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61.1 Constructing a limaçon locus from the cardioid envelope

Published online by Cambridge University Press:  22 September 2016

Peter Catranides
Peter Catranides*
Affiliation:
George Washington High School, 549 Audubon Avenue, New York, NY 10040, USA
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Extract

It is well known to ‘curve-stitchers’ that, if equally spaced points around a circle are numbered 1, 2, 3,..., n (and then repeated cyclically), then the chords joining 1 to 2, 2 to 4, 3 to 6, ..., n to 2n envelop a cardioid. (See [1], p. 41, §16, where the cardioid is described as “the caustic of a circle with respect to a point on its circumference”.) Correspondence with E. H. Lockwood has led to a rather unexpected result from this envelope.

Type
Notes
Information
The Mathematical Gazette , Volume 61 , Issue 415 , March 1977 , pp. 58 - 59
Copyright
Copyright © Mathematical Association 1977

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References

1. Lockwood, E. H., A book of cunes. Cambridge University Press (1961).Google Scholar