Cochleoid

$r=\frac{\sin \theta }{\theta },-20<\theta <20$

cochleoid (solid) and its polar inverse (dashed)

A flexible pole is fixed upright at one end and bent over to always form a circular arc. The other end then traces out a Cochleoid.

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

$r=\frac{a\sin \theta }{\theta },$

the Cartesian equation

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

or the parametric equations

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

The cochleoid is the inverse curve of Hippias' quadratrix.

References

• Template:Cite book
• 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:Issn
• 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
• Template:MathWorld

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