Cochleoid Explained

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

r = (a \sin \theta)/(\theta) , the Cartesian equation(x ^{2+y} ^{2 )\arctan (y)/(x)} = ay, or the parametric equationsx = (a\sin t\cos t)/(t) , y = (a\sin ^{2} t)/(t) .

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

Notes

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

References

• Book: J. Dennis Lawrence . A catalog of special plane curves . Dover Publications . 1972 . 0-486-60288-5 . 192 . registration .
• 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,
• 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