Whichever way you roll them, their width is always the same, although they are not spheres!

A set of 3 solids of constant width, made from solid aluminium, with a width of 35mm. These mathematical curiosities have some intriguing properties. For example, if you place the set of 3 solids on a flat surface and place a book on top of them, you will be able to slide the book in any direction completely smoothly, without any up or down movement. Onlookers might think that only 3 spheres would be able to do this, but solids of constant width can behave in the same way. Whichever way you roll them, their width is always the same. See this article on Solids of Constant Width, called Meissner's Mysterious Bodies, written by Bernd Kawohl and Christof Weber. It was originally written in June 2011, and published in the professional mathematics journal The Mathematical Intelligencer. Included - a set of 3 identical solids of constant width, turned from solid aluminium, with a width of 35mm.

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