Mechanical circle-squaring
RIS ID
29682
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.
Publication Details
Cox, B. & Wagon, S. (2009). Mechanical circle-squaring. College Mathematics Journal, 40 (4), 238-247.