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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 | 2018-03-10 22:46 +0000 |
| Organization | The World : www.TheWorld.com : Since 1989 |
| Message-ID | <p81n8j$9i$4@pcls7.std.com> (permalink) |
| References | (1 earlier) <b97354c2-e1de-43aa-afa5-5b7476925c20@googlegroups.com> <2809ad26-fe8a-4c8f-abb4-9f43751c9846@googlegroups.com> <0e356fd5-8107-409d-9488-3db6e7fd193b@googlegroups.com> <33d57e8c-7bc7-49f8-976e-d6b60431cc28@googlegroups.com> <f870b12e-fe18-49fe-8e2b-f3d976108a0d@googlegroups.com> |
Archimedes Plutonium <plutonium.archimedes@gmail.com> writes:
>And it is nice and fitting, that the mathematician who discovered the Oval
>was a Conic section, never the ellipse, is back again fixing even more Conic
>Section theory,
Oh, so you finally have a proof the ellipse is not a conic section?
Could you please point out the flaw in the following proof that it is an
ellipse?
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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New Chemistry Table-- two superimposed cones Re: AP's Periodic Table of Atoms in light of the fact Real Proton= 840MeV, Real Electron= 105MeV, the .5MeV= monopole Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-03-09 13:50 -0800
New Chemistry Table-- two superimposed cones Re: AP's Periodic Table of Atoms in light of the fact Real Proton= 840MeV, Real Electron= 105MeV, the .5MeV= monopole Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-03-09 14:03 -0800
New Chemistry Table-- two superimposed cones Re: AP's Periodic Table of Atoms in light of the fact Real Proton= 840MeV, Real Electron= 105MeV, the .5MeV= monopole Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-03-09 14:18 -0800
New Chemistry Table-- two superimposed cones Re: AP's Periodic Table of Atoms in light of the fact Real Proton= 840MeV, Real Electron= 105MeV, the .5MeV= monopole Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-03-09 17:26 -0800
called Double Gyres Re: New Chemistry Table-- two superimposed cones Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-03-09 17:40 -0800
Re: called Double Gyres Re: New Chemistry Table-- two superimposed cones Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-03-09 17:55 -0800
Re: called Double Gyres Re: New Chemistry Table-- two superimposed cones moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-03-10 22:46 +0000
Re: called Double Gyres Re: New Chemistry Table-- two superimposed cones moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-03-18 05:01 +0000
Re: called Double Gyres Re: New Chemistry Table-- two superimposed cones Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-03-10 17:34 -0800
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