In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation

cochleoid (solid) and its polar inverse (dashed)

the Cartesian equation

or the parametric equations

The cochleoid is the inverse curve of Hippias' quadratrix.[1]

Notes

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  1. ^ Heinrich Wieleitner: Spezielle Ebene Kurven. Göschen, Leipzig, 1908, pp. 256-259 (German)

References

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  • J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. p. 192. ISBN 0-486-60288-5.
  • Cochleoid in the Encyclopedia of Mathematics
  • Liliana Luca, Iulian Popescu: A Special Spiral: The Cochleoid. Fiabilitate si Durabilitate - Fiability & Durability no 1(7)/ 2011, Editura "Academica Brâncuşi", Târgu Jiu, ISSN 1844-640X
  • Roscoe Woods: The Cochlioid. The American Mathematical Monthly, Vol. 31, No. 5 (May, 1924), pp. 222–227 (JSTOR)
  • Howard Eves: A Graphometer. The Mathematics Teacher, Vol. 41, No. 7 (November 1948), pp. 311–313 (JSTOR)
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