The purpose of this paper is to show that the mathematical treatment of three-dimensional rotations
can be simplified, and its geometrical understanding improved, using the Rodrigues vector
representation. We present a novel geometrical interpretation of the Rodrigues vector. Based on this
interpretation and simple geometrical considerations, we derive the Euler–Rodrigues formula,
Cayley’s rotation formula and the composition law for finite rotations. The level of this discussion
should be suitable for undergraduate physics or engineering courses where rotations are discussed.