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Re: Archimedes "Total Failure" Plutonium flunked the lifetime-generation test

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Math Failure Archimedes Plutonium <plutonium.archimedes@gmail.com> fails:

> Noam Elkies, Dennis Gaitsgory,  of Harvard asked by Volney/Moroney 
> report-- WHY teach ellipse is a conic, when it never was, but a cylinder 
> section (see proof below)

You need to show them the proof as well? Here it is!

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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Noam Elkies, Dennis Gaitsgory,  of Harvard asked by Volney/Moroney report-- WHY teach ellipse is a conic, when it never was, but a cylinder section (see proof below) Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-08-16 21:42 -0700
  Re: Archimedes "Total Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-08-17 15:10 +0000

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