Ride a bike with round wheels and it rolls smoothly on a flat road (i.e., the axle remains level). Can you get a bike with square wheels to roll smoothly on a road of some other shape?
Surprisingly, yes. A road made up of inverted catenaries will do the trick! A catenary is a portion of a cosh curve (higher Mathematics). Figure below shows how such a bike would roll.
(Source: Mudd Math fun fact)