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**What is it?**

What shape is a 50p piece? A heptagon, right? Well, no, actually. Which is a little worrying for me, as I have been using it as a real life example of a hexagon for about the last 10 years. On closer inspection, the edges are curved (so they can roll in vending machines, apparently!). The shape of the coin has a name: the reuleaux heptagon. And it has a fascinating property: each diameter is the same width. And yet it is not a circle! Amazing, right? So, having looked a bit closer at this most interesting of every day objects, the natural question becomes… how do we construct one?

**How can it be used?**

The worksheet from The British Museum is excellent. It gives a number of entry points into the task of constructing the 50p piece. As suggested in the worksheet, you can leave it completely open-ended, or go as far as to show the completed diagram to the students to see if they can recreate it with a compass, ruler and angle measurer. And then the worksheet suggests follow up questions to look more closely at the properties of this lovely shape. Before you know it you will be discussing symmetry, tangents, similarity and much more, all after having refined those all-important loci and construction skills. You may never look at money the same way again!

Thank you for sharing!

Craig Barton

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