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Resources tagged with Continued fractions similar to The Golden Ratio, Fibonacci Numbers and Continued Fractions.:

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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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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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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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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?

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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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More Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:1

Take a look at the video and try to find a sequence of moves that will take you back to zero.

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All Tangled Up

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

Can you tangle yourself up and reach any fraction?

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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?