Intersection of Cone with Plane

Jon

unread,

Nov 6, 2009, 8:12:21 PM11/6/09

to

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

unread,

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

Skybuck Flying

unread,

Nov 12, 2009, 10:31:18 AM11/12/09

to

"Jon" <jon...@peoplepc.com> wrote in message
news:EdKdndQRmvceVGnX...@earthlink.com...

Thanks might come in handy some day...

(Or maybe just to do some "insane ammount of calculations test"... maybe to
determine speed or accuracy of equipment ;))

Anyway... why go through all the trouble of making it impossible to "save
the page" to file ?

(IE8 complains can't save page to file).

For me this is easily solved by copieing and pasting the text inside
frontpage :)

Just requires a little bit more of time ;)

(Maybe it's just a bug in your page ? ;))

Anyway it seems you are on windows using outlook express to post this
message...

The webpage's source code header is:

<HEAD>
<META content="text/html; charset=iso-8859-1"
http-equiv="Content-Type">
<META content="0" http-equiv="Expires">
<META content="1.0" name="TRELLIX_BUILDER_VER"><META
name="TRELLIX_OPEN_SITE_COMMAND"
content="http://twe.peoplepc.com:8080/servlet/SiteBuilderServlet?fUrl=/trellix/sitebuilder/f_error.html&sUrl=/trellix/sitebuilder/f_edit_page.html&Command=OpenSite&FileName=2164488876280563899/site.xml"></META><base
href="http://mypeoplepc.com/members/jon8338/math/index.html"><script
language="Javascript">
document.isTrellix = 1;
</script>
<title>Intersection of a Plane with a Cone, General</title>
</HEAD>

Apperently the webpage was made with a-to-me-unknown-tool called: "TRELLIX
BUILDER".

Maybe it adds some nasty bugs... or maybe it's just a buggy product =D

Hmm further investigation reveals... it's a website builder/webhosting
thingy:

http://www.trellix.com/

Anyway it seems like that.. good luck with it ! ;) :)

(alt.sci.math removed, not available?)
(alt.math.recreationa, to bring it down to 5)

Bye,
Skybuck.

PD

unread,

Nov 12, 2009, 10:52:46 AM11/12/09

to

Congratulations for repeating work already done.

mike

unread,

Nov 15, 2009, 5:59:53 PM11/15/09

to

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

unread,

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