卡西尼曲面[Cassini Surface] - 达人(其实～我是卧底，来自外星)

2005/01/16 | 卡西尼曲面[Cassini Surface]
类别(∑〖数学〗) | 评论(0) | 阅读(23) | 发表于 14:08: The quartic surface obtained by replacing the constant b in the equation of the Cassini ovals with b = z, obtaining
(1)

As can be seen by letting y = 0 to obtain
(2)

(3)

the intersection of the surface with the y = 0 plane is a circle of radius a.

Let a torus of tube radius a be cut by a plane perpendicular to the plane of the torus's centroid. Call the distance of this plane from the center of the torus hole r, let a = r, and consider the intersection of this plane with the torus as r is varied. The resulting curves are Cassini ovals, and the surface having these curves as cross sections is the Cassini surface
(4)

which has a scaled on the right side instead of (Gosper).; 0