  The purpose of this paper is to show that the mathematical treatment of three
dimensional rotations can be simplified, and its geometrical understanding
improved, by 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 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.
