Talk:Hypercone

Spherical cone
"The hypercone and spherical cone are the same object". Where is a reference for this statement? According to http://mathworld.wolfram.com/SphericalCone.html, a spherical cone is something different, namely, the surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere.

Need cleanup
This article needs some cleanup work. I think the geometrical and temporal interpretations should be kept separate (e.g., in the opening paragraph where time is used as an example without adequate explanation of the difference). A fourth spatial dimension (in Euclidean 4-space) should not be conflated with time in Minskowskian space-time (General Relativity). For the latter, there is already an article dedicated to it: light cone. In the original spherical cone article, I purposely kept the two interpretations under separate sections. We should rearrange the material to fit under the appropriate sections.&mdash;Tetracube 04:58, 29 May 2007 (UTC)

--There's also a personal comment in the article about how the hypercone is beautiful. —Preceding unsigned comment added by 128.119.30.47 (talk) 00:24, 16 February 2008 (UTC)

Hypercone re-entry
I believe that the word "hypercone" can also refer to theoretical re-entry structures for space vehicles. —Preceding unsigned comment added by 60.234.52.65 (talk) 07:44, 9 November 2007 (UTC)

others

 * It is a quadric surface, and is one of the possible 3-manifolds which are 4-dimensional equivalents of the conical surface in 3 dimensions. ...

It would be good to mention others. I guess $$w^2 + x^2 = y^2 + z^2$$ is one. —Tamfang (talk) 03:36, 2 October 2014 (UTC)

On that note, a reader who has found an article titled "Hypercone" almost certainly wants to know about every higher-dimensional analogue of the more familiar 3-dimensional cone. I'd add more information about the other forms myself, but that's how *I* got here. I can’t even research the topic, since all I know is the prefix "hyper" and a math equation (you can't Google those). Atimholt (talk) 05:39, 3 October 2019 (UTC)

Remove (or spherical cone) from opening statement
I propose the removal of "(or spherical cone)" from the opening statement. It has been pointed out above that Wolfram MathWorld defines a spherical cone differently from the way we define hypercone. I propose to make this correction and quote the MathWorld definition of spherical cone. RHB100 (talk) 21:28, 21 January 2019 (UTC)

other "hypersonic sections"?
I came looking to see if the "3D -oids" of the various 2D conic sections - circle, ellipse, parabola, hyperbola, such as sphere, paraboloid, ellipsoid, etc. were also 3D sections of the hypercone. From the article, I see that spheres at least meet that criterion, but I don't see the others. It may be that the best approach might be to add another article on this topic with one sentence referring to that article. I recognize this is a fair amount of work for a very small audience. Most of the work would be in presenting the applicable mathematics, and finding the applications that might exist. I suspect there are some applications in physics that are not commonly recognized as such. I'd call the article "Hyperconic Sections". It would take me months or years to learn and present the math, if I'm even capable, which is an open question. Gar37bic (talk) 16:40, 7 April 2023 (UTC)