Continued fractions

There are 17 NRICH Mathematical resources connected to Continued fractions
There's a limit
problem
Favourite

There's a limit

Age
14 to 18
Challenge level
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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?
More Twisting and Turning
problem
Favourite

More twisting and turning

Age
11 to 16
Challenge level
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It would be nice to have a strategy for disentangling any tangled ropes...
Good Approximations
problem

Good approximations

Age
16 to 18
Challenge level
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Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Not Continued Fractions
problem

Not continued fractions

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

Golden fractions

Age
16 to 18
Challenge level
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Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.
Placeholder: several colourful numbers
problem

Resistance

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

All tangled up

Age
14 to 18
Challenge level
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Can you tangle yourself up and reach any fraction?
Symmetric Tangles
article

Symmetric tangles

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