This is the mathematical reason why manhole covers are round

When walking down the street, you probably don’t stop to notice the manholes on the road. And if you have, you may not have realized that nearly all of them are round—or that those with other shapes still behave, in some way, like a circle. According to Spanish newspaper El País, there is a mathematical reason for this: to prevent the lid from falling through the hole.

The newspaper explains that if we define the width of a flat shape as the distance between opposite points on its edge, a circle has a constant width because its diameter—the distance between any two opposite points—remains the same. This ensures that when a circular lid is placed over a hole, it cannot slip through.

However, if the cover is square or rectangular, its width is not constant. The distance between two opposite corners, known as the diagonal, is greater than the length of its sides. In the case of sewers, this means that if a square or rectangular cover is turned diagonally, it could fit through the hole, posing a risk of falling in.

Why are some manhole covers not round?

Given this logical reasoning, you might wonder why some manhole covers come in other shapes, such as squares or rectangles. There is an explanation for that too. These covers are typically used for shallow holes—so even if they fall in, retrieving them is not difficult.

However, circles aren’t the only shapes suitable for covering deep holes. Another popular option, according to El País, is the Reuleaux triangle, designed in the 19th century by German engineer Franz Reuleaux, considered the father of kinematics. Constructing this shape is simple: start with an equilateral triangle, then draw three circles with centers at each vertex and a radius equal to the triangle’s side. The shape that remains in the center is known as the Reuleaux triangle.

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Beyond manhole covers, these shapes have various practical applications due to their constant width. They are used in coin design, drill bits, pencils, and even architecture.

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