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

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.

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.

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

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

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