article
Continued fractions I
An article introducing continued fractions with some simple puzzles for the reader.
Continued fractions
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articleContinued fractions II
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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articleApproximations, Euclid's algorithm and continued fractions
This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.
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articleInfinite continued fractions
In this article we are going to look at infinite continued fractions - continued fractions that do not terminate. -
articleThe golden ratio, Fibonacci numbers and continued fractions
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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articleGolden mathematics
A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers. -
articleTangles
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead? -
articleSymmetric tangles
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why! -
problemGood approximations
Age16 to 18Challenge level
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers. -
problemThere's a limit
Age14 to 18Challenge 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?