Jump to content


From Wikipedia, the free encyclopedia
cochleoid (solid) and its polar inverse (dashed)

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

the Cartesian equation

or the parametric equations

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


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


  • 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)

External links[edit]