On Monday, October 2, 2017 at 8:08:21 AM UTC-7, Archimedes Plutonium wrote: > On Friday, September 29, 2017 at 3:51:35 PM UTC-5, Michael Moroney wrote: > >If you actually have a proof that a conic section is never an ellipse, > >POST IT!!! If not, admit your mistake. > > Geometry proofs that Cylinder section= Ellipse// Conic section= Oval > > Synthetic Geometry & Analytical Geometry Proofs that Conic section = Oval, never an ellipse-- World's first proofs thereof > > _Synthetic Geometry proofs that Cylinder section= Ellipse// Conic section= Oval > > First Synthetic Geometry proofs, later the Analytic Geometry proofs. > > Alright I need to get this prepared for the MATH ARRAY of proofs, that the Ellipse is a Cylinder section, and that the Conic section is an oval, never an ellipse > > PROOF that Cylinder Section is an Ellipse, never a Oval:: > I would have proven it by Symmetry. Where I indulge the reader to place a circle inside the cylinder and have it mounted on a swivel, a tiny rod fastened to the circle so that you can pivot and rotate the circle. Then my proof argument would be to say--when the circle plate is parallel with base, it is a circle but rotate it slightly in the cylinder and determine what figure is produced. When rotated at the diameter, the extra area added to the upper portion equals the extra area added to bottom portion in cylinder, symmetrical area added, hence a ellipse. QED > > Now for proof that the Conic section cannot be an ellipse but an oval, I again would apply the same proof argument by symmetry. > > Proof:: Take a cone in general, and build a circle that rotates on a axis. Rotate the circle just a tiny bit for it is bound to get stuck or impeded by the upward slanted walls of the cone.
> Rotate as far as you possibly can.
You've just said, it's going to get stuck. You cannot rotate this circle that way. Which of course doesn't mean anything.
> Now filling in the area upwards is far smaller than filling in the area downwards. Hence, only 1 axis of symmetry, not 2 axes of symmetry. Define Oval as having 1 axis of symmetry. Thus a oval, never an ellipse. QED