Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: well defining the OVAL, and proving the cone never yields an ellipse Re: the 3, Three Conics/Cylinder EXPERIMENTS
Posted:
Sep 26, 2017 11:57 AM


On September 26, Archimedes Plutonium wrote: > Alright, now I promised I would not leave Conics until I nailed down a well defined Oval. And some good progress on that front already is in, from the study of Ovals produced by conics. > > Now, ovals in Old Math are said to be  ill defined  that is because, noone in Old Math put their minds to it. And, of course, since noone in Old Math realized that a oval was the conic section, never an ellipse, that noone in Old Math could well define oval, for they were dirt dumb ignorant that the Oval was the conic, in which to leverage the conic so as to welldefine Oval. > > So you see, the reason Old Math could not well define oval is because, noone in Old Math realized the oval was a conic that is a framework in which to well define oval. Similarly, if you think that a cross section of a cube is a circle, well, obviously, you will never well define what a circle is. > > So, now, here is a rough ascii art of a oval > > > A > .' '. > .' `. > / \ > ; ; >   > ; ; > \ / > `. .' > `. __ .' > B > > And this Oval is a Conic Section where A is near the Apex of the cone and B is near the Base of the cone. > > Now imagine the knife cutting first at A, and there is a point in which the knife makes FirstContact with the cone and that point is A. Now as the knife continues its cut in a plane it leaves the cone at its furthest point, its last point of the cone which is point B. > > So now we connect AB as a line segment and call it the Major Diameter of the Oval. > > Now, here, here is an important idea which is going to absolutely well define the Oval, provided the idea is true or not true. The question is, the apex point of the cone, dropped down like a plumb line to the center of the base of the cone, does that line segment intersect AB? That is the huge question. If it intersects with line AB then a perpendicular at the intersection creates a second smaller line segment that I call the Minor Diameter of the Oval. > > Picture it here as CD > > > > A > .' '. > .' `. > / \ > ; ; >   > ; C D ; > \ / > `. .' > `. __ .' > B > > So, if I can prove that the plumb line of cone intersects AB, call it the Center of the oval and thus a second diameter is formed of CD. > > Now, in an ellipse, it has two axes of symmetry where AB and CD are the two. But in an oval, only one axis of symmetry the AB. > > Now, are all ovals derived from a Conic section? Here I am guessing, that every oval as described and defined above, every one of them comes from a conic, just as every circle imaginable, comes out of a conic. > > Now, is there an easy proof that no ellipse can come from a conic? I suspect there is, and the easy proof would take advantage of the fact that the Plumb line used from apex to center of basecircle, that every ellipse has a center where its two axes of symmetry intersect. But since an oval has only one axis of symmetry, the plumb line is never going to meet halfway on AB and CD. > > AP
Here is something you can play with:
https://www.intmath.com/planeanalyticgeometry/conicsectionssummaryinteractive.php
If you still can see an oval instead of an ellipse, than you should definitely buy a new pair of glasses or quit drugs...



