A Geometric Representation of Galilean and Lorentz Transformations, Robert W. Brehme, Am. J. Phys. 32, 233 (1964)
The kinematic concepts of special relativity seem best understood by the beginning student if they are presented in purely geometric form. The description of events in space-time is given geometrically as viewed from different coordinate systems in relative motion with one another, both from the classical and relativistic points of view. These geometric representations differ somewhat from those usually seen. Some justification is given the Lorentz transformation by requiring that the velocity of light be the same for all observers and that in the limit of small velocities, the Lorentz transformation reduce to the Galilean transformation. The relativistic contraction of lengths and the dilation of time intervals are deduced.