leeper@mtgzz.UUCP (m.r.leeper) (01/26/86)
I have reason to believe this posting did not get to some systems. I am reposting it: This is kind of a nice, simple problem that I posed for myself and solved. The solution is kind of pleasing too. In a three-space (coordinates x, y and z) you have a cylinder whose equation is x^2 + z^2 = 1. Now if you take planes through the z-axis, each (but for the one containing the y-axis) will intersect the cylinder in an ellipse. Describe the locus of points that are foci of those elipses. What kind of a curve in three-space will the foci trace out as the angle of the plane changes? Express the solution in each of rectangular and polar-coordinates, each is interesting. Mark Leeper ...ihnp4!mtgzz!leeper