DISTANCE GEOMETRY AND GEOMETRIC ALGEBRA

As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-k nown) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordina tes for conformal geometry.((1)) In this paper we show that this const ruction is the Clifford algebra analogue of a hyperbolic model of Eucl idean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a ver y simple representation in this model, as demonstrated by J. J. Seidel ((18)).