波希米亚圆形[Bohemian Dome] - 达人(其实～我是卧底，来自外星)

2005/01/12 | 波希米亚圆形[Bohemian Dome]
类别(∑〖数学〗) | 评论(0) | 阅读(14) | 发表于 12:59: A quartic surface which can be constructed as follows. Given a circle C and plane E perpendicular to the plane of C, move a second circle K of the same radius as C through space so that its center always lies on C and it remains parallel to E. Then K sweeps out the Bohemian dome. It can be given by the parametric equations
(1)

(2)

(3)

where . In the above plot, ,, and c = 1.
The Gaussian curvature and mean curvature of the surface are given by
(4)

(5); 0