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Golden Mathematics
A voyage of discovery through a sequence of challenges exploring
properties of the Golden Ratio and Fibonacci numbers.
Continued fractions
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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! -
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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articleContinued Fractions I
An article introducing continued fractions with some simple puzzles for the reader.
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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.