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: (5)MIT math Harold Stark, Gilbert Strang, Daniel Stroock,- as dumb as
Dan Christensen in math?? question at today's breakfast

Replies: 2   Last Post: Oct 2, 2017 6:36 PM

 Messages: [ Previous | Next ]
 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
(5)MIT math Harold Stark, Gilbert Strang, Daniel Stroock,- as dumb as
Dan Christensen in math?? question at today's breakfast

Posted: Oct 2, 2017 10:24 AM

5)MIT math Harold Stark, Gilbert Strang, Daniel Stroock,- as dumb in math as Dan Christensen??

Will they all in the MIT math dept be fired for unable to teach correctly that the Oval is the conic section, never the ellipse??

On Monday, October 2, 2017 at 7:30:23 AM UTC-5, Dan Christensen wrote:
> On Saturday, September 30, 2017 at 4:53:35 AM UTC-4, Archimedes Plutonium wrote:
> > 3)MIT math dept all fired if unable to teach correct math-- Conic section = Oval, never ellipse//clamors Alouatta
> >

>
> You pathetic old fool. And liar.
>
>
> Dan
>

> >MIT
> >math dept

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. 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. Oval is defined as having only 1 axis of symmetry.

/  \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

AP

MIT math dept.

Artin, Michael
Emeritus Professor of Mathematics
Algebraic Geometry, Non-Commutative Algebra

Bazant, Martin
Professor of Chemical Engineering and Applied Mathematics
Applied Mathematics, Electrokinetics, Microfluidics and Electrochemistry

Berger, Bonnie
Simons Professor of Mathematics
Theoretical Computer Science, Computational Biological Modeling

Bezrukavnikov, Roman
Professor of Mathematics
Representation Theory, Algebraic Geometry

Borodin, Alexei
Professor of Mathematics
Integrable Probability

Bush, John
Professor of Applied Mathematics
Fluid Dynamics

Cheng, Hung
Professor of Applied Mathematics
Theoretical Physics

Chernoff, Herman
Emeritus Professor of Applied Mathematics
Statistics, Probability

Cohn, Henry
Discrete Mathematics

Colding, Tobias Holck
Cecil and Ida Green Distinguished Professor of Mathematics
Pure Mathematics Committee Chair
Differential Geometry, Partial Differential Equations
*On Leave Fall and Spring semesters*

Demanet, Laurent
Associate Professor of Applied Mathematics
Applied analysis, Scientific Computing

Dudley, Richard
Emeritus Professor of Mathematics
Probability, Statistics

Dunkel, Jörn
Assistant Professor of Applied Mathematics
Physical Applied Mathematics

Edelman, Alan
Professor of Applied Mathematics
Parallel Computing, Numerical Linear Algebra, Random Matrices

Etingof, Pavel
Professor of Mathematics
Representation Theory, Quantum Groups, Noncommutative Algebra

Freedman, Daniel
Emeritus Professor of Applied Mathematics
Theoretical Physics, Supergravity, Supersymmetry

Goemans, Michel
Professor of Mathematics
Theoretical Computer Science, Combinatorial Optimization

Assistant Professor of Mathematics
Probability, Representation Theory

Greenspan, Harvey
Emeritus Professor of Applied Mathematics
Fluid Mechanics

Guillemin, Victor
Professor of Mathematics
Differential Geometry

zzzzzzzzzzzzzzzzzzzzzzzzzzz

Guth, Larry
Professor of Mathematics
Metric geometry, harmonic analysis, extremal combinatorics

Helgason, Sigurdur
Emeritus Professor of Mathematics
Geometric Analysis

Hosoi, Anette
Professor of Mechanical Engineering
MacVicar Faculty Fellow
Fluid Dynamics, Numerical Analysis

Jerison, David
Professor of Mathematics
Partial Differential Equations, Fourier Analysis

Johnson, Steven
Professor of Applied Mathematics
Waves, PDEs, Scientific Computing

Kac, Victor
Professor of Mathematics
Algebra, Mathematical Physics

Mark Hyman, Jr. Career Development Associate Professor of Applied Mathematics
Theoretical Computer Science

Kim, Ju-Lee
Professor of Mathematics
On Leave Fall and Spring semesters

Kleiman, Steven
Emeritus Professor of Mathematics
Algebraic Geometry, Commutative Algebra

Kleitman, Daniel
Emeritus Professor of Applied Mathematics
Combinatorics, Operations Research

Lawrie, Andrew
Assistant Professor of Mathematics
Analysis, Geometric PDEs

Leighton, Tom
Professor of Applied Mathematics
Theoretical Computer Science, Combinatorics

Lusztig, George
Abdun-Nur Professor of Mathematics
Group Representations, Algebraic Groups

Mattuck, Arthur
Emeritus Professor of Mathematics
Algebraic Geometry

Maulik, Davesh
Professor of Mathematics
Algebraic Geometry

Melrose, Richard
Professor of Mathematics
Partial Differential Equations, Differential Geometry

Miller, Haynes
Professor of Mathematics
Algebraic Topology

Minicozzi, William
Singer Professor of Mathematics
Geometric Analysis, PDEs

Moitra, Ankur
Rockwell International Career Development Associate Professor of Mathematics
Theoretical Computer Science, Machine Learning

Mossel, Elchanan
Professor of Mathematics
Probability, Algorithms and Inference

Mrowka, Tomasz
Professor of Mathematics
Gauge Theory, Differential Geometry
On Leave Fall and Spring semesters

Munkres, James
Emeritus Professor of Mathematics
Differential Topology

Negu?, Andrei
Assistant Professor of Mathematics
Algebraic Geometry, Representation Theory
On Leave Spring semester

Pixton, Aaron
Class of 1957 Career Development Assistant Professor
Algebraic Geometry
On Leave Spring semester

Poonen, Bjorn
Claude Shannon Professor of Mathematics
Algebraic Geometry, Number Theory

Postnikov, Alexander
Professor of Applied Mathematics
Algebraic Combinatorics

Rigollet, Philippe
Associate Professor of Mathematics
Statistics, Machine Learning

Rosales, Rodolfo
Professor of Applied Mathematics
Nonlinear Waves, Fluid Mechanics, Material Sciences, Numerical pde

Saccà, Giulia
Assistant Professor of Mathematics

Sacks, Gerald
Emeritus Professor of Mathematical Logic
Mathematical Logic, Recursion Theory, Computational Set Theory

Seidel, Paul
Levinson Professor of Mathematics
Mirror Symmetry
On Leave Fall and Spring semesters

Sheffield, Scott
Leighton Family Professor of Mathematics
Probability and Mathematical Physics

Shor, Peter
Applied Mathematics Committee Chair
Quantum Computation, Quantum Information

Emeritus Institute Professor
Differential Geometry, Partial Differential Equations, Mathematical Physics

Sipser, Michael
Dean of School of Science
Donner Professor of Mathematics
MacVicar Faculty Fellow
Algorithms, Complexity Theory

Speck, Jared
Cecil and Ida B. Green Career Development Associate Professor of Mathematics
Analysis related to Mathematical Physics, General Relativity, PDEs

Staffilani, Gigliola
Abby Rockefeller Mauze Professor of Mathematics
Analysis: Dispersive Nonlinear Partial Differential Equations
On Leave Fall and Spring semesters

Stanley, Richard
Professor of Mathematics
Algebraic Combinatorics

Stark, Harold
Emeritus Professor of Mathematics
Number Theory

Strang, Gilbert
MathWorks Professor of Mathematics

Stroock, Daniel
Emeritus Professor of Mathematics
Probability, Stochastic Analysis

Associate Professor of Mathematics
Algebraic Topology, Noncommutative Algebraic Geometry

Toomre, Alar
Emeritus Professor of Applied Mathematics
Astrophysics, Stellar Dynamics, Fluid Mechanics

Vogan, David
Norbert Wiener Professor of Mathematics
Group Representations, Lie Theory

Zhang, Wei
Professor of Mathematics

Zhao, Yufei
Assistant Professor of Mathematics
Combinatorics

Snoop Dog

o-:^>___?
`~~c--^c'

Date Subject Author
10/2/17 plutonium.archimedes@gmail.com
10/2/17 Dan Christensen
10/2/17 Jan Bielawski