Thread: Section of a rt. Circular cylinder vs. cone by plane.

http://www.schoolmath3d.org/e/teache...1/lesson10.htm

This says section of a cylinder is an ellipse.

http://en.wikipedia.org/wiki/Conic_section

This says section of a cone is an ellipse.

What is true?

They are both true.

Think of it like a slinky, only pretend that the slinky starts as just a single elipse. As you pick up the top end of the slinky strait up, it forms a cylinder shape.

Now put the slinky back down until it is only an elipse again. The top end of your slinky now gains the ability to shrink when you pick it up. Doing so should now give you a cone!

I think a right circular cylinder is a special case of a cone where the vertex is at infinity.

A cross section of a cylinder can be either a circle OR an ellipse, depending on the angle you take the cross-section at. Same goes for a circular cone.

This is what I mean.
The incident angle is same for loci of a cyli. to the plane which intersect it. The angle is same as axis to intersecting plane.
For a cone incident angle varies according to curvature, still the intersection is an ellipse!