Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test

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From	moroney@world.std.spaamtrap.com (Michael Moroney)
Newsgroups	sci.math, sci.physics
Subject	Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test
Date	Sun, 7 Oct 2018 03:31:29 +0000 (UTC)
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Math Failure Archimedes Plutonium <plutonium.archimedes@gmail.com> fails:

>Proofs ellipse is never a conic, always a cylinder section by
>Archimedes Plutonium
>--------------------
>AP's proof the ellipse is never a Conic Section, always a Cylinder 
>section, and how the proof works


You need to see Franz's proof yet again?  You should save his proof on
your computer so you can look at it at any time without asking me to post
it for you again each time!


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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Sheldon Axler Racist Mathematicians, AMS, David Weisbart, Fred Wilhelm, Bun Wong, Yulong Xing, Feng Xu, Qi Zhang, John Baez // Ellipse is never a conic (see proof below) Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-10-06 13:52 -0700
  Re: Archimedes "Village Idiot" Plutonium flunked the Math Test of a lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-10-07 03:31 +0000

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