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#### Resources tagged with Continued fractions similar to Farey Fibonacci:

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### There are 15 results

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

### Golden Fractions

##### Stage: 5 Challenge Level:

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

### Golden Mathematics

##### Stage: 5

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

### Continued Fractions I

##### Stage: 4 and 5

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

### Good Approximations

##### Stage: 5 Challenge Level:

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

### Approximations, Euclid's Algorithm & Continued Fractions

##### Stage: 5

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

### The Golden Ratio, Fibonacci Numbers and Continued Fractions.

##### Stage: 4

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.

### Symmetric Tangles

##### Stage: 4

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

### Comparing Continued Fractions

##### Stage: 5 Challenge Level:

Which of these continued fractions is bigger and why?

### There's a Limit

##### Stage: 4 and 5 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?

### Not Continued Fractions

##### Stage: 4 and 5 Challenge Level:

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

### Tangles

##### Stage: 3 and 4

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

### Euclid's Algorithm and Musical Intervals

##### Stage: 5 Challenge Level:

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

### Continued Fractions II

##### Stage: 5

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

### Infinite Continued Fractions

##### Stage: 5

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

### Resistance

##### Stage: 5 Challenge Level:

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