Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 plutonium.archimedes@gmail.com Posts: 18,572 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

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

Date Subject Author
10/2/17 plutonium.archimedes@gmail.com
10/2/17 Me
10/6/17 plutonium.archimedes@gmail.com
10/6/17 Me
10/7/17 plutonium.archimedes@gmail.com
10/7/17 Jan Bielawski