by proper velocities with vector addition given by the proper velocity addition formula:
where is the beta factor given by .
This formula provides a model that uses a whole space compared to other models of hyperbolic geometry which use discs or half-planes.
A proper velocity gyrovector space is a real inner product space V, with the proper velocity gyrogroup addition and with scalar multiplication defined by r v = s sinh(r sinh−1(|v|/s))v/|v| where r is any real number, v ∈ V, v ≠ 0 and r 0 = 0 with the notation v r = r v.
Read more about this topic: Gyrovector Space
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