Lorentz velocity addition

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This post follows on the Gamma factor post here.

The form of velocity addition based on the Lorentz transformation is related to a combination of arithmetic and harmonic addition. Galilei velocity addition is

u=v+u'

or

Lorentz velocity addition is

which equals

u=\frac{v+u'}{1+\frac{vu'}{c^{2}}}

In this way the Lorentz transformation attempts to combine arithmetic and harmonic addition.