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Drilling for Polygons

Barry Cox and Stan Wagon
The American Mathematical Monthly
Vol. 119, No. 4 (April 2012), pp. 300-312
DOI: 10.4169/amer.math.monthly.119.04.300
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Page Count: 13
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Drilling for Polygons
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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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