# 箕舌线

（重定向自阿涅西的女巫

## 方程

${\displaystyle x=2a\tan \theta ,\ y=2a\cos ^{2}\theta .\,}$

${\displaystyle x=2a\cot \theta ,\ y=2a\sin ^{2}\theta .\,}$

## 性质

• 箕舌线与渐近线之间的面积是圆面积的四倍（也就是${\displaystyle 4\pi a^{2}}$）。
• 箕舌线绕着渐近线旋转，则旋转体的体积为${\displaystyle 4\pi ^{2}a^{3}}$
• 曲线的重心位于${\displaystyle (0,{\frac {a}{2}})}$

## 歷史

versiera這個字是衍生自拉丁文的vertere，但後者也是義大利文avversiera（女魔鬼）的縮寫。英格蘭有些聰敏者將之翻譯成女巫（英语：witch），而這好笑的雙關語仍存於多數的英文教材裡。在費馬的著作（Oeuvres, I, 279-280; III, 233-234）就已經出現這條曲線，其名稱versiera是格蘭迪取的，在牛頓的曲線分類中，它是第63類……第一個使用女巫來描述這條曲線的可能是威廉森在1875年的《Integral calculus》中首次使用[9]

## 参考文献

1. ^ John H. Lienhard M.D. Anderson Professor of Mechanical Engineering and History University of Houston (Emeritus). The Engines of Our Ingenuity : An Engineer Looks at Technology and Culture: An Engineer Looks at Technology and Culture. Oxford University Press. 29 June 2000 [9 January 2014]. ISBN 978-0-19-803103-1 （英语）.
2. ^ John H. Lienhard. The Witch of Agnesi. The Engines of Our Ingenuity. 第1741集http://www.uh.edu/engines/epi1741.htm |transcripturl=缺少标题 (帮助). 2002. NPR. KUHF-FM Houston.
3. ^ 埃里克·韦斯坦因. 箕舌线. MathWorld.
4. C. Truesdell, "Correction and Additions for 'Maria Gaetana Agnesi'", Archive for History of Exact Science 43 (1991), 385-386. doi:10.1007/BF00374764
• Per Grandi: "...nata da' seni versi, che da me suole chiamarsi la Versiera in latino pero Versoria..."
5. ^ Pietro Fanfani, Vocabolario dell' uso toscano, p. 334
6. ^ Women in Mathematics By Lynn M. Osen (1975) p. 45
7. ^ "Fermat's Enigma" by Simon Singh p. 100
8. ^ The universal book of mathematics: from Abracadabra to Zeno's paradoxes By David J. Darling (2004) p. 8
9. ^ "173 Find the area between the witch of Agnesi ${\displaystyle xy^{2}=4a^{2}(2a-x)}$ and its asymptote." (Oxford English Dictionary)
10. ^ S.M.Stigler, "Cauchy and the witch of Agnesi: An historical note on the Cauchy distribution", Biometrika, 1974, vol. 61, no.2 p. 375-380
11. ^ 存档副本 (PDF). [2014-01-06]. （原始内容 (PDF)存档于2006-09-10）.
12. ^ "Mountain Waves the construction of analytical solutions", http://www.cpom.org/people/jcrh/jfm-152.pdf
13. ^ "Press 1 Numerical simulations of stratified inviscid flowover a smooth obstacle", K.G.Lamb, http://mseas.mit.edu/download/evheubel/LambJFM1994.pdf