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From: moroney@world.std.spaamtrap.com (Michael Moroney)
Newsgroups: sci.math
Subject: Re: called Double Gyres Re: New Chemistry Table-- two superimposed cones
Date: Sun, 18 Mar 2018 05:01:31 +0000 (UTC)
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Archimedes Plutonium <plutonium.archimedes@gmail.com> writes:

[nothing]

>Michael Moroney        wrote
>4:46 PM (2 hours ago)

>>Oh, so you finally have a [proof the ellipse is not a conic section?]

Archie posted that snippet yet again, even though it's a week old now.
At least 10 times in (at least) two groups. Guess it must really bug
him that he still has no proof the ellipse is not a conic section.

It continues to amuse me how kooks do something totally illogical, and
then do it over and over again.  Like how Archie quotes a contextless
snippet of what I wrote, to the wrong topic, and frequently in the wrong
group, and says nothing about it himself. And he keeps doing that.

Why?  Dementia? Autism? Senility? OCD? Schizophrenia?

Or maybe he just wants to see this proof that the ellipse can be a conic
section again.


Below you will find a simple *proof* that shows that certain conic 
sections are ellipses.

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