Can you tangle yourself up and reach any fraction?
It would be nice to have a strategy for disentangling any tangled
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?
Take a look at the video and try to find a sequence of moves that will take you back to zero.
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!
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
An article introducing continued fractions with some simple puzzles for the reader.