I’m very pleased to announce that my second book, Geometry Snacks is now shipping from Tarquin Publications. The book is coauthored by Vincent Pantaloni, a fantastic French mathematician who helped design over 50 geometric puzzles as well as some of the creative solution approaches to each one.

Geometry Snacks is a mathematical puzzle book filled with geometrical figures and questions designed to challenge, confuse and ultimately enlighten enthusiasts of all ages.

Each puzzle is carefully designed to draw out interesting phenomena and relationships between the areas and dimensions of various shapes. Furthermore, unlike most puzzle books, we offer multiple approaches to solutions so that once a puzzle is solved, there are further surprises, insights and challenges to be had.

As a teaching tool, Geometry Snacks enables teachers to promote deep thinking and debate over how to solve geometry puzzles. Each figure is simple, but often deceptively tricky to solve – allowing for great classroom discussions about ways in which to approach them. By offering numerous solution approaches, the book also acts as a tool to help encourage creativity and develop a variety of strategies to chip away at problems that often seem to have no obvious way in.

The inspiration for the book came from the responses to puzzles I have created here, and the different ways in which people solved them. Take the figure below for example:

(not included in the book!)

This puzzle requires you to find what fraction of the whole regular shape the shaded section represents (constructed using midpoints).

Here is one possible solution:

You can see that the pink area covers half of each vertical pair of rectangles, and that is equal to 4 of the congruent triangles. So the answer must be 4/12 = 1/3

But there’s more life in this puzzle yet! Can you see an alternative approach? Can your students?

How about this submission:

Shearing the parallelogram into a rectangle, then reconstructing the entire shape into a quadrilateral! It’s a lovely approach, and one I wouldn’t necessarily think of myself.

By sharing multiple approaches both to the reader and potentially with a class, everyone learns from new insights and styles of problem solving in geometry – and each puzzle teaches us something new even if we can solve it!

As such each puzzle in the book includes at least 2 solution approaches.

If you have enjoyed my puzzles over the last five years, consider buying this book. It ships internationally, and I think you’ll like it a lot.

I think this solves a problem. What to buy my self for Christmas.

Phil

I think you’ll like it 🙂

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