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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“As an individual, I myself feel impelled to fancy ... a limitless succession of Universes.... Each exists, apart and independently, in the bosom of its proper and particular God.”
—Edgar Allan Poe (1809–1849)
“No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.”
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As take from me thyself and not me too.”
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