Below is a proof that oval is a conic section, never an ellipse. And I have been patient for a year or so now on this topic, for a year is long enough for people to make correction changes, yet Stanford math dept still teaches young students a lie-- conic section is ellipse. A falsehood, and so students never deserve to be taught liarings and falsehoods. Math teachers at Stanford are apparently no better than the insane Jan Bielawski.
So unless the Stanford math faculty admits that the oval is the conic section, I recommend the entire department be fired and install people who can and will do true math.
Subject: Two proofs are in, and Corollary is the same as Nesting Re: two regions in oval Re: the 3, Three Conics/Cylinder EXPERIMENTS From: Archimedes Plutonium <plutonium....@gmail.com> Injection-Date: Wed, 27 Sep 2017 01:33:01 +0000
Two proofs are in, and Corollary is the same as Nesting Re: two regions in oval Re: the 3, Three Conics/Cylinder EXPERIMENTS
- hide quoted text - On Tuesday, September 26, 2017 at 7:18:36 PM UTC-5, Archimedes Plutonium wrote: > On Tuesday, September 26, 2017 at 6:55:50 PM UTC-5, Archimedes Plutonium wrote: > > On Tuesday, September 26, 2017 at 6:11:50 PM UTC-5, Archimedes Plutonium wrote: > > > Now this would be a pretty theorem, pretty, pretty, pretty, for it ties together the two longest points of an oval with the plumb line of cone apex and center of cone base. It seems no reason, no reason in the world why those two should be connected at all. Connecting oval major diameter with cone plumb line-- no real reason in the world why they should be connected, but they are. > > > > > > > > > > Now some call this a axis of the cone, but I like Plumb line from apex to circle base center, calling it a plumb line rather than axis for a axis sounds stationary while a plumb line is in the act of creating a line from apex to base center is a active creation of a line segment. > > > > And here the question, most profound, is, why in the world would that plumb line ever have to intersect with the LONGEST LINE SEGMENT in each conic section-- OVAL? > > > > Why should that axis or plumbline have to meet that longest line segment? Why? > > > > From our intuition standpoint, seems like no reason why that plumbline, that axis should go through each and every LONGEST LINE segment of a Oval? > > > > So, why is it? > > > > > > Now, here is a picture I drew earlier, a oval inside a cone, a conic section. > > > > A > .-' '-. > .' `. > / \ > ; ; > | | > ; C D ; > \ / > `. .' > `-. __ .-' > B > So I need to prove that AB intersects with the cone axis, the plumb line and produces a center of the oval from which a perpendicular is drawn which is CD, giving us the major and minor diameters of the OVAL (the kooks of Old Math would be calling this a ellipse with 2 foci and a ellipse center). We in New Math have more brains of math than all those in Old Math. > > Now, a question quickly arises. > > Does the center of the oval with its major and minor diameters, does that minor diameter separate out two sort of regions of a oval. For the region CBD appears to be more "circular" than the region CAD which looks more "oblong". In this sense, we are asking if the reason for a oval is caused by inordinate stretching of CAD while the portion CBD was not stretched so much and retains much of its circular or ellipse shape. This would lead us to a better understanding of circle, ellipse and oval. Take a circle and give it uniform stretching , say at C and D and you end up with ellipse, but if you stretched a circle ABCD and pulled only at A, you end up with an oval. > > So, here the question arises, is the center of the oval as defined by the intersection of the axis of cone, always dividing the oval into two regions,-- one region that retains its circle shape for the most part, and the other region that was terribly stretched to form the oval. > >
Alright, the proof looks daunting, really daunting as to how do you prove the plumb line, the axis of the cone intersects with the longest line in the oval-- the initial point in the entry cut and the very last point, on the other side, as the knife exits the conic section. This I called the Major Diameter.
Very, daunting-- how to prove they meet, and meet in what I call the Oval center point?
Well, as in many, many proofs in Geometry, especially third dimensional geometry, we need some structure, some larger structure to often prove something. We need a surrounding edifice, scaffolding is a proper analogy. And in this situation, we use the CYLINDER as a larger outer structure for which the cone and its section are embedded inside. (Now, the many kooks in Old Math that insist the Conic section is a ellipse, are just about to have chocolate cream pie, cherry pie, lemon meringue pie and apple pecan pie all thrown and smeared all over their faces.) For, these goon clods are insisting that the conic section is an ellipse and also the cylinder section is an ellipse, boy oh boy, what awful and ugly goons they are-- and many are teachers of math-- which makes you want to think-- these are not teachers but propaganda throwing nutballs.
So, as I was saying, -- often in math, we have to build a larger structure, in order to prove something in a lower, more simple structure.
We need to prove the plumb line the axis of the cone intersects with the longest line segment in the conic section, what I drawn above as AB. In order to do that proof we nest inside a Cylinder the entire Cone and the same section of Conic we extend to the Cylinder. Now we have two FIGURES to look at, we have a Conic Oval and we have a Cylinder Ellipse. And the plumbline the conic axis must be the center of the Ellipse and the ellipse major axis must coincide with the Oval major-diameter. Thus, the plumbline does indeed intersect with the longest line segment in the conic section.
This goes even further, for it proves the conic section is never an ellipse because that would mean the intersection point meets halfway in both cone and cylinder, yet, the cylinder Major Axis is far larger than the Cone's Major Diameter.
Now, I learned something super special in this, not only a proof. I learned that what is considered a Corollary proof given a larger overriding proof such as Fermat's Last Theorem is proven once we prove Generalized FLT, then FLT falls out as a corollary proof, that such a proof in Algebra is the same as in Geometry where we take a larger figure-- more general and nest the smaller figure inside it to gain the proof wanted. You see, when proving Generalized FLT and then able to prove FLT from that, is the same as proving conic section is an Oval by nesting the cone inside a more general figure-- the cylinder.
So in Algebra, we call it Corollary proving, while in Geometry, we may as well call it Nesting proving. Corollary and Nesting are the same things only in different arenas of mathematics.
So the above is two proofs, for I proved the plumbline or axis of cone is on AB. But also, I proved that no conic section is ever a ellipse-- but rather, always a oval.
Ever since Stanford as a school was formed, it has taught that a ellipse is a conic section, never really examining that idea up close. Never any close examination. And thus Stanford, when the oval is the conic section, not the ellipse has been spreading pollution-math, not real math, and thus, making fools Californian citizens like Alouatta and Jan Bielawski. Such fools that can only understand the OVAL is the conic section when Stanford math professors tell Jan and Alouatta such. Until then, fools be fools,,,,
NEVER REALLY EXAMINING THE CONIC SECTIONS UP CLOSE WITH AN ACTUAL MODEL, always, just fallible minds imagining and thinking-- thinking about conic sections but never hands on models to guide the thought process.
For in fact the Oval is a conic section not an ellipse, and the ellipse is only found in a Cylinder section, never in a Conic. So it is the duty, responsibility of Stanford to now undo the damage they have done. To actually discover with models, that the ellipse is a cylinder section, never a conic and what is produced from the cone cut is a OVAL. This means the Dandelin Spheres theorem is false and needs refurbished.
On Tuesday, September 19, 2017 at 2:00:30 PM UTC-5, Archimedes Plutonium wrote:
> > So, you have an entry cut, say here > entry cut up high > /\/ > / \ > // \ > exit > > So, you have entry cut up high where the curvature is small like this ) > > ( > and you have exit cut below where curvature is large like this ( > (
Only one axis of symmetry in that Conic section = Oval, never ellipse. To get an ellipse, you need a Cylinder section.
This means the Dandelin proof is wrong, for it is intended for a cylinder not a cone.
Stanford University, math dept.
Brumfiel, Gregory Professor Emeritus
Bump, Daniel Professor
Candès, Emmanuel Professor; Barnum-Simons Chair in Mathematics and Statistics; Professor of Electrical Engineering (by courtesy)
Carlsson, Gunnar Professor Emeritus
Charikar, Moses Professor of Computer Science and, by courtesy, of
Chatterjee, Sourav Professor of Mathematics and Professor of Statistics
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz Church, Tom Assistant Professor
Cohen, Ralph Barbara Kimball Browning Professor in the School of Humanities and Sciences
Conrad, Brian Professor
Conrey, Brian Consulting Professor
Dembo, Amir Marjorie Mhoon Fair Professor in Quantitative Science; Professor (Mathematics & Statistics and, by courtesy, Electrical Enginerring)
Diaconis, Persi Mary V. Sunseri Professor of Statistics and Mathematics
Eliashberg, Yakov Herald L. and Caroline L. Ritch Professor of Mathematics
Finn, Robert Professor Emeritus
Fox, Jacob Professor
Fredrickson, Laura Szegö Assistant Professor
Galatius, Søren Professor
George, Schaeffer Lecturer
Hershkovits, Or Szegö Assistant Professor
Hoffman, David Consulting Professor
Ionel, Eleny Professor and Chair
Kallosh, Renata Professor (Physics and, by courtesy, Mathematics)
Katznelson, Yitzhak Professor Emeritus
Kazeev, Vladimir Szegö Assistant Professor
Kemeny, Michael Szegö Assistant Professor
Kerckhoff, Steven Robert Grimmett Professor in Mathematics
Kimport, Susie Lecturer
Li, Jun Professor
Liu, Tai-Ping Professor Emeritus
Lucianovic, Mark Senior Lecturer
Luk, Jonathan Assistant Professor
Manners, Frederick Szegö Assistant Professor
Mazzeo, Rafe Professor
Milgram, R. James Professor Emeritus
Mirzakhani, Maryam Professor
Mueller, Stefan Visiting Assistant Professor
Ohrt, Christopher Szegö Assistant Professor
Ornstein, Donald Professor Emeritus
Papanicolaou, George Robert Grimmett Professor of Mathematics
Ryzhik, Lenya Professor
Schoen, Richard Professor Emeritus
Simon, Leon Professor Emeritus
Sommer, Rick Lecturer
Soundararajan, Kannan Professor
Tokieda, Tadashi Teaching Professor
Tsai, Cheng-Chiang Szegö Assistant Professor
Vakil, Ravi Professor
Vasy, András Professor
Venkatesh, Akshay Professor
Vondrák, Jan Associate Professor
White, Brian Robert Grimmett Professor of Mathematics