Euler’s fixed point theorem: The axis of a rotation

We give an elementary proof of what is perhaps the earliest fixed point theorem; namely Leonhard Euler’s theorem of 1775 on the existence of an axis v for any three-dimensional rotation R. The proof is constructive and shows that no multiplications are required to compute v. Dedicated to the memory of Leonhard Euler, “The Master of us all”, on the occasion of the 300th anniversary of his birth