 |
(1)
|
可以用于角的三等分。它由 Ceva 于 1699 年设计，他称之为 cycloidum anomalarum (Loomis 1968, p. 29)。它具有笛卡尔方程
 |
(2)
|
它具有面积
 |
(3)
|
和弧长
 |  | ![a[16E(k)-3K(k)+3Pi(1/4,k)]](/images/equations/CycloidofCeva/Inline3.svg) |
(4)
|
 |  |  |
(5)
|
(OEIS A138497), 其中 
, 其中 
, 
, 并且 
分别是第一类、第二类和第三类完全椭圆积分。
弧长函数是一个稍微复杂的表达式，可以用椭圆函数的闭合形式表示，曲率由下式给出
![kappa(t)=(3[9+4cos(2t)-2cos(4t)])/([11+4cos(2t)-6cos(4t)]^(3/2)).](/images/equations/CycloidofCeva/NumberedEquation4.svg) |
(6)
|
Ceva 摆线
另请参阅
角的三等分, 摆线, 三等分角曲线使用 Wolfram|Alpha 探索
参考文献
Loomis, E. S. "The Cycloid of Ceva." §2.7 in The Pythagorean Proposition: Its Demonstrations Analyzed and Classified and Bibliography of Sources for Data of the Four Kinds of "Proofs," 2nd ed. Reston, VA: National Council of Teachers of Mathematics, pp. 29-30, 1968.Loy, J. "Trisection of an Angle." http://www.jimloy.com/geometry/trisect.htm#curves.Sloane, N. J. A. Sequence A138497 in "The On-Line Encyclopedia of Integer Sequences."Yates, R. C. The Trisection Problem. Reston, VA: National Council of Teachers of Mathematics, 1971.请将此页引用为
Weisstein, Eric W. "Cycloid of Ceva." 来自 MathWorld--Wolfram Web 资源. https://mathworld.net.cn/CycloidofCeva.html