  This article explores the geometric algebra of Minkowski spacetime, and its
relationship to the geometric algebra of Euclidean 4-space. Both of these
geometric algebras are algebraically isomorphic to the 2x2 matrix algebra over
Hamilton's famous quaternions, and provide a rich geometric framework for
various important topics in mathematics and physics, including stereographic
projection and spinors, and both spherical and hyperbolic geometry. In
addition, by identifying the time-like Minkowski unit vector with the extra
dimension of Euclidean 4-space, David Hestenes' Space-Time Algebra of Minkowski
spacetime is unified with William Baylis' Algebra of Physical Space.
