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.