Exams have a nasty habit of sucking the joy out of a subject. My interest in proper literature was dulled by A-Level English, and I celebrated my way out of several GCSE papers – in subjects I’d picked because I enjoyed them – saying “I’ll never have to do that again.”
Geometry is a topic that generally suffers badly from this – but fortunately, Ed Southall and Vincent Pantaloni’s Geometry Snacks is here to set that right.
Geometric reasoning is joyful and beautiful. Memorising the difference between complementary and supplementary angles… rather less so. Geometry Snacks doesn’t shy away from the vocabulary of geometry, but its focus is squarely on the key ideas.
It’s a gorgeous little book (16cm by 16cm, 80 pages), with a stylised doughnut on the front to represent the bite-sized problems inside. It’s in five sections, covering “find the fraction” puzzles, angle-finding, proofs, areas and sangaku, lovely 17th- to 19th-century Japanese puzzles largely involving circles.
What makes it special for me is the clarity and elegance of the diagrams. Careful use of grey and red shading generally makes it obvious what they’re asking for; a lot of thought has gone into making the pictures pop (it’s not as colourful as Byrne’s Elements, but it’s probably clearer). I particularly like the device of using used and unused matchstick heads to define points!
The authors also take care to offer multiple solutions to problems, where appropriate. My one niggle with the book, though, is that the solution pages are more cluttered and harder to follow than the puzzles – in a perfect world, there would be a little more space for the answers. That said, I gather the publishers are set to release a special e-reader version of Geometry Snacks, in which some of the solutions will be animated. (The book mentions exploring the puzzles with GeoGebra, but it’s not clear whether that’s part of the e-reader version or just something recommended.)
Like all good puzzle books, Geometry Snacks goes from the straightforward (a parallelogram is inscribed in a square, with two opposite vertices at the midpoints of opposite sides of the square – what fraction is shaded?) to the much trickier (such as question 47, pictured). There’s something here for just about anyone with more than a passing familiarity with geometry – and especially for teachers looking for interesting extension problems.
It might be a little late to put it on your Christmas list (and certainly don’t let it replace The Maths Behind, that would be foolish), but Geometry Snacks is an excellent use for a book token, Amazon voucher or Christmas money.
Geometry Snacks is published by Tarquin and is available at the time of writing for £7.95.