Continued fractions

Can you tangle yourself up and reach any fraction?

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

Find the equation from which to calculate the resistance of an infinite network of resistances.

Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave.

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

Which of these continued fractions is bigger and why?

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?

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.