Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
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.
It would be nice to have a strategy for disentangling any tangled ropes...
Can you tangle yourself up and reach any fraction?
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
Take a look at the video and try to find a sequence of moves that will take you back to zero.
An article introducing continued fractions with some simple puzzles for the reader.