I have worked out the general case for the intersection of any plane with any cone.
This has already been discovered, but it is not proprietary information. It is the foundation for parabolas, ellipses, hyperbolas, hyperbolics, or anything having to do with sections of a cone.
Don't be perplexed by the long equations. It is only algebra.
On Nov 6, 5:12 pm, "Jon" <jon8...@peoplepc.com> wrote:
> I have worked out the general case for the intersection of any plane with > any cone.
> This has already been discovered, but it is not proprietary information. It > is the foundation for parabolas, ellipses, hyperbolas, hyperbolics, or > anything having to do with sections of a cone.
> Don't be perplexed by the long equations. It is only algebra.
Jon wrote: > I have worked out the general case for the intersection of any plane with > any cone.
> This has already been discovered, but it is not proprietary information. It > is the foundation for parabolas, ellipses, hyperbolas, hyperbolics, or > anything having to do with sections of a cone.
> Don't be perplexed by the long equations. It is only algebra.
>I have worked out the general case for the intersection of any plane with >any cone.
> This has already been discovered, but it is not proprietary information. > It is the foundation for parabolas, ellipses, hyperbolas, hyperbolics, or > anything having to do with sections of a cone.
> Don't be perplexed by the long equations. It is only algebra.
On Nov 6, 7:12 pm, "Jon" <jon8...@peoplepc.com> wrote:
> I have worked out the general case for the intersection of any plane with > any cone.
> This has already been discovered, but it is not proprietary information. It > is the foundation for parabolas, ellipses, hyperbolas, hyperbolics, or > anything having to do with sections of a cone.
> Don't be perplexed by the long equations. It is only algebra.
> On Nov 6, 7:12 pm, "Jon" <jon8...@peoplepc.com> wrote: > > I have worked out the general case for the intersection of any plane with > > any cone.
> > This has already been discovered, but it is not proprietary information. It > > is the foundation for parabolas, ellipses, hyperbolas, hyperbolics, or > > anything having to do with sections of a cone.
> > Don't be perplexed by the long equations. It is only algebra.
mike wrote: > In article <5df09ccc-23b4-4da4-9d3e-b0f129823513 > @p35g2000yqh.googlegroups.com>, thedraperfam...@gmail.com says... >> On Nov 6, 7:12 pm, "Jon" <jon8...@peoplepc.com> wrote: >>> I have worked out the general case for the intersection of any plane with >>> any cone.
>>> This has already been discovered, but it is not proprietary information. It >>> is the foundation for parabolas, ellipses, hyperbolas, hyperbolics, or >>> anything having to do with sections of a cone.
>>> Don't be perplexed by the long equations. It is only algebra.
>>> Jon Giffen >> Congratulations for repeating work already done.
> Maybe he should look at the much more interesting problem of the > intersection of a parabola of rotation with a plane.
> Mike
A nice curiosity:
Consider intersections of a paraboloid of revolution with planes that are not parallel to its axis AoR of revolution.
The parallel projection of any such intersection along AoR onto the tangent plane at the vertex of the paraboloid is a circle. In this way each circle in that plane is the projection of an intersection of the paraboloid with a plane.
The proof by analytic geometry is a piece of cake; the proof by Euclidean solid geometry is not too easy and IMO much more delightful.
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