Continued fractions

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

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?

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

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

Can you tangle yourself up and reach any fraction?

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

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

Which of these continued fractions is bigger and why?

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