In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation
r = a sin θ θ , {\displaystyle r={\frac {a\sin \theta }{\theta }},}
the Cartesian equation
( x 2 + y 2 ) arctan y x = a y , {\displaystyle (x^{2}+y^{2})\arctan {\frac {y}{x}}=ay,}
or the parametric equations
x = a sin t cos t t , y = a sin 2 t t . {\displaystyle x={\frac {a\sin t\cos t}{t}},\quad y={\frac {a\sin ^{2}t}{t}}.}
The cochleoid is the inverse curve of Hippias' quadratrix.
Notes
References 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
cochleoid at 2dcurves.com Weisstein, Eric W. "Cochleoid". MathWorld.