Making Shapes of Constant Width


I've built a set of shapes of constant width!

You can roll on top of them much like circles, but they are definitely not circles, and it seems like they're defying everything we know about rolling. They are super fun to play with.

You can download the templates I used here:

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​If you want to transfer them on to the wood like I did, don't forget to flip the page before printing

If you have access to a laser cutter, you should definitely use it! The more precise your shapes are, the better they will roll. I have svg files for laser cutting on my thingiverse page.

The shape I made in this video (the bottom left in the template page) is not trivial. It's not a classic reuleaux triangle, or one of its derivatives. It actually does not contain any circular arcs. It's constructed by half an ellipse for the top, the bottom part is created by "sliding" a line with constant length (90mm) on the perimeter of the semi-ellipse, so it's always perpendicular, and marking its trace. This construction makes sure this shape has a constant width.

I got a lot of the info about these shapes from the great book "How Round Is Your Circle", including the construction of the unique shape I made.

You can buy it here (affiliate link):

https://amzn.to/2pT72JK

MathsGear sell a set of shapes of constant width

https://mathsgear.co.uk/collections/shapes/products/shapes-of-constant-width-in-acrylic-set-of-4?variant=876663997

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