14 Feb
2007
14 Feb
'07
6:35 p.m.
Dandelin's proof (which I call the "ice cream cone proof") of ellipses from sections of cones is one of the coolest proofs from "The Book". Too bad my high school teacher didn't use it instead of "some math, some garbage"... http://en.wikipedia.org/wiki/Dandelin_spheres BTW, "oval" at MIT used to mean "Springfield oval" (Google it!) At 12:05 PM 2/14/2007, R. William Gosper wrote:
Some find it counterintuitive that slicing a cone gives an ellipse and not an oval. What about slicing a paraboloid of rotation? More generally how can eliminating a quadratic mumbloid vs a linear (planar) equation yield anything but a quadratic (conic)? --rwg