This article sets some puzzles and describes how Euclid's algorithm
and continued fractions are related.
Use Euclid's algorithm to get a rational approximation to the
number of major thirds in an octave.
Solve quadratic equations and use continued fractions to find
rational approximations to irrational numbers.
Which of these continued fractions is bigger and why?
In this article we are going to look at infinite continued
fractions - continued fractions that do not terminate.
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
Which rational numbers cannot be written in the form x + 1/(y +
1/z) where x, y and z are integers?
An article introducing continued fractions with some simple puzzles for the reader.
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you
notice when successive terms are taken? What happens to the terms
if the fraction goes on indefinitely?
A voyage of discovery through a sequence of challenges exploring
properties of the Golden Ratio and Fibonacci numbers.
Find the link between a sequence of continued fractions and the
ratio of succesive Fibonacci numbers.
A personal investigation of Conway's Rational Tangles. What were
the interesting questions that needed to be asked, and where did
Find the equation from which to calculate the resistance of an
infinite network of resistances.
The tangles created by the twists and turns of the Conway rope
trick are surprisingly symmetrical. Here's why!
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.