An algorithm for constructing diagrams of two-bridge knots and links with period two

Abstract

In this paper we review the connections between two-bridge knots and links, continued fractions and generalized Euclidean algorit.hms. Then, using a generalized Euclidean algorithm in which each partial quotient is even, we provide a constructive method demonstrating that every two-bridge knot and link has period two. Using the algorithm we develop, we are also able to obtain an additional method for computing the linking number of two-bridge links.