Anyone applying for a job with Microsoft in the past used to get asked the question: "Why are manhole covers round?" The way a candidate answered the problem, explained their thinking and defended ideas was taken to be a good measure of creative thinking. It's a good question to ask children too.
Not all manhole covers are round. Some are square and others hexagonal, but the circle is the better choice. Why? A round lid won't fall through the opening.
There is no way of orienting a circular lid so that it fits through a hole of the same geometry but slightly smaller size because of its constant diameter. But what about other shapes? Investigating which other shapes fall through their holes can be tested using card, pencil and scissors.
It soon becomes apparent that a scalene triangle (three different length sides) is out of the running, but there are other shapes that are up to the job. One such shape is a curved equilateral triangle called a Reuleaux triangle (left), named after Franz Reuleaux, the engineer. This can fit snugly into a square hole and rotate freely.
Asking quirky questions is always worth it in maths. Why are plug holes always round as well?
John Dabell is a teacher at Lawn Primary School in Derby.