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Michael Artin, Martin Bazant, Bonnie Berger of MIT asked by Volney/Moroney report-- WHY teach ellipse is a conic, when it never was, but a cylinder section (see proof below)

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  Michael Artin, Martin Bazant, Bonnie Berger of MIT asked by Volney/Moroney report-- WHY teach ellipse is a conic, when it never was, but a cylinder section (see proof below) Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-08-16 21:30 -0700
    Re: Archimedes "Total Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-08-17 15:13 +0000

#421468 — Michael Artin, Martin Bazant, Bonnie Berger of MIT asked by Volney/Moroney report-- WHY teach ellipse is a conic, when it never was, but a cylinder section (see proof below)

Michael Artin, Martin Bazant, Bonnie Berger of MIT asked by Volney/Moroney report-- WHY teach ellipse is a conic, when it never was, but a cylinder section (see proof below)

Re: 2g,Clumsily let us reprimand AP for pretending he was proving a ellipse is a cylinder section, never a conic section
By Volney 1 post 2 views updated 7:14 PM


On Wednesday, December 6, 2017 at 12:30:22 AM UTC-6, Michael Moroney wrote: 
> 
> Silly boy, that's off by more than 12.6 MeV, or 12% of the mass of a muon. 
> Hardly "exactly" 9 muons. 
Wednesday, December 6, 2017 at 9:52:21 AM UTC-6, Michael Moroney wrote: 
> 
> Or, 938.2720813/105.6583745 = 8.88024338572.  A proton is about the mass 
> of 8.88 muons, not 9. About 12% short. 

MIT math dept. 

Michael Artin, Martin Bazant, Bonnie Berger, Roman Bezrukavnikov, Alexei Borodin, John Bush, Herman Chernoff, Henry Cohn, Laurent Demanet*, Richard Dudley, Jörn Dunkel, Alan Edelman, Pavel Etingof, Daniel Freedman, Michel Goemans, Vadim Gorin, Harvey Greenspan, Victor Guillemin, Larry Guth, Sigurdur Helgason, Anette Hosoi, David Jerison, Steven Johnson, Victor Kac, Steven Kleiman, Daniel Kleitman, Andrew Lawrie, Tom Leighton, George Lusztig, Arthur Mattuck, Davesh Maulik, Richard Melrose, Haynes Miller, William Minicozzi, Ankur Moitra, Elchanan Mossel, Tomasz Mrowka, James Munkres, Andrei Negut, Aaron Pixton, Bjorn Poonen, Alexander Postnikov, Philippe Rigollet, Rodolfo Rosales, Giulia Saccà, Gerald Sacks, Paul Seidel, Scott Sheffield, Peter Shor, Isadore Singer, Michael Sipser, Jared Speck, Gigliola Staffilani, Richard Stanley, Harold Stark, Gilbert Strang, Daniel Stroock, Goncalo Tabuada, Alar Toomre, David Vogan 

President: L. Reif (electrical engineer) 

 
Drs.Noam Elkies, Dennis Gaitsgory, Robin Gottlieb of Harvard, teach percentages correctly-- Moroney//Volney has a difficult time of percentages of how much is 938 short of 945. But worse yet, why do you keep teaching the ellipse is a conic when it never was, but rather the ellipse is always a cylinder section.

President Larry Summers 

Harvard Math dept 


Noam Elkies, Dennis Gaitsgory, Robin Gottlieb, Benedict Gross, Joseph Harris, Heisuke Hironaka, Michael Hopkins, Arthur Jaffe, David Kazhdan, Mark Kisin, Peter Kronheimer, Jacob Lurie, Eric Maskin, Barry Mazur, Curtis McMullen, David Mumford, Martin Nowak, Gerald Sacks, Wilfried Schmid, Yum-Tong Siu, Shlomo Sternberg, John Tate, Cliff Taubes, Hugh Woodin, Horng-Tzer Yau, Shing-Tung Yau

   /\-------/\ 
   \::O:::O::/ 
  (::_  ^  _::) 
   \_`-----'_/ 
You mean the classroom is the world, not just my cubbyhole in Boston? 
And, even though you-- professors of math who never want to fix and clean up error filled mathematics, your students deserve better, and you should quit teaching if you cannot come around to admitting a ellipse is a cylinder section, never a conic section. For it is embarrassing to have students smarter than the math professor who by taking a cone, cylinder can and a round lid, can prove on the spot, in the classroom that the cone yields an oval, never an ellipse.

Proofs ellipse is never a conic, always a cylinder section by
Archimedes Plutonium
--------------------
Conics = oval, 2 proofs, synthetic, analytic

Synthetic Geometry & Analytical Geometry Proofs that Conic section =
Oval, never an ellipse-- World's first proofs thereof
by Archimedes Plutonium
_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. 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

The above two proofs are Synthetic Geometry proofs, which means they
need no numbers, just some concepts and axioms to make the proof work.
A Synthetic geometry proof is where you need no numbers, no coordinate
points, no arithmetic, but just using concepts and axioms. A Analytic
Geometry proof is where numbers are involved, if only just coordinate
points.

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

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, 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

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#421517 — Re: Archimedes "Total Failure" Plutonium flunked the lifetime-generation test

Math Failure Archimedes Plutonium <plutonium.archimedes@gmail.com> fails:

> Michael Artin, Martin Bazant, Bonnie Berger of MIT asked by 
> Volney/Moroney report-- WHY teach ellipse is a conic, when it never was, 
> but a cylinder section (see proof below)

You are sure telling lots of people about the proof the ellipse is a conic
section. Here it is for you again!

Some preliminaries:

Top view of the conic section and depiction of the coordinate system used 
in the proof:

              ^ x
              |
             -+- <= x=h
         .'   |   `.
        .     |     .
        |     |     |
        '     |     '      
         `.   |   .'
 y <----------+ <= x=0
             
Cone (side view):
                 .
                /|\
               / | \
              /b |  \
             /---+---' <= x = h
            /    |'   \
           /   ' |     \
          / '    |      \
x = 0 => '-------+-------\
        /    a   |        \

Proof:

r(x) = a - ((a-b)/h)x  and  d(x) = a - ((a+b)/h)x,  hence

y(x)^2 = r(x)^2 - d(x)^2 = ab - ab(2x/h - 1)^2 = ab(1 - 4(x - h/2)^2/h^2.

Hence (1/ab)y(x)^2 + (4/h^2)(x - h/2)^2 = 1  ...equation of an ellipse

qed

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