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There are **17** NRICH Mathematical resources connected to **Continued fractions**, you may find related items under Fractions, decimals, percentages, ratio and proportion.

Problem
Primary curriculum
Secondary curriculum
### More Twisting and Turning

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### There's a Limit

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?

Age 14 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Symmetric Tangles

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

Age 14 to 16

Article
Primary curriculum
Secondary curriculum
### Tangles

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### Resistance

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Euclid's Algorithm and Musical Intervals

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Golden Mathematics

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### The Golden Ratio, Fibonacci Numbers and Continued Fractions.

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

Age 14 to 16

Problem
Primary curriculum
Secondary curriculum
### Golden Fractions

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Infinite Continued Fractions

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

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Approximations, Euclid's Algorithm & Continued Fractions

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Continued Fractions II

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Continued Fractions I

An article introducing continued fractions with some simple puzzles for the reader.

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Comparing Continued Fractions

Which of these continued fractions is bigger and why?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Not Continued Fractions

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Good Approximations

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

Age 16 to 18

Challenge Level