A literal square wheel is a wheel that, instead of being circular, has the shape of a square. A more common use is as slang, meaning stereotypically bad or naïve engineering (see reinventing the square wheel). A driving wheel on a steam locomotive. ... Circle illustration In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ... In plane (Euclidean) geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides. ... Reinventing the square wheel is the practice of unnecessarily engineering artifacts that provide functionality already provided by existing standard artifacts (reinventing the wheel) and ending up with a worse result than the standard (a square wheel). ...

A square wheel can roll smoothly if the ground consists of evenly shaped inverted catenaries of the right size and curvature. In the 1990s Stan Wagon, a mathematician at Macalester College, constructed a bicycle with square wheels, together with a special track for riding it on. In mathematics, the catenary is the shape of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight). ... Macalester College (commonly called Mac by those affiliated with the college) is a privately supported, coeducational liberal arts college in Saint Paul, Minnesota. ... This article is becoming very long. ...

A different type of square-wheeled vehicle was invented in 2006 by Jason Winckler of Global Composites, Inc. in the U.S.A. (see link below). 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). A mite next to a gear set produced using MEMS. Courtesy Sandia National Laboratories, SUMMiTTM Technologies, www. ...

It should be noted that a square wheel can roll perfectly smoothly if the road has evenly spaced bumps in the shape of a series of inverted catenary curves.

For other improbable wheels, see Reuleaux polygon. A Reuleuax polygon is a polygon that is a curve of constant width - that is, a curve in which all diameters are the same length. ...

External links

• "Riding on Square Wheels", Ivars Peterson, Science News, Week of April 3, 2004; Vol. 165, No. 14.
• "Square Wheel Car Propels Itself by Shifting Weight - Possible MEMS Locomotion", Global Composites Inc. press release, December 2, 2005 (with link to video of prototype)

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