2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168789We present a unifying framework for understanding several different versions of the Hopf fibration, and use this framework to reconcile two methods of representing rotations of 3-space by unitary matrices--the mathematician's convention based on quaternion algebra, and the physicist's convention based on the Bloch sphere.8 pages, revised 11 September 2008, new introduction, reference added, some notation change for consistency and clarity, expanded appendixMathematical Physics15A90; 22E70text