Abstract
A geometrical description of the composition law for pure inertial transformations in relativity is developed, in close analogy with the description of rotations by means of turns. This affords a very intuitive and visual image of all problems involving a composition of velocities, and clearly shows the appearance of hyperbolic geometry in relativistic kinematics. The pertinent geometrical constructions as well as some applications are discussed. For the case of light the preceding constructions are surprisingly simple, and from them emerges a connection between the geometrical idea of parallelism angle and the physical Doppler effect. A slide rule which can be used to carry out all needed computations is also described.
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