Square wheel

A square wheel is a wheel that, instead of being circular, has the shape of a square. While literal square wheels exist, a more common use is as a metaphor meaning stereotypically bad or naïve engineering (see reinventing the wheel).
An animation of a square wheel rolling smoothly over inverted catenaries.

A square wheel can roll smoothly if the ground consists of evenly shaped inverted catenaries of the right size and curvature.[1][2][3]

A different type of square-wheeled vehicle was invented in 2006 by Jason Winckler of Global Composites, Inc. in the United States. This has square wheels, linked together and offset by 22.5°, rolling on a flat surface. The prototype appears ungainly, but the inventor proposes that the system may be useful in microscopic-sized machines (MEMS).[4]

In 1997 Macalester College mathematics professor Stan Wagon constructed the first prototype of a catenary tricycle. An improved model made out of modern materials was built when the original vehicle wore out in April, 2004.[5]

In 2012, MythBusters experimented with modifying vehicles with square tires, determining that, with speed, a truck fitted with square wheels can deliver a relatively smooth ride.
See also

Reuleaux triangle
Non-circular gear

References

Peterson, Ivars (4 April 2004), "Riding on Square Wheels", Science News 165 (14), retrieved 2009-05-03
A Catenary Road and Square Wheels, New Trier High School, Winnetka, Illinois, archived from the original on September 20, 2006, retrieved 2009-05-03
Non-Circular Wheels, Physics and Astronomy Lecture Demonstrations, University of Iowa, retrieved 2009-05-03
Square Wheel Car Propels Itself by Shifting Weight - Possible MEMS Locomotion, Global Composites, 2 December 2005, retrieved 2009-05-03
Wagon, Stan. "Untitled". Retrieved 19 May 2010.

Mathematics Encyclopedia