In LaTeX, is there way to define a custom continued fraction formula \mycfrac{an}{bn} with a single continuous zickzack fraction line?I am not quite satisfied with this code\textnormal{\LARGE K}_{n=1}^\infty \frac{\left.a_n\right|}{...

Hi math. For the last few months I have been fairly obsessed with continued fractions, and I have implemented some basic operations in Scheme. Great fun!Unfortunately there is almost no information available on the subject that I ca...

I recently read a charming little paper: Quasi-elliptic integrals and periodic continued fractions, by van der Poorten and Tran. Most of us who have taken a number theory course of some kind learned how to solve Pell’s equation: wh...

Here's a question. Why is the period of the quotients in the continued fraction of N1/2 "usually" even? For example, if N runs over the ninety non-squares less than 100, then only 20 times does the continued fraction expansion of ...

I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to have time to write while I'm away, I'm taking the opportunity to re-run an old classic series of posts on numbers, which were first posted in t...

> {-# LANGUAGE MultiParamTypeClasses,FunctionalDependencies,FlexibleInstances,GeneralizedNewtypeDeriving #-}> module Main where> import qualified Data.Map as M> import Control.Monad> import Prelude> import Ratio hiding (numerator,de...

> {-# LANGUAGE MultiParamTypeClasses,FunctionalDependencies,FlexibleInstances,GeneralizedNewtypeDeriving #-}> module Main where> import Test.QuickCheck> import qualified Data.Map as M> import Control.Monad> import Ratio> infixl 5 .+...

It's time to return to the vector space monad. But first, after some Haskell preamble, I need to talk about the Einstein summation convention.> {-# LANGUAGE MultiParamTypeClasses,FlexibleInstances,FunctionalDependencies #-}> module ...

Recall that I defined a rational tangle to be what you get by starting with a pair of untangled strings whose ends are at infinity and then sliding the strings around as much as you like keeping the ends at infinity. If you don't li...

Continuing from before It's time now do discuss the problem of forming a representation of a knot or tangle in machine readable form.I've defined rational tangles but I should set that in a wider context. A knot is essentially a sin...

A rational tangle is what you get when you take two initially separate lengths of rope and then allow them to interact while keeping the ends 'at infinity'. You're allowed to do whatever tangling you like with the proviso that you c...