An article introducing continued fractions with some simple puzzles for the reader.

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

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 they lead?

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?

It would be nice to have a strategy for disentangling any tangled ropes...

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!