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The Wonder Book of Geometry - David Acheson ****

If ever you wanted a paradox, this book provides it in a remarkable way. Geometry, with its grinding pyramid of step-by-step proofs was my least favourite aspect of maths at school - I much preferred the puzzle-solving aspects of algebra, for example. David Acheson has failed to convince me that I was should really have loved it... however, this is by far the most approachable book on geometry I've ever read, and I wish it had been around in my day.

It's a textbook the way a textbook should be. There is context, from ancient Egyptian rope stretchers to those who have given the parallel postulate a good working over (including an oddity from Lewis Carroll). One of the worst things about the way I was taught geometry is that there was no consideration of applications, just those wretched theorems. Here, plenty of the geometry is introduced through a potential application. There's also some good historical background, including a regular view on Euclid from different points in history. Acheson has achieved something genuinely brilliant.

The only reason I can't get more excited about it is that is still, under cover of this beautiful facade, a textbook. It still spends far too long telling me about the details of, say, the midpoint theorem that I really don't care about. Although many aspects of it could fit within popular mathematics, this is not a popular maths book. However, if you need to learn the basics of geometry for whatever reason (there must be several reasons, surely) then this blows every known textbook on the topic out of the water. You may not get all the detail of all the theorems, but what's far more important is that you get an understanding of what is going on.

The Wonder Book of Geometry does what it does wonderfully. Acheson has done a remarkable job. But I'm afraid geometry still wasn't for me. I wasn't converted to be a fan of the subject - but I am of the book.

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Review by Brian Clegg
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