In this paper we present a generalization of the continued fraction algorithm, based on a geometric and matrix-theoretic approach.
We first give a geometric representation in the plane R^2, of the simple continued fraction algorithm, described in terms of geometric and arithmetic properties of 2 X 2 matrices with nonnegative integer entries and determinant 1. The algorithm of this paper is then derived as a natural generalization of the situation in R^2. We describe a computational procedure for our algorithm, and give several examples.