Transformation Geometry: An Application of Physics

Although the ideas and techniques of transformation geometry are very different from those of Euclidean geometry, the standard applications of transformation geometry tend to be to problems that can also be solved using Euclidean methods. This fact can easily lead students to question the value of studying both. As a partial response to this difficulty, I would like to present an application of transformation geometry to physics, in particular, special relativity, which uses the transformation ideas in a nontrivial way and for which there is no Euclidean counterpart.