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Cochleoid - Wikipedia

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

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

the Cartesian equation

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

or the parametric equations

{\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.[1]

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

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