John Hendow

One of the (supposed) classic interview questions posited to Microsoft applicants is “why are manhole covers round?”. This is intended to be an assessment of the applicant’s problem solving abilities, rather than a test of whether they know the answer. Everyone has heard this question and its answer which is “because that’s the only shape that ensures it can’t fall into the hole.”

This weekend a few of us were sitting around backstage before our set, and someone raised the question. After the classic answer was given I started to recall something from a calculus class, which means some rusty file drawer in my brain was getting delved into. The crucial characteristic that makes a circle the correct answer is that it has a constant diameter; regardless of where you measure a circle the diameter is the same and therefore it cannot be manipulated or turned in such a way that it could fall down into the hole. But a dim lightbulb was sparking in my head and I thought perhaps there was something geeky to add to the conversation. After a minute or so, I remembered it. Actually there is another shape that fulfills the requirement and would be a good alternate answer if you’re ever asked that question. That shape is the Reuleaux triangle.

Understanding the nature of this shape is fundamental to being able to justify it as a good answer to the manhole cover question. If you were to start with a standard equilateral triangle and dig out your compass (if you’re under 30 you probably didn’t ever use a compass in geometry), you place the point in one corner of the triangle and sweep between the other two points. The resulting shape is three sided but possesses the unusual characteristic of having a constant diameter. If a manhole cover was fabricated in this shape it would never fall into the hole.