蝸牛線

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

蝸牛線（實線）和其極座標上的反曲線（虛線）

蝸牛線（英語：cochleoid）是一種蝸牛形的曲線，類似環索線，其極坐標系方程如下：

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

其笛卡兒坐標系方程如下

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

其參數方程如下

$x={\frac {a\sin t\cos t}{t}}$

$y={\frac {a\sin ^{2}t}{t}}$

蝸牛線是希皮亞斯割圓曲線的反曲線。

參考資料

• J. Dennis Lawrence. A catalog of special plane curves. Dover Publications. 1972: 192. ISBN 0-486-60288-5. 
• 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, ISSN 1844-640X
• 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)

外部連結

• cochleoid at 2dcurves.com
• 埃里克·韋斯坦因. Cochleoid. MathWorld.