A friend recently asked me a puzzle.
The engineers at NASA needed to verify that a fuel storage unit had a circular cross-section. They measured the width of the cross-section in all directions and concluded that the cross-section is circular. Were the engineers correct.
I thought that they were. A 2D object with constant width in all directions ought to be a circle. Right? I was wrong and here is a simple counterexample.
Take an equilateral triangle, and from each corner draw an arc connecting the other two corners.
All widths are equals, but this is clearly not a circle. Maybe the NASA engineers should have also checked if the circumference equals πd