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Continued Fraction and Twist Vector Converter

·166 words·1 min

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: $$\LB a\ b\ c\RB=c+\frac{1}{b+\frac{1}{a}}$$


Twist vectors here are space seperated lists of integers.

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


  1. 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.
  2. Kauffman, Louis H., and Sofia Lambropoulou. “On the Classification of Rational Knots,” 2002.
Joe Starr
Joe Starr
Knot theorist with a background in automotive software engineering.