Monday, 28 November 2011

Book recommendation

I have finally got round to reading Alex's Adventures in Numberland, by Alex Bellos (Bloomsbury, 2010). I recommend it! It's written in an engaging and entertaining style, with a wide range of mathematical content.

I particularly enjoyed learning that the flight path of a peregrine falcon descending on its prey is a logarithmic spiral - the same curve as you will see in a nautilus shell. Falcons have eyes at the sides of their heads so they cannot see straight ahead without turning their heads through at least 40 degrees. If they did this they could fly in a straight line at their prey. But turning their head through such a large angle produces too much wind resistance, so they opt for the most aerodynamic position, which they maintain throughout the descent. This means that they are always looking through one eye at their prey and turning towards the prey at the same angle: precisely the geometric requirement for tracing a logarithmic spiral.

The logarithmic spiral turns up in the chapter on Fibonacci numbers and the golden section. This because a logarithmic spiral appears when a golden rectangle is repeatedly subdivided into a square and a smaller golden rectangle.

My own humble contribution to this field was an article I had published in Mathematics Teaching in 1978 (I was very young at the time), volume 84, pages 56-7, entitled 'The Golden Section in Beethoven's Fifth'. I'm surprised – and amused – to see that my little article still gets occasional references on websites devoted to this fascinating area of mathematics.

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