In my post, I made a comment in passing that continued fractions have applications to knot theory. Now A Neighborhood of Infinity has a series of posts on the very topic I had in mind, namely the theory of *rational tangles*. Much of the theory is due to the great John Horton Conway.

### Our other blog

### Blog Stats

- 269,899 hits

### Recent Comments

### Top Posts

- Platonic Solids and Euler's Formula for Polyhedra
- Integration Bee, Challenging Integrals
- High IQ and Mathematics
- Analyzing the hairy ball theorem
- Continued fraction for e
- Solution to POW-10: Another hard integral?
- Boolean algebras, Boolean rings, and baby Stone duality
- Toward Stone Duality: Posets and Meets
- Stolz-Cesàro Theorem
- Using Mathematical Induction to "disprove" the foundation of Calculus!

### Archives

### Categories

- Abstract Algebra
- Algebraic Geometry
- Boolean Algebra
- Category Theory
- Category Theory for Beginners
- Elementary Math Problem Solving
- Exposition
- Geometric Algebra
- Math Conferences
- Math Topics
- Mathematical philosophy
- Mathematics
- Music
- Naive Set Theory
- Philosophy & Logic
- Physics
- Posets and Lattices
- Problem Corner
- Problem of the Week (POW)
- Propositional Calculus
- Puzzles
- Some theorems
- Uncategorized

### Blogroll

- A Dialogue on Infinity
- A Mind for Madness
- A Neighborhood of Infinity
- A Singular Contiguity
- Absolutely Useless
- AMS Graduate Student Blog
- Antimeta
- Arcadian Functor
- Ars Mathematica
- Complex Zeta
- Courtney Gibbons
- Danielle Fong
- Epsilonica
- Game Theorist
- Global Dashboard
- God Plays Dice
- Jocelyn Paine
- Lambda the Ultimate
- Language Log
- Louis Yang Liu
- Mark Reid
- Musings on general topology and order
- Noncommutative Geometry
- Reasonable Deviations
- Recursivity
- Reperiendi
- Rigorous trivialities
- SbSeminar
- The Accidental Mathematician
- The Everything Seminar
- The Infinite Seminar
- The n-Category Cafe
- Theoretical Atlas
- XOR’s Hammer

### chess

### Computers and Technology

### Elementary Math Problem Solving

### Fun, Humor

### Higher Mathematics

### Math Education

### Non-technical

### People in Computer Science

### People in mathematics

### Philosophy & Logic

### Physics

### Politics, News

### Sciences

### Useful general links

### Useful Math Links

### Tag Cloud

advice
andreescu
Aussonderungsaxiom
Axiom of Extension
Axiom of pairing
axiom of powers
Axiom of Specification
axiom of unions
blog
Boolean Algebra
career
carnival of mathematics
Category Theory
chess
complements
continued fractions
definite integrals
elementary
emil artin
empty set
Exposition
Fermat's Last Theorem
Geometric Algebra
golberg
hard integral
Harvard College Mathematics Review
heyting algebra
identities
identity
inclusion-exclusion principle
Inequality
integration
integration bee
intersections
Invariant
lattices
log
love
mason-stothers theorem
math
mathematical
Mathematical Reflections
mathematics
math puzzle
naive set theory
noah snyder
number
oleg
Oxford
Paul Halmo
Paul Halmos
Polya
polynomial
power set
prime
principle of duality
problem
Propositional Calculus
propositional logic
puzzle
reflections
russell's paradox
Simon Singh
singleton
stone duality
Szego
Tao
Terence
Terry Tao
theory
titu
topos theory
universe
Valentine's day
Yakov Perelman

## 1 comment

Comments feed for this article

August 26, 2008 at 5:21 pm

John BaezPeople who want to learn about rational tangles may also want to try my quick intro to rational tangles in week228, which has links to these papers:

Jay R. Goldman and Louis H. Kauffman, Rational tangles, Advances in

Applied Mathematics 18 (1997), 300-332. Also available at

http://www.math.uic.edu/~kauffman/RTang.pdf

Louis H. Kauffman and Sofia Lambropoulou, On the classification of

rational tangles, available as math.GT/0311499.

Later I learned a lot more, and wrote about rational tangles, the three-strand braid group and elliptic curves in week233.

Todd has probably talked with Jim Dolan about generalizations of these ideas involving braid groups with more strands, and hyperelliptic curves. I would like to learn more about these and write about ‘em sometime.