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).
回复Comments
{commenttime}{commentauthor}
{CommentUrl}
{commentcontent}