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Topic: How we get a Ellipse from a Conic, and how we get a Oval from
Cylinder Sections-- knifes that are V and asymmetrical V shaped

Replies: 27   Last Post: Oct 8, 2017 12:41 AM

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 plutonium.archimedes@gmail.com Posts: 17,520 Registered: 3/31/08
The butterfly cut, a V cut into conics Re: How we get a Ellipse from
a Conic

Posted: Oct 5, 2017 10:28 PM

On Thursday, October 5, 2017 at 8:59:20 PM UTC-5, Archimedes Plutonium wrote:
> On Thursday, October 5, 2017 at 4:55:17 PM UTC-5, qbwr...@gmail.com wrote:

>
> Well thanks for the thoughts, but I already proved several times over that a cone is always a Oval section unless of course your cut is a V shaped cut not a regular planar cut of /
>
> But if you can manufacture a nice parallelepiped out of pine wood of the size of a football for it is parallelepiped that have been my bugaboo throughout my life, would be of help. One with nice noticeable slanted angles on its sides.

Now, this V cut, let me call it the butterfly cut rather than the planar cut. For the butterfly cut seems to restore symmetry, and a butterfly is symmetrical on a axis.

But now, let us look at other figures rather than a cone and look at a tetrahedron and a square pyramid for both look like a cone adaption.

Now what happens with planar cuts in tetrahedron for they are triangles. Only a parallel to base cut is another equilateral triangle. But, if we make a V cut, a butterfly cut into the tetrahedron, then, unfold that cut on the dihedral angle, I sort of think we get a larger equilateral triangle if the cut is on the axis of the tetrahedron.

Now looking at the pyramid with a butterfly cut, and we get a rectangle.

So, this suggests that the butterfly cut into the cone can deliver also a circle as well as a ellipse.

AP