Mechanical Circle-Squaring

Authors: Cox, Barry; Wagon, Stan

Source: The College Mathematics Journal, Volume 40, Number 4, September 2009 , pp. 238-247(10)

Publisher: Mathematical Association of America

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Abstract:

A technique discovered in 1939 can be used to build a device that is driven by standard circular motion (as in a drill press) and drills exact square holes. This device is quite different from the classic design by Watts, which uses a Reuleaux triangle and drills a hole that is almost, but not exactly, square. We describe the device in detail, deriving the equations needed to make a computer simulation. Then we investigate the extension to other polygons and show how the basic idea can be combined with some knowledge of envelopes to produce a device that traces out an exact hexagon.

Document Type: Research article

DOI: 10.4169/193113409X458679

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