Shapes of Constant Width

Did you know a circle is not the only shape that maintains the same width as you rotate it? There are other, lesser known, ‘shapes of constant width’. In this set of resources students can explore what it means for a shape to have ‘constant width’, learn how to construct shapes of constant width using a pair of compasses and discover some real life shapes of constant width.

Equipment needed

Card, rulers, compasses, scissors.

Curriculum Topics Covered

Construction with compasses, geometrical reasoning. 

More Details

Activities include: 

-Explore what ‘constant width’ means with a simple practical investigation (use Shapes of constant width worksheet, Shapes to cut out printed on card, scissors and scrap card for parallel sides).

-Use geometrical reasoning to prove some shapes based on an equilateral triangle are not of constant width (Shapes of constant width worksheet). Can you now create and construct your own shape based on an equilateral triangle that is a shape of constant width? (Use Triangles for construction sheet).

-Learn how to construct the Reuleaux Triangle and other shapes of constant width including those based around an irregular polygon, and 20p and 50p coins that are both shapes of constant width! (Constructing shapes of constant width sheets).

Note: This constructions worksheet is our updated version and was uploaded on 23rd June 2018 – the version prior to this contained an error. Use this new sheet! 

To find out more about shapes of constant width watch the Numberphile video with Steve Mould featured below, and a video by Steve Mould and Matt Parker on the Maths Gear YouTube channel:

A set of four shapes of constant width can be purchased on the Maths Gear website at