Continued Fraction and Twist Vector Converter
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Rational Tangles
A rational tangle is given by alternating NE,SE and SE,SW twisting of the $0$ tangle${}^{[2]}$${}^{[1]}$. Discussion of canonicality of this construction of twist vector can be found in ${}^{[2]}$. A twist vector encodes these alternating twists as a list of integers. This induces a unique map from the rational tangles onto the rational numbers${}^{[2]}$. We accomplish this by interpreting a twist vector as a sequence for a continued fraction as: $$\LB a\ b\ c\RB=c+\frac{1}{b+\frac{1}{a}}$$
Instructions
Twist vectors here are space seperated lists of integers.
A rational number here is “/” seperating two integers.
Cite
- Conway, J.H. “An Enumeration of Knots and Links, and Some of Their Algebraic Properties.” In Computational Problems in Abstract Algebra, 329-58. Elsevier, 1970. https://doi.org/10.1016/B978-0-08-012975-4.50034-5.
- Kauffman, Louis H., and Sofia Lambropoulou. “On the Classification of Rational Knots,” 2002. https://doi.org/10.48550/ARXIV.MATH/0212011.
Joe Starr
Graduate Teaching Assistant
Skilled embedded software engineer with a passion for problem solving.