Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: _Symmetry proof that conic is Oval, never ellipse// Plus PROOF that
Oval is Conic, never ellipse

Replies: 16   Last Post: Sep 29, 2017 9:49 PM

 Messages: [ Previous | Next ]
 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
_Symmetry proof that conic is Oval, never ellipse// Plus PROOF that
Oval is Conic, never ellipse

Posted: Sep 28, 2017 3:40 AM

Symmetry proof that conic is Oval, never ellipse// Plus PROOF that Oval is Conic, never ellipse
- hide quoted text -

On Thursday, September 28, 2017 at 1:55:37 AM UTC-5, Archimedes Plutonium wrote:
> Quoting from Mathworld::
>
> A cylindric section is the intersection of a plane with a right circular cylinder. It is a circle (if the plane is at a right angle to the axis), an ellipse, or, if the plane is parallel to the axis, a single line (if the plane is tangent to the cylinder), pair of parallel lines bounding an infinite rectangle (if the plane cuts the cylinder), or no intersection at all (if the plane misses the cylinder entirely; Hilb...
>
> End quote

Now the reason I quoted that, was only to check and see if the Old Math community had at least a few items correct in conic sections and other sections. I mean, I had to be sure that Old Math realized a cylinder section was an ellipse. No telling what Old Math could have had for cylinder sections seeing that they are outright pathetic about a conic section being an ellipse, when in truth it is an oval.

And here, one has to wonder, why was everyone in math such a blithering nattering nutter, to come to think that Cylinder section was ellipse, yet they also thought Conic section was ellipse. I mean, did no-one have a good sound mind from Apollonius of Ancient Greeks to AP? Could no-one say-- this is blithering stupid to think that TWO dissimilar figures are going to produce the very same section cut. Intelligence of a spoiled cucumber or tomato, but not a mathematician.

So, now, I wonder how is the easiest proof in Old Math that they established correctly that a Cylinder Section is a ellipse. How did Old Math go about proving that fact?

PROOF::
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-- at diameter as swivel the extra area added to the upper portion equals the extra area added to bottom portion, 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 on the slanted walls of the cone upward. Rotate as far as you possible can. 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, thus a oval. QED

Now I bet in Old Math, they could not allow such proofs as above, allow them to be accepted as proofs, partially because people in Old Math were too severely toilet trained when a toddler, and secondly, none in Old Math has an amount of logic that a apricot has logic.

In Old Math, the airheads always insist on you doing "numbers" petty numbers here and there, even when numbers are totally unnecessary. And the reason they want you to do numbers in every proof, is not for the sake of a valid proof, but only because in Old Math, losers want to inflict pain on those doing math, not understanding and not logic, but just pain because they are losers of math themselves and the only thing that math affords losers of math, is to inflict pain on those getting ahead in math.

AP