The Circle: A Mathematical Exploration Beyond The Line by Alfred S. Posanebtuer & Robert Geretschläger (book review).

Picking out books to review months in advance can lead to some interesting choices. Take Alfred S. Posanebtuer & Robert Geretschläger’s book, ‘The Circle: A Mathematical Exploration Beyond The Line’, for instance. I was expecting something along the lines (sic) of the circle’s importance in trigonometry. It does but it is also a primer in its use in all kinds of things from laying out tins in boxes to make the most of its space, although not in the standard way and you do have to ask why this isn’t followed in real life to origami and how a basic circle can lead out to several points, useful in making appendages. In many respects this is more a primer for a mathematical student or a designer who needs all the formulas to sort out a mathematical problem. I never knew that the Reuleaux triangle is the basis for the wrench and why kids in New York can no long open fire hydrants on hot days to cool out on the streets. The Reuleaux triangle crops up later in the book as a shape on a sphere, showing how it makes that perfect fit.


What was weird reading the maths and illustrations for Apollonius and how the centres of different circles are parallel was expanded with lines and it looked like vanishing points that we use in art. With the circle centres, if we didn’t get that right, it would make drawn people look like they were wading through the ground.

Occasionally, I did think calling the book ‘The Circle’ a bit of a misnomer as there is a lot of discussion on tangents, triangles and cogs. If you’re familiar with the old ‘Spirograph’ toy and wondered about the maths that ensured your lines met at the end, then they explain how it was calculated. I bet you thought it was all random. Hah!

Although I suspect some of the maths, let alone working your way through the examples, might be going back to school, it does make this an ideal book for trigonometry students. For me, the biggest insight was seeing something I recognise from my art background and seeing a proof link into maths that links them together. Considering a circle is something that we all take for granted in our everyday lives, an understanding into how the other math lives makes me hope these authors explore other shapes in a similar way.

GF Willmetts

October 2016

(pub: Prometheus Books. 349 page illustrated indexed hardback. Price: $25.00 (US), $26.50 (CAN), £19.30 (UK). ISBN: 978-1-63388-167-9)

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