Cochleoid

r = \frac{\sin θ}{θ}, - 20 < θ < 20

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

r = \frac{a \sin θ}{θ},

(x^{2} + y^{2}) \arctan \frac{y}{x} = a y,

x = \frac{a \sin t \cos t}{t}, y = \frac{a \sin^{2} t}{t} .

Notes

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

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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, Template:Catalog lookup linkScript error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".Script error: No such module "check isxn".
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)