Author： Cox Barry Wagon Stan
Publisher： Mathematical Association of America
ISSN： 1930-0972
Source： American Mathematical Monthly, Vol.119, Iss.4, 2012-04, pp. : 300-312
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Abstract
We solve the problem of designing a simple device that uses rotary motion to drill a hole with a cross-section that is a regular polygon with an odd number of sides: the main idea is to use a polygonal trammel and a family of rotors. By using different rotors, one can produce a hole with a cross-section that is in any proportion of the trammel size from zero to exactly one. The key geometric idea is a result about the envelope of an edge of a triangle that rotates so that the other two edges maintain tangential contact with two fixed circles.
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