problem All tangled up Age 14 to 18 Challenge level Can you tangle yourself up and reach any fraction?

problem More Twisting and Turning Age 11 to 16 Challenge level It would be nice to have a strategy for disentangling any tangled ropes...

problem Resistance Age 16 to 18 Challenge level Find the equation from which to calculate the resistance of an infinite network of resistances.

problem Euclid's Algorithm and Musical Intervals Age 16 to 18 Challenge level Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave.

problem Golden Fractions Age 16 to 18 Challenge level Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

problem Comparing Continued Fractions Age 16 to 18 Challenge level Which of these continued fractions is bigger and why?

problem Not Continued Fractions Age 14 to 18 Challenge level Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

problem There's a limit Age 14 to 18 Challenge level 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?

problem Good Approximations Age 16 to 18 Challenge level Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

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