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Topic: Synthetic Geometry proof and Analytical Geometry proof that Conic is
a Oval, never an ellipse// yes Apollonius was wrong

Replies: 5   Last Post: Oct 7, 2017 1:48 AM

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plutonium.archimedes@gmail.com

Posts: 17,500
Registered: 3/31/08
mounting evidence Re: ..proof that Conic is a Oval, never an
ellipse// yes Apollonius was wrong

Posted: Oct 6, 2017 6:02 AM
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Now we have more and more supporting evidence coming in that Conic section is an Oval, never an ellipse.

1) in order to get a ellipse out of a cone, what we have to do is use a knife that makes a butterfly cut
such as this

\ /
\ /

And once cut we flatten out the butterfly cut to be an ellipse

And in the same manner, a Cylinder section is always a Ellipse, and to get a oval from cylinder we use this Butterfly cut, an asymmetrical butterfly cut.

2) Another new supporting evidence is the square pyramid replacing the cone. Now a square pyramid section if the conic was a ellipse, we should expect the pyramid section to be a rectangle, for the rectangle is the analog of the ellipse. Instead, what we get in a cut is a trapezoid, the analog of a oval.

So, more and more evidence mounts, that the conic section is oval, never ellipse.

AP




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