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Resources tagged with Continued fractions similar to Sums and Products of Digits and SP Numbers:

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

Infinite Continued Fractions

Stage: 5

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

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.

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/...)).

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?

Symmetric Tangles

Stage: 4

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

Continued Fractions I

Stage: 4 and 5

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

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?

Comparing Continued Fractions

Stage: 5 Challenge Level:

Which of these continued fractions is bigger and why?

Approximations, Euclid's Algorithm & Continued Fractions

Stage: 5

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

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?

Good Approximations

Stage: 5 Challenge Level:

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

Golden Mathematics

Stage: 5

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

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.

Golden Fractions

Stage: 5 Challenge Level:

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

Resistance

Stage: 5 Challenge Level:

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