We provide three examples of the use of geometric reasoning with three-dimensional spacetime diagrams, rather than algebraic manipulations using three-dimensional Lorentz transformations, to analyze problems in special relativity. The examples are the “rising manhole” paradox, the “moving spotlight” problem, and Einstein's light-clock derivation of time dilation.
This figure appears opposite the title page of Ref. 7 and is used with permission; the following discussion is adapted from Sec. 6.4 of that reference.