When a cylinder intersects with a plane, what are the resultant shapes and curves? I think that the curves are hyperbola, parabola and line, and the shapes are circle, ellipse, rectangle and trapezium. For shapes, we ignore 'weird' ones like the 'filled parabola shape' and so on. Are these correct, and is there any more shapes and curves that I missed?
Asked
Active
Viewed 33 times
0
-
Two parallel lines. Also, I have a tough time seeing how you're going to get a parabola. Wait... seeing "rectangle" in your list, I suspect that by "cylinder" you mean a finite cylinder rather than an infinitely long one, and your finite cylinder has end-caps, too. Even so, a parabola isn't possible -- only a partial-ellipse. It's probably easier to think through the possibilities for an infinite cylinder, and then think about truncating each of these. – John Hughes May 31 '18 at 12:25
-
Why a parabola is impossible for a finite cylinder? – Al Z. May 31 '18 at 21:21
-
If we consider the cylinder as an extreme case of a cone with its top sliced off, then a parabola and a hyperbola should be possible. – Al Z. May 31 '18 at 21:26
-
1Not in a Euclidean space. – amd May 31 '18 at 22:21
-
Then is hyperbola possible? (Ignoring the two parallel lines case) – Al Z. May 31 '18 at 22:35
-
Nope -- no (nondegenerate) hyperbolas either. – John Hughes Jun 01 '18 at 11:19