Curves of Constant Width

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Curves of Constant Width:  regardless of the precise shape, any curve of constant width has a perimeter equal to pi times its width! These convex shapes will roll because like a circle they have the same diameter from one side to the other no matter their orientation. Here are two famous examples: the Reuleaux triangle (found in rotary engines) and a Reuleaux pentagon- note how the two straightedge rulers remain parallel as the shapes rotate between them, just as one would expect circles to behave! These physical representations of the special curves seen here are produced by Maths Gear (Matt Parker and Steve Mould).