# Resources tagged with: Continued fractions

### There are 17 results

Broad Topics >

Fractions, Decimals, Percentages, Ratio and Proportion > Continued fractions

##### Age 16 to 18

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

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 18

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

##### Age 14 to 16

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 16 to 18 Challenge Level:

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

##### Age 16 to 18

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

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

##### Age 11 to 16 Challenge Level:

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

##### Age 14 to 18 Challenge Level:

Can you tangle yourself up and reach any fraction?

##### Age 14 to 16

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

##### Age 14 to 18 Challenge Level:

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 16 to 18

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

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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

##### Age 11 to 16

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

##### Age 16 to 18 Challenge Level:

Which of these continued fractions is bigger and why?