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Rational Tangles

A rational tangle is given by alternating NE,SE and SE,SW twisting of the $0$ tangle [1]. Discussion of canonicality of this construction of twist vector can be found in [2]. A twist vector encodes these alternating twists as a list of integers. This induces a unique map from the rational tangles onto the rational numbers [1][2][3]. We accomplish this by interpreting a twist vector as a sequence for a continued fraction as: $$\LB a\ b\ c\RB=c+\frac{1}{b+\frac{1}{a}}$$

Instructions

Twist vectors here are space separated lists of integers.

A rational number here is “/” separating two integers.

1. J. Conway, An enumeration of knots and links, and some of their algebraic properties, in Computational Problems in Abstract Algebra, Elsevier, 1970, pp. 329–358.doi:10.1016/B978-0-08-012975-4.50034-5
2. J. Goldman and L. Kauffman, Rational Tangles, Advances in Applied Mathematics, vol. 18, no. 3, pp. 300–332, 1997. doi:10.1006/aama.1996.0511
3. L. Kauffman and S. Lambropoulou, On the Classification of Rational Knots, arXiv: Geometric Topology, 2002. doi:10.48550/ARXIV.MATH/0212011