Continued fractions

problem
Favourite

More Twisting and Turning

Age

11 to 16

Challenge level

2 out of 3

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

There's a Limit

Age

14 to 18

Challenge level

1 out of 3

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

1 out of 3

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

Comparing Continued Fractions

Age

16 to 18

Challenge level

2 out of 3

Which of these continued fractions is bigger and why?
problem

Euclid's Algorithm and Musical Intervals

Age

16 to 18

Challenge level

2 out of 3

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

3 out of 3

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

Resistance

Age

16 to 18

Challenge level

3 out of 3

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

Not Continued Fractions

Age

14 to 18

Challenge level

1 out of 3

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

All Tangled Up

Age

14 to 18

Challenge level

2 out of 3

Can you tangle yourself up and reach any fraction?
article
Infinite Continued Fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.