One of the issues that came up during the challenger explosion investigation was whether some port had a circular opening. The engineers had taken two parallel planes, placed the port between them, measured the distance between the planes, and then rotated & repeated. Since all the measured distances were equal, they concluded the port was circular.
Anyone who's studied a bit of geometry knows this is an error. There are curves of constant width that are not circles -- a good counterexample is the 50p coin if you have some UK currency.
It's easy to extend this into a discussion of whether manhole covers need to be circular. Any manhole cover that's a curve of constant width cannot fall into its hole.
