AP's thoughts as of 5JAN2019// three proofs that ellipse is never a conic

Newsgroups	sci.math
Date	2019-01-05 07:19 -0800
Message-ID	<17674064-528b-436c-abef-e44ddb32429d@googlegroups.com> (permalink)
Subject	AP's thoughts as of 5JAN2019// three proofs that ellipse is never a conic
From	Archimedes Plutonium <plutonium.archimedes@gmail.com>

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Alright the first proof is my historical first proof, in late 2016, I was messing around with the sine function and the cone, ellipse came to mind in that playful messing around. And it struck me, my mind just could not see how a slant cut into the cone yields an ellipse-- but some odd shaped figure with only one axis of symmetry, not two axes that the ellipse requires. So my first proof was a hands on. I went for a stiff waxy paper (magazine cover) and rolled it into a cone shape, then inserted a Mason or Kerr jar lid and then tilted it to see if I could get a ellipse. No ellipse is ever possible for the lid has just one axis of symmetry.

The second proof is a standard High School type of geometry proof and is fully laid out here:

Proofs ellipse is never a conic, always a cylinder section by
Archimedes Plutonium
--------------------
AP's proof the ellipse is never a Conic Section, always a Cylinder section, and how the proof works

Let us analyze AP's Proof

On Friday, September 14, 2018 at 6:57:36 PM UTC-5, Archimedes Plutonium wrote:

Array:: Analytic Geometry proof that Cylinder section= Ellipse//Conic
section = Oval, never ellipse
Now I did 3 Experiments and 3 models of the problem, but it turns out
that one model is superior over all the other models. One model is the
best of all.
That model is where you construct a cone and a cylinder and then
implant a circle inside the cone and cylinder attached to a handle so
that you can rotate the circle inside. Mine uses a long nail that I
poked holes into the side of a cylinder and another one inside a cone
made from heavy wax paper of magazine covers. And I used a Mason or
Kerr used lid and I attached them to the nail by drilling two holes
into each lid and running a wire as fastener. All of this done so I
can rotate or pivot the circle inside the cylinder and cone. You need
a long nail, for if you make the models too small or too skinny, you
lose clarity.
ARRAY, Analytic Geometry Proof, Cylinder Section is a Ellipse::
E
__
.-' `-.
.' `.
/ \
; ;
| G c | H
; ;
\ /
`. .'
`-. _____ .-'
F

Alright, focus on the distance from c to F in the cone-cut compared to the distance from c to E

In a Cylinder cut, those two distances are the same because a cylinder has two axes of symmetry.

The side view of a cylinder is this

| |
| |
| |

That allows cE to be the same distance as cF

But the side view of the cone is

/\E
/c \
F / \

The distance c to E is shorter because the slant of the side walls of the cone are in the direction of shortening cE, whereas the slant opposite c in cF make that distance larger than cE

The above is a view of a ellipse with center c and is produced by the
Sectioning of a Cylinder as long as the cut is not perpendicular to
the base, and as long as the cut involves two points not larger than
the height of the cylinder walls. What we want to prove is that the
cut is always a ellipse, which is a plane figure of two axes of
symmetry with a Major Axis and Minor Axis and center at c.
Side view of Cylinder EGFH above with entry point cut at E and exit
point cut at F and where c denotes the central axis of the cylinder
and where x denotes a circle at c parallel with the base-circle of
cylinder
| |
| | E
| |
| |
|x c |x
| |
| |
| |
|F |
| |
| |
| |

So we can see that the distance cE = cF in cylinder for the walls are Parallel to one another, giving distance symmetry

But in the Cone, the walls are not parallel, shortening the distance cE compared to cF. Leaving only one axis of symmetry that of EF. The oval is the conic section of a cut at a slant, while the cylinder cut at a slant is a ellipse. The Oval has just one axis of symmetry.

So, what is the proof that figure EGFH is always an ellipse in the
cylinder section? The line segment GH is the diameter of the circle
base of cylinder and the cylinder axis cuts this diameter in half such
that Gc = cH. Now we only need to show that Fc = cE. This is done from
the right triangles cxF and cxE, for we note that by Angle-Side-Angle
these two right triangles are congruent and hence Fc = cE, our second
axis of symmetry and thus figure EGFH is always an ellipse. QED
Array proof:: Analytic Geometry proof that Conic section= Oval// never ellipse
ARRAY, Analytic Geometry Proof, Conic Section is a Oval, never an ellipse::
A
,'" "`.
/ \
C | c | D
\ /
` . ___ .'
B
The above is a view of a figure formed from the cut of a conic with
center c as the axis of the cone and is produced by the Sectioning of
a Cone as long as the cut is not perpendicular to the base, and as
long as the cut is not a hyperbola, parabola or circle (nor line).
What we want to prove is that this cut is always a oval, never an
ellipse. An oval is defined as a plane figure of just one axis of
symmetry and possessing a center, c, with a Major Diameter as the axis
of symmetry and a Minor Diameter. In our diagram above, the major
diameter is AB and minor diameter is CD.
Alright, almost the same as with Cylinder section where we proved the
center was half way between Major Axis and Minor Axis of cylinder,
only in the case of the Conic, we find that the center is half way
between CD the Minor Diameter, but the center is not halfway in
between the Major Diameter, and all of that because of the reason the
slanted walls of the cone cause the distance cA to be far smaller than
the distance cB. In the diagram below we have the circle of x centered
at c and parallel to base. The angle at cx is not 90 degrees as in
cylinder. The angle of cAx is not the same as the angle cBx, as in the
case of the cylinder, because the walls of the cone-for line segments-
are slanted versus parallel in the cylinder. Triangles cAx and cBx are
not congruent, and thus, the distance of cA is not equal to cB,
leaving only one axis of symmetry AB, not CD.
/ \A
x/ c \x
B/ \
Hence, every cut in the Cone, not a hyperbola, not a parabola, not a
circle (not a line) is a Oval, never an ellipse.
QED
--Archimedes Plutonium

The third proof was discovered just yesterday, in playing around with ellipses of long and skinny shapes.

So imagine a Sequence of Ellipses in terms of semimajor axis to semiminor axis:

10by1 ellipse, then 100by1 ellipse, then 1000by1 ellipse, etc etc

All of them legitimate ellipses only in a Sequence form.

So now, if an ellipse was ever a conic, there must be a cone which holds each and every one of these singular ellipses.

Now there sure enough is a Sequence of Cylinders that holds each and every one of those ellipses in terms of Radius of cylinders the Sequence is this:

10by1radius cylinder, then 100by1radius cylinder, then 1000by1radius cylinder, etc etc.

But, there never exists a single cone that can hold a 10by1 ellipse, nor a 100by1 ellipse, etc etc. Why is that?

Because no cone is uniform as we go from top to bottom of cone, and a ellipse needs uniformity.

Now this proof goes and impacts on another idea in mathematics-- the limit of calculus. Let me remind the reader the history of the Limit concept goes to Cauchy in around early mid 1800s. His students-- the bright students kept bothering Cauchy about the calculus for the calculus taught in the 1800s and up to modern day times is flawed. Severely flawed, and is the crippled calculus being taught today around the world in colleges. It is pathetically fake calculus for it has the students believe that you can have a rectangle with area yet have 0 width. And the reason you have such fakery tauted as true is because Old Math never defined infinity as a borderline which would give Calculus a small finite infinitesimal such as 1/10^604, so that the calculus integral can always be at least a summation of strips of area that are 1/10^604 wide. Always a finite positive width for the calculus integral. But in Cauchy's time, these bright students kept bothering him about 0 width, for that is what Cauchy was teaching and that is what college professors to this very day are teaching in colleges throughout the world-- teaching a huge lie. All because they are too lazy and too dumb to define infinity with a borderline.

So what Cauchy did to silence and muffle the bright smart young students of the world, is that Cauchy invented a liar's paradise that would sweep all smart students complaints under the rug of shame. Cauchy invented the Limit to silence smart students. So that if a bright smart student said to Cauchy, your integral calculus is the sum of rectangles of 0 width. Then Cauchy would react and reply-- well, you just do not understand the Limit. But the truth is, Cauchy and modern day math professors are liars and cheats of the truth of reality and the world. For the bright smart student understands that when you never define infinity properly-- you have contradictions of a 0 width rectangle.

And now, in geometry, we can display the hypocrisy and the vile vulgar contradiction of a Limit in math. For if you consider a cone and very elongated ellipses 10to1 , 100to1, 1000to1, in terms of semimajor and semiminor axes, a going to infinity sequence of long skinny ellipses, there are no Cones to handle these ellipses as conics. No, there are none. But Cauchy and today's dunce math professors would argue that in the Limit of cones-- you somehow pull out a 1000to1 ellipse or a 10000to1 ellipse. Ellipses are a geometrical Limit argument with Cones. Because no ellipse can ever be got from a cone, none. All ellipses come from a Cylinder, every single ellipse that exists has to come from a cylinder, never a cone.

So, I have three proofs that a ellipse is a cylinder cut, never a conic cut.

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AP's thoughts as of 5JAN2019// three proofs that ellipse is never a conic Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 07:19 -0800
  Legitimate geometry question on cone-plane intersection moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-05 17:48 +0000
    Re: Legitimate geometry question on cone-plane intersection Alan Mackenzie <acm@muc.de> - 2019-01-05 18:58 +0000
      Re: Legitimate geometry question on cone-plane intersection moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-05 19:44 +0000
        Re: Legitimate geometry question on cone-plane intersection Peter Percival <peterxpercival@hotmail.com> - 2019-01-05 20:15 +0000
        Re: Legitimate geometry question on cone-plane intersection Alan Mackenzie <acm@muc.de> - 2019-01-07 03:15 +0000
          Re: Legitimate geometry question on cone-plane intersection moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-07 04:44 +0000
      Re: Legitimate geometry question on cone-plane intersection Peter Percival <peterxpercival@hotmail.com> - 2019-01-05 20:13 +0000
        My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 13:44 -0800
          try wrapping a ellipse in a cone wrapper Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 14:24 -0800
            Re: try wrapping a ellipse in a cone wrapper Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 14:40 -0800
              researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 17:37 -0800
                researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 21:13 -0800
                Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-06 05:55 +0000
                not even a constant percentage in the rectangles Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 21:59 -0800
                no percentage formula Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 22:14 -0800
                not even rectangles Re: no percentage formula Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 23:02 -0800
                directrix Re: not even rectangles Re: no percentage formula Re: researching if the ellipse has an internal universal constant of 1/137 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 23:34 -0800
                understanding the Ellipse well,is the same as understanding angular momentum of physics well Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-01-05 23:51 -0800
                Re: understanding the Ellipse well,is the same as understanding angular momentum of physics well Me <franz.fritschee.ff@gmail.com> - 2019-01-06 03:10 -0800
          Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Me <franz.fritschee.ff@gmail.com> - 2019-01-06 03:08 -0800
          Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse Alan Mackenzie <acm@muc.de> - 2019-01-06 11:17 +0000
            Re: My third proof ellipse is never a conic is that the tip end of cone and bottom flared-out end can never yield a 1000to1 ellipse moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-01-06 18:42 +0000
  Re: AP's thoughts as of 5JAN2019// three proofs that ellipse is never a conic Jan <filmart@gmail.com> - 2019-01-06 21:47 -0800

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