Reaction to Chapter 4 of Beyond the Third Dimension

Andy Miller 

Comments on Professor Banchoff's Dandelin Page

The explanation of Dandelin's proof that the intersection of a plane and a circular cylinder is an ellipse is enhanced by the use of colors, series of changing images, and see-through pictures (not solid). The explanation proceeds logically from a reminder of the properties of ellipses to a complex three dimensional figure of two spheres, a plane and a cylinder (all of different colors), showing that, by the definition of an ellipse, the intersection of a cylinder and a plane must be an ellipse. The last diagram was a bit confusing to me. I could not fully understand how the description following the picture related to the the picture.

Relevant Links

Prof. Banchoff's response