Abstract
The geometry of Minkowski space is investigated by using concepts such as hyperbolic angles, hyperbolic curves, and hyperbolic arc lengths. The hyperbolic angle between two inertial observers is given by θ = 1 2 log{(1 + v)/(1− v)}. The usual scalar product between any two Lorentz vectors can be written in terms of the hyperbolic angle between them. The scalar product of two timelike vectors A and B, for example, can be written as A ·B = |A||B| coshθ, where |A| and |B| are their Lorentz invariant lengths. This is a natural generalizations of Euclidean geometry.
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