CochleoidSpiral curve of the form r = a*sin(θ)/θ / From Wikipedia, the free encyclopedia 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 r={\frac {a\sin \theta }{\theta }},} r = sin θ θ , − 20 < θ < 20 {\displaystyle r={\frac {\sin \theta }{\theta }},-20<\theta <20} cochleoid (solid) and its polar inverse (dashed) the Cartesian equation ( x 2 + y 2 ) arctan y x = a y , {\displaystyle (x^{2}+y^{2})\arctan {\frac {y}{x}}=ay,} or the parametric equations x = a sin t cos t t , y = a sin 2 t t . {\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]
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 r={\frac {a\sin \theta }{\theta }},} r = sin θ θ , − 20 < θ < 20 {\displaystyle r={\frac {\sin \theta }{\theta }},-20<\theta <20} cochleoid (solid) and its polar inverse (dashed) the Cartesian equation ( x 2 + y 2 ) arctan y x = a y , {\displaystyle (x^{2}+y^{2})\arctan {\frac {y}{x}}=ay,} or the parametric equations x = a sin t cos t t , y = a sin 2 t t . {\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]