Continued Fraction and Twist Vector Converter

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
Graduate Teaching Assistant

Skilled embedded software engineer with a passion for problem solving.