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Intersection of Cone with Plane

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Jon

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Nov 6, 2009, 8:12:21 PM11/6/09
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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.

http://mypeoplepc.com/members/jon8338/math/id51.html

Jon Giffen


JEMebius

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Nov 7, 2009, 2:50:53 PM11/7/09
to Jon

Suggestion for your next post:

INTERSECTION OF A PLANE WITH A CONE, SPECIAL

You will treat there the pair of intersecting straight lines - yes: that is a conic
section too! This observation may involve proprietary information.

Looking forward: Johan E. Mebius

PD

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Nov 12, 2009, 10:52:46 AM11/12/09
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Congratulations for repeating work already done.

mike

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Nov 15, 2009, 5:59:53 PM11/15/09
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In article <5df09ccc-23b4-4da4-9d3e-b0f129823513
@p35g2000yqh.googlegroups.com>, thedrap...@gmail.com says...
Maybe he should look at the much more interesting problem of the
intersection of a parabola of rotation with a plane.

Mike

JEMebius

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Nov 15, 2009, 6:52:03 PM11/15/09
to 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.

Johan E. Mebius

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