1. An introduction to continued fractions
- Author
-
A.J. van der Poorten
- Subjects
Combinatorics ,Formalism (philosophy of mathematics) ,Number theory ,Diophantine equation ,Applied mathematics ,Mathematics - Abstract
Our remark sets up a correspondence ↔ between certain products of 2×2 matrices and continued fractions, which we shall exploit below. Of course this correspondence has an immediate geometric interpretation (cf Stark [1], Chap. 7). However, we shall obtain the usual properties of the continued fraction algorithm directly from the formalism rather than from the geometry. For example, we read that { pn+1 = cn+1pn + pn−1 qn+1 = cn+1qn + qn−1 n = 0, 1, 2, . . .
- Published
- 1986