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Resources tagged with Continued fractions similar to Over the Pole:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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Good Approximations

Stage: 5 Challenge Level: Challenge Level:1

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

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There's a Limit

Stage: 4 and 5 Challenge Level: Challenge Level:1

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?

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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.

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Golden Fractions

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Resistance

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Golden Mathematics

Stage: 5

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

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Approximations, Euclid's Algorithm & Continued Fractions

Stage: 5

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

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Euclid's Algorithm and Musical Intervals

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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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/...)).

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Symmetric Tangles

Stage: 4

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

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Continued Fractions I

Stage: 4 and 5

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

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Comparing Continued Fractions

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these continued fractions is bigger and why?

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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?

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Infinite Continued Fractions

Stage: 5

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

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Not Continued Fractions

Stage: 4 and 5 Challenge Level: Challenge Level:1

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