Not Round?!

Hi everyone. Have you ever imagined the wheels on a car not being a circle?

Well it does seem strange. However, there are shapes that are round but not round at the same time! A circle is a shape with one side and a constant width to it. This make it perfect for a smooth ride in a care. There are other shapes that have a consistent diameter all around, for example the Reuleaux Triangle. This is a triangle of constant width, however its edges are pointy. It is made up of of parts of three circles joined together.

You notice that when a circle is rolled or turned inside a square it fits and keeps touching the sides proving its constant width. The Reuleaux triangle can also be rotated in a square as shown with it touching the sides showing the constant width of the triangle. However, it is still not a really good shape for a wheel because it will not work with a fixed point in the middle but it is still able to roll smoothly if it is rolling without a fixed point of rotation.

There are also other Reuleaux polygons that consist of shapes with odd number of sides and a constant width. The more sides in a Reuleaux polygon, the rounder it is and the closer it gets to being a circle. A famous example of Reuleaux shapes are the British 20p and 50p coins which are both Reuleaux heptagons (as they have constant width, they will also not get stuck in a vending machine). There are also pencils that are a Reuleaux triangle as it is thought to be more comfortable due to the roundness than the typical hexagonal shape. Due to their constant width, there can also be shapes with a constant width other than a sphere.

It also answers the riddle of “Other than a circle, what shape can you make a manhole cover so that it cannot fall down through the hole?” The Reuleaux triangle can also be used as a drill bit if it was not fixed and a single point in the middle! 

Do you know of any objects that are a Reuleaux polygon, or do you have anything else to add on this topic?

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