Discussion:
Ellipse only comes out of a Cylinder Section, never a Conic section//Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Archimedes Plutonium
2017-08-12 17:05:09 UTC
Raw Message
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor

Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval

Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.

So, this is a major mistake in geometry started since Ancient Greek times way back to Euclid.

Now the Ancient Greeks seldom if ever did a hands on experiment. They liked to do everything in their head, which often can get you the wrong answer.

Now, in modern times there is no excuse for not doing this experiment. You simply get a cylinder and a cone of about the same size and you make a oblique angle cut and see what figure comes out. In the Cylinder cut, the figure is a ELLIPSE, yet in the Cone cut the figure is a OVAL.

Array proof Re: Proof that oval is the conic section, never the ellipse

Alright, I need to prepare this proof for the Proof Array, where the proofs are all pared down to just their motors on how they work, no extras, no frills, just bare bone essentials.

Theorem Statement:: Conic Sections are never ellipses. We have cuts or sections in cylinders and in two cones stacked apex to apex, but here we need only one cone. A cylinder is itself the stacking of equal circles, while the cone is a stacking of progressive smaller circles. We define a ellipse as a planar figure that has two axes of symmetry, and a oval as a planar figure of only one axis of symmetry. A cut parallel to base is a circle in each. But a cut at a diagonal to base is always a ellipse in the cylinder section and always a oval in the conic section.

Proof Statement:: The diagonal cut in the cylinder has an entry cut and a exit cut. Since a cylinder is composed of equal circles stacked, means the entry cut circle equals the exit cut circle, hence 2 axes of symmetry. The conic section, the entry circle is far smaller than exit circle, hence only 1 axis of symmetry. QED

Picture of the proof

A             A

A        B     B        A

A     B    --|--     B     A

A   B               B    A

A   B             B  A

The proof is simple, but what history is going to endlessly talk about, is how in the world can something so simple so easy, escape the attention of the best of mathematicians for 2,500 years. If this had been biology, biologists would only now be recognizing that mammals that live in the oceans are not fish.

The word "scatterbrained" is apt for mathematicians from Ancient Greek times to now, scatterbrained.

Now here is a short list of math failures who just cannot be bothered to hands on experiment but rather are failures of mathematics for all they can do is dictate that the ellipse is a conic section. Dictate because they are far far too stupid to ever actually experiment to see if their memorized crap on conics is really true, or, just memorized crap.

Markus Klyver
Jan Burse
Dan Christensen
Jan Bielawski
Terry Tao
Andrew Wiles
John Conway
Appel & Haken
qbwrfmix
Eastside
Konyberg KON
Beal, of Beal conjecture
Robin Hartshorne
John Milnor

All of them, failures of mathematics, for they never are able to get beyond memorization of mathematics, whether utterly false math, and worst yet, they preach this crap to younger generations and scold the young students-- who are smarter than the mathematician on conics.

So, I discovered the oval was the conic section, never the ellipse and I discovered that in 2016, and yet, here it is 2017, and one would think the math community would be grateful for the correction to their error. Instead, the math community continues to ignore anyone outside the inner circle of mathematics, who shows where they are fully mistaken.

I always thought until the last 25 years that mathematicians are some of the most honest people in the world, when it comes to truth, but in fact, I keep finding out that mathematicians are one of the most corrupt crazy minds in science.

It has been a year since the discovery of Oval is ellipse, and still not a peep out of math community.

Newsgroups: sci.math
Date: Wed, 28 Dec 2016 13:25:46 -0800 (PST)

Subject: getting an ellipse from a conic cut-- possible or impossible??
probably a unique cut
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Wed, 28 Dec 2016 21:25:47 +0000

Discoveries like this deserve attention, and not hidden by suppression fools with their own greedy axes to grind. So, I list the names of everyone in geometry, who should have cleared up and cleaned out the mistake, but is hiding and ignoring, and failing mathematics with their ignoring.

AP
b***@gmail.com
2017-08-12 17:08:12 UTC
Raw Message
AP brain farto, for what do you want credit?
For being studpid? You got this credit already. (*)

For non-planar projection, like for example spherical
projections, like in a fish-eye camera or as an

approximation for the human retina, you might possibly
get ovals, and not what you can measure when you

take your hands and touch the conic sections. Or
are the rules in your mongo math home also bent?

(*)
Its all over the internet. Not a single line of
math, only spamming sci.math by creepy a**hole AP.
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
So, this is a major mistake in geometry started since Ancient Greek times way back to Euclid.
Now the Ancient Greeks seldom if ever did a hands on experiment. They liked to do everything in their head, which often can get you the wrong answer.
Now, in modern times there is no excuse for not doing this experiment. You simply get a cylinder and a cone of about the same size and you make a oblique angle cut and see what figure comes out. In the Cylinder cut, the figure is a ELLIPSE, yet in the Cone cut the figure is a OVAL.
Array proof Re: Proof that oval is the conic section, never the ellipse
Alright, I need to prepare this proof for the Proof Array, where the proofs are all pared down to just their motors on how they work, no extras, no frills, just bare bone essentials.
Theorem Statement:: Conic Sections are never ellipses. We have cuts or sections in cylinders and in two cones stacked apex to apex, but here we need only one cone. A cylinder is itself the stacking of equal circles, while the cone is a stacking of progressive smaller circles. We define a ellipse as a planar figure that has two axes of symmetry, and a oval as a planar figure of only one axis of symmetry. A cut parallel to base is a circle in each. But a cut at a diagonal to base is always a ellipse in the cylinder section and always a oval in the conic section.
Proof Statement:: The diagonal cut in the cylinder has an entry cut and a exit cut. Since a cylinder is composed of equal circles stacked, means the entry cut circle equals the exit cut circle, hence 2 axes of symmetry. The conic section, the entry circle is far smaller than exit circle, hence only 1 axis of symmetry. QED
Picture of the proof
A             A

A        B     B        A
A     B    --|--     B     A

A   B               B    A
A   B             B  A
The proof is simple, but what history is going to endlessly talk about, is how in the world can something so simple so easy, escape the attention of the best of mathematicians for 2,500 years. If this had been biology, biologists would only now be recognizing that mammals that live in the oceans are not fish.
The word "scatterbrained" is apt for mathematicians from Ancient Greek times to now, scatterbrained.
Now here is a short list of math failures who just cannot be bothered to hands on experiment but rather are failures of mathematics for all they can do is dictate that the ellipse is a conic section. Dictate because they are far far too stupid to ever actually experiment to see if their memorized crap on conics is really true, or, just memorized crap.
Markus Klyver
Jan Burse
Dan Christensen
Jan Bielawski
Terry Tao
Andrew Wiles
John Conway
Appel & Haken
qbwrfmix
Eastside
Konyberg KON
Beal, of Beal conjecture
Robin Hartshorne
John Milnor
All of them, failures of mathematics, for they never are able to get beyond memorization of mathematics, whether utterly false math, and worst yet, they preach this crap to younger generations and scold the young students-- who are smarter than the mathematician on conics.
So, I discovered the oval was the conic section, never the ellipse and I discovered that in 2016, and yet, here it is 2017, and one would think the math community would be grateful for the correction to their error. Instead, the math community continues to ignore anyone outside the inner circle of mathematics, who shows where they are fully mistaken.
I always thought until the last 25 years that mathematicians are some of the most honest people in the world, when it comes to truth, but in fact, I keep finding out that mathematicians are one of the most corrupt crazy minds in science.
It has been a year since the discovery of Oval is ellipse, and still not a peep out of math community.
Newsgroups: sci.math
Date: Wed, 28 Dec 2016 13:25:46 -0800 (PST)
Subject: getting an ellipse from a conic cut-- possible or impossible??
probably a unique cut
Injection-Date: Wed, 28 Dec 2016 21:25:47 +0000
Discoveries like this deserve attention, and not hidden by suppression fools with their own greedy axes to grind. So, I list the names of everyone in geometry, who should have cleared up and cleaned out the mistake, but is hiding and ignoring, and failing mathematics with their ignoring.
AP
b***@gmail.com
2017-08-12 17:11:31 UTC
Raw Message
Do you have bent rules and compass in your home?
Or is it the crystal meth halluzinations that let

them appear like this to you, and you cannot use
your hands anymore, since youre most of the time

vegetating on the floor, slowly wasting away...
the only thing that works at your home is the

copy paste button, for the many spams.
Post by b***@gmail.com
AP brain farto, for what do you want credit?
For being studpid? You got this credit already. (*)
For non-planar projection, like for example spherical
projections, like in a fish-eye camera or as an
approximation for the human retina, you might possibly
get ovals, and not what you can measure when you
take your hands and touch the conic sections. Or
are the rules in your mongo math home also bent?
(*)
Its all over the internet. Not a single line of
math, only spamming sci.math by creepy a**hole AP.
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
So, this is a major mistake in geometry started since Ancient Greek times way back to Euclid.
Now the Ancient Greeks seldom if ever did a hands on experiment. They liked to do everything in their head, which often can get you the wrong answer.
Now, in modern times there is no excuse for not doing this experiment. You simply get a cylinder and a cone of about the same size and you make a oblique angle cut and see what figure comes out. In the Cylinder cut, the figure is a ELLIPSE, yet in the Cone cut the figure is a OVAL.
Array proof Re: Proof that oval is the conic section, never the ellipse
Alright, I need to prepare this proof for the Proof Array, where the proofs are all pared down to just their motors on how they work, no extras, no frills, just bare bone essentials.
Theorem Statement:: Conic Sections are never ellipses. We have cuts or sections in cylinders and in two cones stacked apex to apex, but here we need only one cone. A cylinder is itself the stacking of equal circles, while the cone is a stacking of progressive smaller circles. We define a ellipse as a planar figure that has two axes of symmetry, and a oval as a planar figure of only one axis of symmetry. A cut parallel to base is a circle in each. But a cut at a diagonal to base is always a ellipse in the cylinder section and always a oval in the conic section.
Proof Statement:: The diagonal cut in the cylinder has an entry cut and a exit cut. Since a cylinder is composed of equal circles stacked, means the entry cut circle equals the exit cut circle, hence 2 axes of symmetry. The conic section, the entry circle is far smaller than exit circle, hence only 1 axis of symmetry. QED
Picture of the proof
A             A

A        B     B        A
A     B    --|--     B     A

A   B               B    A
A   B             B  A
The proof is simple, but what history is going to endlessly talk about, is how in the world can something so simple so easy, escape the attention of the best of mathematicians for 2,500 years. If this had been biology, biologists would only now be recognizing that mammals that live in the oceans are not fish.
The word "scatterbrained" is apt for mathematicians from Ancient Greek times to now, scatterbrained.
Now here is a short list of math failures who just cannot be bothered to hands on experiment but rather are failures of mathematics for all they can do is dictate that the ellipse is a conic section. Dictate because they are far far too stupid to ever actually experiment to see if their memorized crap on conics is really true, or, just memorized crap.
Markus Klyver
Jan Burse
Dan Christensen
Jan Bielawski
Terry Tao
Andrew Wiles
John Conway
Appel & Haken
qbwrfmix
Eastside
Konyberg KON
Beal, of Beal conjecture
Robin Hartshorne
John Milnor
All of them, failures of mathematics, for they never are able to get beyond memorization of mathematics, whether utterly false math, and worst yet, they preach this crap to younger generations and scold the young students-- who are smarter than the mathematician on conics.
So, I discovered the oval was the conic section, never the ellipse and I discovered that in 2016, and yet, here it is 2017, and one would think the math community would be grateful for the correction to their error. Instead, the math community continues to ignore anyone outside the inner circle of mathematics, who shows where they are fully mistaken.
I always thought until the last 25 years that mathematicians are some of the most honest people in the world, when it comes to truth, but in fact, I keep finding out that mathematicians are one of the most corrupt crazy minds in science.
It has been a year since the discovery of Oval is ellipse, and still not a peep out of math community.
Newsgroups: sci.math
Date: Wed, 28 Dec 2016 13:25:46 -0800 (PST)
Subject: getting an ellipse from a conic cut-- possible or impossible??
probably a unique cut
Injection-Date: Wed, 28 Dec 2016 21:25:47 +0000
Discoveries like this deserve attention, and not hidden by suppression fools with their own greedy axes to grind. So, I list the names of everyone in geometry, who should have cleared up and cleaned out the mistake, but is hiding and ignoring, and failing mathematics with their ignoring.
AP
Archimedes Plutonium
2017-08-13 19:48:48 UTC
Raw Message
My detractors are between a rock and a hard spot, for they want to cling to a ellipse as conic but then what does that leave the cylinder section, duh
konyberg
2017-08-13 22:45:42 UTC
Raw Message
Post by Archimedes Plutonium
My detractors are between a rock and a hard spot, for they want to cling to a ellipse as conic but then what does that leave the cylinder section, duh
Are you serious?
And a circle has only two symmetry axes?
Can you give them to me?
An experiment for you:
A circle and two axes!
Now you have two new symmetry axes as you are looking down at the circle.
Looking down; any figure can be distorted, even an ellipse!

KON
FredJeffries
2017-08-13 22:05:24 UTC
Raw Message
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
I'm guessing that the phenomenon referred to is the fact that the center of the cone section does not coincide with the center line of the cone.

For a related phenomenon, see Dandelin spheres

https://en.wikipedia.org/wiki/Dandelin_spheres
http://mathworld.wolfram.com/DandelinSpheres.html
Archimedes Plutonium
2017-08-13 23:26:50 UTC
Raw Message
Well then the immediate question is, does the center of a cylinder section align with the center of the cylinder.

I reduced the problem to the number of axes of symmetry and you reduced it to center alignment. Not sure if one or the other is more intuitive or more economical in proof write up.

AP
Archimedes Plutonium
2017-08-14 01:10:33 UTC
Raw Message
The centers are less intuitive and less economical of a proof than is a proof based on entry cut versus exit cut.

AP
Archimedes Plutonium
2017-08-14 06:02:34 UTC
Raw Message
Post by Archimedes Plutonium
The centers are less intuitive and less economical of a proof than is a proof based on entry cut versus exit cut.
Speaking of intuitive, can we say every rectangular solid and parallelepiped cross section is a rectangle or parallelogram? These things are sometimes tricky

Even more tricky, a wedge, when is the cross section a rectangle, when a triangle?

Now, if we take an ellipse and form it into a 3D ellipsoid, now can we get a circle out of some cross section? I am confident someone must have worked this out beforehand. Now we take an egg, a oval in 3rd D, can we get a circle out of it? Can we get a ellipse out of a oval 3D? Then can we get a oval out of a ellipsoid?

So many questions, so little time.

AP
Archimedes Plutonium
2017-08-14 06:27:32 UTC
Raw Message
Post by FredJeffries
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
I'm guessing that the phenomenon referred to is the fact that the center of the cone section does not coincide with the center line of the cone.
For a related phenomenon, see Dandelin spheres
https://en.wikipedia.org/wiki/Dandelin_spheres
http://mathworld.wolfram.com/DandelinSpheres.html
Alright, I looked that up, the Dandelin spheres and apparently, the proof is fake because they start out
assuming the oval is a ellipse, and the aim of the proof is that the small sphere and larger sphere contact the plane at a focus.

So apparently, if Dandelin had started out his proof without the assumption the section was a ellipse, instead that the section was a oval, puff, his proof goes all up in a cloud of smoke and dust.

Now, Dandelin is probably not the first mathematician with a tacit-hidden-assumption that wrecks his fake proof. History of math is littered with these guys.

Fred, can you spot a Dandelin proof where he proves the section is a ellipse in the first beginning and then follows up.

Apparently this is a huge gap in math, that a fakery like Dandelin was so undetected.

AP
Archimedes Plutonium
2017-08-14 10:55:55 UTC
Raw Message
Now the literature says that the oval is not well defined.

They probably say that because it has no center to speak of, nor does it have a focus.

But, we can well define oval as a ellipse with just one axis of symmetry.

We surely well define a rectangle as all four angles 90 and two different sides, then define square as four 90 degree angles and only one side. Likewise, in analogy, a ellipse is a smooth closed curve which has two axes of symmetry, while oval just one. End of story, morning glory.

AP
b***@gmail.com
2017-08-14 11:37:31 UTC
Raw Message
AP brain farto, cant admit his mistake.
What a miserable creature. A complete

wako, probably sniffing glue the whole
day. Not a single line of math for 30 years.
Post by Archimedes Plutonium
Now the literature says that the oval is not well defined.
They probably say that because it has no center to speak of, nor does it have a focus.
But, we can well define oval as a ellipse with just one axis of symmetry.
We surely well define a rectangle as all four angles 90 and two different sides, then define square as four 90 degree angles and only one side. Likewise, in analogy, a ellipse is a smooth closed curve which has two axes of symmetry, while oval just one. End of story, morning glory.
AP
Archimedes Plutonium
2017-08-14 17:17:30 UTC
Raw Message
Post by Archimedes Plutonium
Post by FredJeffries
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
I'm guessing that the phenomenon referred to is the fact that the center of the cone section does not coincide with the center line of the cone.
For a related phenomenon, see Dandelin spheres
https://en.wikipedia.org/wiki/Dandelin_spheres
http://mathworld.wolfram.com/DandelinSpheres.html
Looking at those Dandelin Spheres in Wikipedia, not only do they have a fake proof, since they assume the section is a ellipse, when in fact it is a oval with just one axis of symmetry, and thus, no foci.

But, I think in that picture, another huge mistake is showing. I think they show a latitude line on big sphere and latitude line on little sphere as being ellipses also. When we all know that every cross section of a sphere that is not a tangent point, ends up being a circle.

Now, when was it proven true that every sphere cross section by a plane, is a circle (unless it is a tangent point).

Now in that picture, they do show the two spheres on the centerline axis of the cone.

Somewhere I read where to construct a OVAL you take two different size circles, and by a technique you append part of the arc of the smaller circle onto the larger circle, forming a oval. The only tricky part is to not have two vertices.

So in that construction of a oval from two different sized circles, is what the Dandelin spheres were groping for, groping for a proof, that Dandelin spheres is the 3rd dimension analog of construction of a oval in 2nd dimension by the blending of a small circle being incorporated upon a larger circle forming a oval.

Now, I find it almost miraculously annoying that a Dandelin fake proof exists to this day, when surely, someone would have constructed a hands on Cone and tried to stuff a ellipse inside that cone. It is very easy to roll up a sheet of paper into a cone and try to stuff a ellipse into it. So how in the world could this fake proof, have lasted all these centuries without anyone hands on doing it. And we see the power of fake math community proofs, the power to crush rational logical reasoning, once a fakery is published. Once a fake is published, it is as if almost everyone in math is void of logical thought on any aspect of the fakery. As if mathematicians worship publication, and drained of any logical intelligence.
Post by Archimedes Plutonium
Alright, I looked that up, the Dandelin spheres and apparently, the proof is fake because they start out
assuming the oval is a ellipse, and the aim of the proof is that the small sphere and larger sphere contact the plane at a focus.
So apparently, if Dandelin had started out his proof without the assumption the section was a ellipse, instead that the section was a oval, puff, his proof goes all up in a cloud of smoke and dust.
Now, Dandelin is probably not the first mathematician with a tacit-hidden-assumption that wrecks his fake proof. History of math is littered with these guys.
Fred, can you spot a Dandelin proof where he proves the section is a ellipse in the first beginning and then follows up.
Apparently this is a huge gap in math, that a fakery like Dandelin was so undetected.
So, who was the first to prove that all sections except a tangent point of a sphere are all circles? Seems so obvious that likely, no-one thought such a proof was necessary. How is it proved? Anyway?

AP
Don Redmond
2017-08-14 17:43:05 UTC
Raw Message
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
AP
As I've mentioned before, but apparently you don't care, go read Apollonius. In his treatise on conic sections he proves that the oblique cut gives an ellipse. It's a curve with two foci, two axes of symmetry and has the reflection property.

You know what they say: if it symmetrizes like an ellipse and reflects like an ellipse, it's an ellipse.

Don
Archimedes Plutonium
2017-08-14 17:52:34 UTC
Raw Message
Post by Don Redmond
As I've mentioned before, but apparently you don't care, go read Apollonius. In his treatise on conic sections he proves that the oblique cut gives an ellipse. It's a curve with two foci, two axes of symmetry and has the reflection property.
You know what they say: if it symmetrizes like an ellipse and reflects like an ellipse, it's an ellipse.
Don
Better yet, why not do a hands-on experiment, rather than go looking for a ancient 2,000 year old fake proof written in foreign language and in terms that are almost unintelligible to modern math standards. Why labor for 2 days, when in 2 minutes you can roll up a paper, scotch tape it and cut a oblique section and see for yourself that you --Have No Ellipse, but rather a Oval.

Are you past being reasonable Don? Does old age for you mean-- never experiment, only read ancient crap that reinforces your prejudice. Does old age for you mean-- believe in print, never do hands on experiment.

AP
Archimedes Plutonium
2017-08-14 23:21:50 UTC
Raw Message
Newsgroups: sci.physics
Date: Mon, 14 Aug 2017 16:12:42 -0700 (PDT)

Subject: Re: Displacement current replaced by Capacitor current Re:
PreliminaryPage22, 3-7, AP-Maxwell Equations of New Physics/
Atom-Totality-Universe/ textbook 8th ed
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Mon, 14 Aug 2017 23:12:43 +0000

Re: Displacement current replaced by Capacitor current Re: PreliminaryPage22, 3-7, AP-Maxwell Equations of New Physics/ Atom-Totality-Universe/ textbook 8th ed

***@gmail.com
5:42 PM (27 minutes ago)

This may also be regarded as a continuation,,,,,,,,,

--------

Hey, Rockbr, thanks, I was hoping someday, someone would post the Maxwell Eq, so I did not have to track down the symbols::

∇⋅B = 0

∇⋅D = ρ

∇×E = - ∂B/∂t

∇×H =  ∂D/∂t + J
Archimedes Plutonium
2017-08-15 06:14:35 UTC
Raw Message
Post by Archimedes Plutonium
Post by Don Redmond
As I've mentioned before, but apparently you don't care, go read Apollonius. In his treatise on conic sections he proves that the oblique cut gives an ellipse. It's a curve with two foci, two axes of symmetry and has the reflection property.
You know what they say: if it symmetrizes like an ellipse and reflects like an ellipse, it's an ellipse.
Don
Better yet, why not do a hands-on experiment, rather than go looking for a ancient 2,000 year old fake proof written in foreign language and in terms that are almost unintelligible to modern math standards. Why labor for 2 days, when in 2 minutes you can roll up a paper, scotch tape it and cut a oblique section and see for yourself that you --Have No Ellipse, but rather a Oval.
Are you past being reasonable Don? Does old age for you mean-- never experiment, only read ancient crap that reinforces your prejudice. Does old age for you mean-- believe in print, never do hands on experiment.
Physicists would be horrified if one of their own, claimed that a 2,000 year old write up on ellipse and conic section is a more valid proof, than is a immediate hands on demonstration. Like saying that a idea 2,000 years old is no match for a physics experiment result of today.

But that is what math academia is mostly about, defend what is published and in print. Never believe nor accept a demonstration, because the truth is best and higher if in print, not hands on demonstration.

Maybe it is the academic environment these days that seems to sap out all the Logic in one's head. That if you go to graduate school with a fair share of logical mind, that it is all gone when you come out of school.

AP
Jan
2017-08-15 07:04:30 UTC
Raw Message
Post by Archimedes Plutonium
Post by Archimedes Plutonium
Post by Don Redmond
As I've mentioned before, but apparently you don't care, go read Apollonius. In his treatise on conic sections he proves that the oblique cut gives an ellipse. It's a curve with two foci, two axes of symmetry and has the reflection property.
You know what they say: if it symmetrizes like an ellipse and reflects like an ellipse, it's an ellipse.
Don
Better yet, why not do a hands-on experiment, rather than go looking for a ancient 2,000 year old fake proof written in foreign language and in terms that are almost unintelligible to modern math standards. Why labor for 2 days, when in 2 minutes you can roll up a paper, scotch tape it and cut a oblique section and see for yourself that you --Have No Ellipse, but rather a Oval.
Are you past being reasonable Don? Does old age for you mean-- never experiment, only read ancient crap that reinforces your prejudice. Does old age for you mean-- believe in print, never do hands on experiment.
Physicists would be horrified if one of their own, claimed that a 2,000 year old write up on ellipse and conic section is a more valid proof, than is a immediate hands on demonstration. Like saying that a idea 2,000 years old is no match for a physics experiment result of today.
But that is what math academia is mostly about, defend what is published and in print. Never believe nor accept a demonstration, because the truth is best and higher if in print, not hands on demonstration.
Maybe it is the academic environment these days that seems to sap out all the Logic in one's head. That if you go to graduate school with a fair share of logical mind, that it is all gone when you come out of school.
AP
Stop talking nonsense.

--
Jan
Me
2017-08-15 07:24:58 UTC
Raw Message
why not do a hands-on experiment ...
Yeah, see:

and

b***@gmail.com
2017-08-15 07:31:01 UTC
Raw Message
BTW the dandelian spheres also work for the other conic
sections, not only ellipse, for visual hints see here:

Vladimir Serdarushich - Hyperbola and Parabola
http://www.nabla.hr/PC-ConicsProperties2.htm

F1 P - F2 P = constant

F P - F N = 0
Post by Me
why not do a hands-on experiment ...
http://youtu.be/psvT5Xzh5cA
and
http://youtu.be/5kM39HZDQ5s
Archimedes Plutonium
2017-08-16 01:00:15 UTC
Raw Message
Post by b***@gmail.com
Vladimir Serdarushich - Hyperbola and Parabola
Too bad that Jan Burse is too dumb and lazy to understand that cutting a cone at diagonal never yields a ellipse for an ellipse has two axes of symmetry.

But Jan is far too insane in math to do the experiment, but Terry Tao, Thomas Hales are not insane in math, just misguided. Can either one of those math professors acknowledge the oval as a conic section and the ellipse is ever more a cylinder section. Can Tao and Hales admit the truth; for we know Burse is insane and wouldn't know the truth from a fence post.
Me
2017-08-16 01:22:00 UTC
Raw Message
too dumb and lazy to understand that cutting a cone at diagonal [...] yields a[n] ellipse
Yeah, see:

http://youtu.be/psvT5Xzh5cA
and
http://youtu.be/5kM39HZDQ5s

b***@gmail.com
2017-08-14 17:47:07 UTC
Raw Message
The Dandelin Spheres proof is relatively simple. But it is
not the only proof to show that a conic section is an ellipse,

pitty you even dont understand this simple proof. AP brain
farto, not a single line of math, already for 30 years.
Post by Archimedes Plutonium
Post by Archimedes Plutonium
Post by FredJeffries
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
I'm guessing that the phenomenon referred to is the fact that the center of the cone section does not coincide with the center line of the cone.
For a related phenomenon, see Dandelin spheres
https://en.wikipedia.org/wiki/Dandelin_spheres
http://mathworld.wolfram.com/DandelinSpheres.html
Looking at those Dandelin Spheres in Wikipedia, not only do they have a fake proof, since they assume the section is a ellipse, when in fact it is a oval with just one axis of symmetry, and thus, no foci.
But, I think in that picture, another huge mistake is showing. I think they show a latitude line on big sphere and latitude line on little sphere as being ellipses also. When we all know that every cross section of a sphere that is not a tangent point, ends up being a circle.
Now, when was it proven true that every sphere cross section by a plane, is a circle (unless it is a tangent point).
Now in that picture, they do show the two spheres on the centerline axis of the cone.
Somewhere I read where to construct a OVAL you take two different size circles, and by a technique you append part of the arc of the smaller circle onto the larger circle, forming a oval. The only tricky part is to not have two vertices.
So in that construction of a oval from two different sized circles, is what the Dandelin spheres were groping for, groping for a proof, that Dandelin spheres is the 3rd dimension analog of construction of a oval in 2nd dimension by the blending of a small circle being incorporated upon a larger circle forming a oval.
Now, I find it almost miraculously annoying that a Dandelin fake proof exists to this day, when surely, someone would have constructed a hands on Cone and tried to stuff a ellipse inside that cone. It is very easy to roll up a sheet of paper into a cone and try to stuff a ellipse into it. So how in the world could this fake proof, have lasted all these centuries without anyone hands on doing it. And we see the power of fake math community proofs, the power to crush rational logical reasoning, once a fakery is published. Once a fake is published, it is as if almost everyone in math is void of logical thought on any aspect of the fakery. As if mathematicians worship publication, and drained of any logical intelligence.
Post by Archimedes Plutonium
Alright, I looked that up, the Dandelin spheres and apparently, the proof is fake because they start out
assuming the oval is a ellipse, and the aim of the proof is that the small sphere and larger sphere contact the plane at a focus.
So apparently, if Dandelin had started out his proof without the assumption the section was a ellipse, instead that the section was a oval, puff, his proof goes all up in a cloud of smoke and dust.
Now, Dandelin is probably not the first mathematician with a tacit-hidden-assumption that wrecks his fake proof. History of math is littered with these guys.
Fred, can you spot a Dandelin proof where he proves the section is a ellipse in the first beginning and then follows up.
Apparently this is a huge gap in math, that a fakery like Dandelin was so undetected.
So, who was the first to prove that all sections except a tangent point of a sphere are all circles? Seems so obvious that likely, no-one thought such a proof was necessary. How is it proved? Anyway?
AP
b***@gmail.com
2017-08-14 18:06:08 UTC
Raw Message
The sketch of the proof is here:
http://mathworld.wolfram.com/DandelinSpheres.html

cant even do Peano induction, you even don't know

what integers are. Your geothermal posts recently,
are the echo of your totally void brain.

Let me think, you we get a quadratic, if the sum of
the distance two the two foci is constant?

P (x,y)

F1 F2
+---|---+

F1 P = sqrt(x^2+(y+e)^2)

F2 P = sqrt(x^2+(y-e)^2)

F1 P + F2 P = sqrt(x^2+(y+e)^2)+sqrt(x^2+(y-e)^2) = 2a

Now eliminate sqrt:

sqrt(x^2+(y+e)^2) = 2a-sqrt(x^2+(y-e)^2)

x^2+(y+e)^2 = 4a^2 - 4a*sqrt(x^2+(y-e)^2) + x^2+(y-e)^2

y*e-a^2 = a*sqrt(x^2+(y-e)^2)

y^2*e^2-2*y*e*a^2+a^4 = a^2*x^2+a^2*y^2-2*y*e*a^2+a^2*e^2

a^2*(a^2-e^2) = a^2*x^2 + (a^2-e^2)*y^2

Use a new variable b^2 = a^2-e^2:

a^2*b^2 = a^2*x^2+b^2*y^2

1 = x^2/b^2 + y^2/a^2.

Still an ellipse.
Post by b***@gmail.com
The Dandelin Spheres proof is relatively simple. But it is
not the only proof to show that a conic section is an ellipse,
pitty you even dont understand this simple proof. AP brain
farto, not a single line of math, already for 30 years.
Post by Archimedes Plutonium
Post by Archimedes Plutonium
Post by FredJeffries
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
I'm guessing that the phenomenon referred to is the fact that the center of the cone section does not coincide with the center line of the cone.
For a related phenomenon, see Dandelin spheres
https://en.wikipedia.org/wiki/Dandelin_spheres
http://mathworld.wolfram.com/DandelinSpheres.html
Looking at those Dandelin Spheres in Wikipedia, not only do they have a fake proof, since they assume the section is a ellipse, when in fact it is a oval with just one axis of symmetry, and thus, no foci.
But, I think in that picture, another huge mistake is showing. I think they show a latitude line on big sphere and latitude line on little sphere as being ellipses also. When we all know that every cross section of a sphere that is not a tangent point, ends up being a circle.
Now, when was it proven true that every sphere cross section by a plane, is a circle (unless it is a tangent point).
Now in that picture, they do show the two spheres on the centerline axis of the cone.
Somewhere I read where to construct a OVAL you take two different size circles, and by a technique you append part of the arc of the smaller circle onto the larger circle, forming a oval. The only tricky part is to not have two vertices.
So in that construction of a oval from two different sized circles, is what the Dandelin spheres were groping for, groping for a proof, that Dandelin spheres is the 3rd dimension analog of construction of a oval in 2nd dimension by the blending of a small circle being incorporated upon a larger circle forming a oval.
Now, I find it almost miraculously annoying that a Dandelin fake proof exists to this day, when surely, someone would have constructed a hands on Cone and tried to stuff a ellipse inside that cone. It is very easy to roll up a sheet of paper into a cone and try to stuff a ellipse into it. So how in the world could this fake proof, have lasted all these centuries without anyone hands on doing it. And we see the power of fake math community proofs, the power to crush rational logical reasoning, once a fakery is published. Once a fake is published, it is as if almost everyone in math is void of logical thought on any aspect of the fakery. As if mathematicians worship publication, and drained of any logical intelligence.
Post by Archimedes Plutonium
Alright, I looked that up, the Dandelin spheres and apparently, the proof is fake because they start out
assuming the oval is a ellipse, and the aim of the proof is that the small sphere and larger sphere contact the plane at a focus.
So apparently, if Dandelin had started out his proof without the assumption the section was a ellipse, instead that the section was a oval, puff, his proof goes all up in a cloud of smoke and dust.
Now, Dandelin is probably not the first mathematician with a tacit-hidden-assumption that wrecks his fake proof. History of math is littered with these guys.
Fred, can you spot a Dandelin proof where he proves the section is a ellipse in the first beginning and then follows up.
Apparently this is a huge gap in math, that a fakery like Dandelin was so undetected.
So, who was the first to prove that all sections except a tangent point of a sphere are all circles? Seems so obvious that likely, no-one thought such a proof was necessary. How is it proved? Anyway?
AP
b***@gmail.com
2017-08-14 18:09:10 UTC
Raw Message
Variable names a, e, b from here:
https://de.wikipedia.org/wiki/Ellipse#Gleichung
Post by FredJeffries
http://mathworld.wolfram.com/DandelinSpheres.html
cant even do Peano induction, you even don't know
what integers are. Your geothermal posts recently,
are the echo of your totally void brain.
Let me think, you we get a quadratic, if the sum of
the distance two the two foci is constant?
P (x,y)
F1 F2
+---|---+
F1 P = sqrt(x^2+(y+e)^2)
F2 P = sqrt(x^2+(y-e)^2)
F1 P + F2 P = sqrt(x^2+(y+e)^2)+sqrt(x^2+(y-e)^2) = 2a
sqrt(x^2+(y+e)^2) = 2a-sqrt(x^2+(y-e)^2)
x^2+(y+e)^2 = 4a^2 - 4a*sqrt(x^2+(y-e)^2) + x^2+(y-e)^2
y*e-a^2 = a*sqrt(x^2+(y-e)^2)
y^2*e^2-2*y*e*a^2+a^4 = a^2*x^2+a^2*y^2-2*y*e*a^2+a^2*e^2
a^2*(a^2-e^2) = a^2*x^2 + (a^2-e^2)*y^2
a^2*b^2 = a^2*x^2+b^2*y^2
1 = x^2/b^2 + y^2/a^2.
Still an ellipse.
Post by b***@gmail.com
The Dandelin Spheres proof is relatively simple. But it is
not the only proof to show that a conic section is an ellipse,
pitty you even dont understand this simple proof. AP brain
farto, not a single line of math, already for 30 years.
Post by Archimedes Plutonium
Post by Archimedes Plutonium
Post by FredJeffries
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
I'm guessing that the phenomenon referred to is the fact that the center of the cone section does not coincide with the center line of the cone.
For a related phenomenon, see Dandelin spheres
https://en.wikipedia.org/wiki/Dandelin_spheres
http://mathworld.wolfram.com/DandelinSpheres.html
Looking at those Dandelin Spheres in Wikipedia, not only do they have a fake proof, since they assume the section is a ellipse, when in fact it is a oval with just one axis of symmetry, and thus, no foci.
But, I think in that picture, another huge mistake is showing. I think they show a latitude line on big sphere and latitude line on little sphere as being ellipses also. When we all know that every cross section of a sphere that is not a tangent point, ends up being a circle.
Now, when was it proven true that every sphere cross section by a plane, is a circle (unless it is a tangent point).
Now in that picture, they do show the two spheres on the centerline axis of the cone.
Somewhere I read where to construct a OVAL you take two different size circles, and by a technique you append part of the arc of the smaller circle onto the larger circle, forming a oval. The only tricky part is to not have two vertices.
So in that construction of a oval from two different sized circles, is what the Dandelin spheres were groping for, groping for a proof, that Dandelin spheres is the 3rd dimension analog of construction of a oval in 2nd dimension by the blending of a small circle being incorporated upon a larger circle forming a oval.
Now, I find it almost miraculously annoying that a Dandelin fake proof exists to this day, when surely, someone would have constructed a hands on Cone and tried to stuff a ellipse inside that cone. It is very easy to roll up a sheet of paper into a cone and try to stuff a ellipse into it. So how in the world could this fake proof, have lasted all these centuries without anyone hands on doing it. And we see the power of fake math community proofs, the power to crush rational logical reasoning, once a fakery is published. Once a fake is published, it is as if almost everyone in math is void of logical thought on any aspect of the fakery. As if mathematicians worship publication, and drained of any logical intelligence.
Post by Archimedes Plutonium
Alright, I looked that up, the Dandelin spheres and apparently, the proof is fake because they start out
assuming the oval is a ellipse, and the aim of the proof is that the small sphere and larger sphere contact the plane at a focus.
So apparently, if Dandelin had started out his proof without the assumption the section was a ellipse, instead that the section was a oval, puff, his proof goes all up in a cloud of smoke and dust.
Now, Dandelin is probably not the first mathematician with a tacit-hidden-assumption that wrecks his fake proof. History of math is littered with these guys.
Fred, can you spot a Dandelin proof where he proves the section is a ellipse in the first beginning and then follows up.
Apparently this is a huge gap in math, that a fakery like Dandelin was so undetected.
So, who was the first to prove that all sections except a tangent point of a sphere are all circles? Seems so obvious that likely, no-one thought such a proof was necessary. How is it proved? Anyway?
AP
b***@gmail.com
2017-08-14 18:21:59 UTC
Raw Message
Corr:

F1 P = sqrt(y^2+(x+e)^2)

F2 P = sqrt(y^2+(x-e)^2)

F1 P + F2 P = sqrt(y^2+(x+e)^2)+sqrt(y^2+(x-e)^2) = 2a

Now eliminate sqrt:

sqrt(y^2+(x+e)^2) = 2a-sqrt(y^2+(x-e)^2)

y^2+(x+e)^2 = 4a^2 - 4a*sqrt(y^2+(x-e)^2) + y^2+(x-e)^2

x*e-a^2 = a*sqrt(y^2+(x-e)^2)

x^2*e^2-2*x*e*a^2+a^4 = a^2*y^2+a^2*x^2-2*x*e*a^2+a^2*e^2

a^2*(a^2-e^2) = (a^2-e^2)*x^2 + a^2*y^2

Use a new variable b^2 = a^2-e^2:

a^2*b^2 = b^2*x^2+a^2*y^2

1 = x^2/a^2 + y^2/b^2.
Post by FredJeffries
http://mathworld.wolfram.com/DandelinSpheres.html
cant even do Peano induction, you even don't know
what integers are. Your geothermal posts recently,
are the echo of your totally void brain.
Let me think, you we get a quadratic, if the sum of
the distance two the two foci is constant?
P (x,y)
F1 F2
+---|---+
F1 P = sqrt(x^2+(y+e)^2)
F2 P = sqrt(x^2+(y-e)^2)
F1 P + F2 P = sqrt(x^2+(y+e)^2)+sqrt(x^2+(y-e)^2) = 2a
sqrt(x^2+(y+e)^2) = 2a-sqrt(x^2+(y-e)^2)
x^2+(y+e)^2 = 4a^2 - 4a*sqrt(x^2+(y-e)^2) + x^2+(y-e)^2
y*e-a^2 = a*sqrt(x^2+(y-e)^2)
y^2*e^2-2*y*e*a^2+a^4 = a^2*x^2+a^2*y^2-2*y*e*a^2+a^2*e^2
a^2*(a^2-e^2) = a^2*x^2 + (a^2-e^2)*y^2
a^2*b^2 = a^2*x^2+b^2*y^2
1 = x^2/b^2 + y^2/a^2.
Still an ellipse.
Post by b***@gmail.com
The Dandelin Spheres proof is relatively simple. But it is
not the only proof to show that a conic section is an ellipse,
pitty you even dont understand this simple proof. AP brain
farto, not a single line of math, already for 30 years.
Post by Archimedes Plutonium
Post by Archimedes Plutonium
Post by FredJeffries
Post by Archimedes Plutonium
Oval is conic section, never ellipse; ellipse is cylinder section// Failures of geometry conic sections-- Wiles, Hales, Conway, Hartshorne, Tao, Milnor
Easy experiment, easy, even the High School student can verify in a half hour, that the conic section is never an ellipse but an oval
Get some stiff wax paper like a magazine cover and roll it into a cylinder and with scotch tape tape it secure, then roll another into a cone shape and scotch tape. now get a scissors (or paper cutter unless dangerous) and proceed to cut the cone and cut the cylinder. You will find that the cylinder section is truly a ellipse, but the cone section is going to be a oval. A ellipse has two axes of symmetry while the oval has only one axis of symmetry. The reason no ellipse can come from a cone is the fact that the upper parts of the section have far less area than the lower section. In a cylinder, the upper and lower are equals.
I'm guessing that the phenomenon referred to is the fact that the center of the cone section does not coincide with the center line of the cone.
For a related phenomenon, see Dandelin spheres
https://en.wikipedia.org/wiki/Dandelin_spheres
http://mathworld.wolfram.com/DandelinSpheres.html
Looking at those Dandelin Spheres in Wikipedia, not only do they have a fake proof, since they assume the section is a ellipse, when in fact it is a oval with just one axis of symmetry, and thus, no foci.
But, I think in that picture, another huge mistake is showing. I think they show a latitude line on big sphere and latitude line on little sphere as being ellipses also. When we all know that every cross section of a sphere that is not a tangent point, ends up being a circle.
Now, when was it proven true that every sphere cross section by a plane, is a circle (unless it is a tangent point).
Now in that picture, they do show the two spheres on the centerline axis of the cone.
Somewhere I read where to construct a OVAL you take two different size circles, and by a technique you append part of the arc of the smaller circle onto the larger circle, forming a oval. The only tricky part is to not have two vertices.
So in that construction of a oval from two different sized circles, is what the Dandelin spheres were groping for, groping for a proof, that Dandelin spheres is the 3rd dimension analog of construction of a oval in 2nd dimension by the blending of a small circle being incorporated upon a larger circle forming a oval.
Now, I find it almost miraculously annoying that a Dandelin fake proof exists to this day, when surely, someone would have constructed a hands on Cone and tried to stuff a ellipse inside that cone. It is very easy to roll up a sheet of paper into a cone and try to stuff a ellipse into it. So how in the world could this fake proof, have lasted all these centuries without anyone hands on doing it. And we see the power of fake math community proofs, the power to crush rational logical reasoning, once a fakery is published. Once a fake is published, it is as if almost everyone in math is void of logical thought on any aspect of the fakery. As if mathematicians worship publication, and drained of any logical intelligence.
Post by Archimedes Plutonium
Alright, I looked that up, the Dandelin spheres and apparently, the proof is fake because they start out
assuming the oval is a ellipse, and the aim of the proof is that the small sphere and larger sphere contact the plane at a focus.
So apparently, if Dandelin had started out his proof without the assumption the section was a ellipse, instead that the section was a oval, puff, his proof goes all up in a cloud of smoke and dust.
Now, Dandelin is probably not the first mathematician with a tacit-hidden-assumption that wrecks his fake proof. History of math is littered with these guys.
Fred, can you spot a Dandelin proof where he proves the section is a ellipse in the first beginning and then follows up.
Apparently this is a huge gap in math, that a fakery like Dandelin was so undetected.
So, who was the first to prove that all sections except a tangent point of a sphere are all circles? Seems so obvious that likely, no-one thought such a proof was necessary. How is it proved? Anyway?
AP
Jan
2017-08-13 23:56:49 UTC