Rapidity: The physical meaning of the hyperbolic angle in special relativity

In Special Relativity the Galilean law of addition of velocities is replaced by a law of composition formally identical to the addition formula of the hyperbolic tangent. So a simple additive law can be obtained by inverting the hyperbolic tangent and passing to the hyperbolic angle, called rapidity. This article intends to demonstrate that the use of the hyperbolic angle is not a mere mathematical trick but that rapidity admits a simple physical meaning.