RATIONAL TANGLES

This paper gives an elementary and self-contained proof of Conway's Ba sic Theorem on rational tangles. This theorem states that two rational tangles are topologically equivalent if and only if they have the sam e associated rational fraction. Our proof divides into a geometric hal f that relates the arithmetic of continued fractions to the topology o f tangles and an algebraic part that defines the fraction of any tangl e via the bracket model far the Jones polynomial. We present an applic ation to molecular biology. (C) 1997 Academic Press.