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