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Cochleoid information

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

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

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

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

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

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Cochleoid

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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...

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Gallery of curves

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curve Brachistochrone Butterfly curve (transcendental) Catenary Clélies Cochleoid Cycloid Horopter Isochrone Pursuit curve Rhumb line Syntractrix Tractrix...

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List of curves

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curve Brachistochrone Butterfly curve (transcendental) Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone of Huygens (Tautochrone) Isochrone...

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List of mathematical shapes

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surface Bowditch curve Brachistochrone Butterfly curve Catenary Clélies Cochleoid Cycloid Horopter Isochrone Isochrone of Huygens (Tautochrone) Isochrone...

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Quadratrix

Last Update: 2023-12-03T08:26:09Z

been used to square the circle include the Archimedean spiral and the cochleoid. This article incorporates text from a publication now in the public...

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