Talk:Cone

Cone (solid) vs Right circlar cone

Now there seems to be an issue with cone (geometry) and right circular cone. I'm inclined to redirect the latter here; most of the links in require the 'right circular' meaning of cone.

Charles Matthews 18:54, 5 Jul 2004 (UTC)

Where was "here"? The talk for cone (geometry) redirects here.

--Jerzy (t) 20:09, 2005 May 4 (UTC)

Cone (geometry) vs Cone (linear algebra) vs Cone (solid)

This section is obsolete now --Jorge Stolfi 03:51, 23 December 2005 (UTC) The redirect links between these articles don't really make sense. The more abstract definition of cone is the following: A subset ${\mathcal {C}}$ of a vector space is a cone if $x\in {\mathcal {C}}$ implies $\lambda x\in {\mathcal {C}}$ for any $\;\lambda >0$.

The article for Cone (solid) seem to be for a right cylindrical cone in 3-space. Since this is a particular instance of a cone, so it probably should be listed as an example under Cone (geometry).

Also, I think the definition for pointed cone is incorrect. Counterexample: R^3 is a cone that contains the origin. It is not pointed.

I don't know the definition of pointed for a general cone. For a polyhedral cone, I believe pointed means that ${\mathcal {C}}$ contains an extreme point. --Scott 17:45, 12 August 2005 (UTC)

Cone (geometry) vs Cone (solid)

WARNING - this section does not make sense any more because some well-meaning soul "fixed" the original links so they are all "cone (geometry)" now. Anyway the move happened and this section is moot. --Jorge Stolfi (talk) 09:38, 8 February 2010 (UTC)

Until 2005/dec/22, the article cone (geometry) was about a concept of linear algebra, and the common geometrical shape was described in cone (geometry). There were may pages pointing at the former when they should point to the latter. So I renamed cone (geometry) to cone (linear algebra) and changed all links to cone (geometry) to point to the appropriate article. Now cone (geometry) points back to the cone disamb page.

But now there still one inconsistency: articles on geometric solids are usually named xxx (geometry), not xxx (solid). Perhaps we should now delete cone (geometry), move cone (geometry) to cone (geometry), and fix again all the links... Jorge Stolfi 03:51, 23 December 2005 (UTC)

Survey

Add *Support or *Oppose followed by an optional one-sentence explanation, then sign your opinion with ~~~~

• Support --Swift 07:39, 30 June 2006 (UTC)
• Support --Usgnus 13:51, 28 July 2006 (UTC)
• Support. – Axman (☏) 09:44, 30 July 2006 (UTC)
• Support --Edgelord 06:13, 31 July 2006 (UTC)

Discussion

I see why my links to http://www.mathguide.com/lessons/Volume.html and http://www.mathguide.com/lessons/SurfaceArea.html were deleted on this page. However, by Wikipedia's own definition of spam, my links are clearly not spam, as there is no advertising or commercial products being sold.

I taught math for 13 years. There's substantial educational practice that students need access to auxiliary information beyond the classroom to understand a topic. Also, my site offers free dynamic quizzes to help students learn.

I do understand that there are rules for linking to one's own website. If someone finds this section of my site relevant, please link to it.

Why is the volume 1/3 of the volume of a cylinder?

i am just wondering how did anyone justify as it is? we cannot really assume anything. is there really any proof to it? in a triangular pyramid we can still prove it. how could we prove it on a cone?

This result goes back to Archimedes. If you believe it for a pyramid, just put the cone inside a cylinder, then slice the cylinder into a gazillion wedges like a panettone. (But anyway in WP one does not give proofs, just results.) Jorge Stolfi 09:54, 21 February 2006 (UTC)

See http://www.mathguide.com/lessons/Volume.html#cones as this bears out experimentally.

Im knew to wikipedia editing (long time reader) so please delete this if its out of line etc... 1/3 can be proven using calculus by integrating a function r(z)(radius wrt height) over the interval (0, h),this definite interval yields the formula for the volume of a cone. — Preceding unsigned comment added by 128.227.12.206 (talk • contribs) 19:20, 25 August 2006 (UTC)

No, I wouldn't say out of line at all. Such discussion, however, usually takes place on the Reference desk. The talk pages being for discussing article content. Glad you've deceided to test the edit button :-). --Swift 20:42, 25 August 2006 (UTC)

Page moved

This article has been renamed as the result of a move request. Vegaswikian 17:18, 4 August 2006 (UTC)

Merge proposal

I've put up a proposal to merge Right circular cone into this article. The RCC is a special case of a cone and I don't think it needs a page for itself. --Swift 07:32, 30 June 2006 (UTC)

I've added Conic solid, Projective cone and Conical surface to this proposal. --Swift 20:19, 17 August 2006 (UTC)

Right circular cone should definitely be merged, but I'm not sure about the others. The combined article would need some major restructurting, but that might be a good thing. Let's try it. —Keenan Pepper 01:59, 18 August 2006 (UTC)

Strong support, these pages are a mess. I might do this myself if I get time. -Ravedave ^{(help name my baby)} 17:39, 26 September 2006 (UTC)

I've done a sloppy merger and added a {{cleanup}} tag. I didn't merge the Projective cone since that article is quite a bit more mathmatical than I think a *_(geometry) article should be (I wasn't even sure if the sub-section on the parametrization of the conic solid was too much). If everyone is happy, I'll AfD the merged ones in the next few days. --Swift 05:51, 28 September 2006 (UTC)

Don't AFD them, they should be redirected per Wikipedia:Merging_and_moving_pages. I have redirected Conic solid. I removed the template from Projective cone and improved that article a bit. It looks like Conical surface still needs to be worked in and then redirected. -Ravedave ^{(help name my baby)} 01:24, 29 September 2006 (UTC)

I undid the merge of 'conical surface' into 'cone (geometry)'. The two concepts are as different as spheres and circles. Most concepts (axis, base, radius, directrix, frustum, volume, etc.) either are defined for only one case, or require a separate definition for each case. Merging the two articles saves very little text and creates a lot of confusion. Jorge Stolfi 15:22, 30 September 2007 (UTC)

Surface area of a cone

In my math textbook, it says that the surface area of a cone is found using this formula: A=(pi)rl, where l is the slant height, r is the radius of the circular base, and A is the surface area of the cone. I am not sure if this is just for right circular cones, but the area formulas in the article seem a little complicated... this is what the article says: $A=\pi r^{2}+\pi rs$, where $s={\sqrt {r^{2}+h^{2}}}$ is the slant height. and S(t,u) = (ucosθcost,ucosθsint,usinθ), if any of you guys know a simpler way of expressing this which most people will understand, please do... 4.253.120.50 19:23, 23 March 2007 (UTC)

The $A=\pi rl$ formula is the area of the side. $A=\pi r^{2}$ is added to give the total surface area, which includes the area of the base. Also, s here means the same thing as l in your textbook. Finally, I'm putting your math formulas in the math style, and I hope it's okay with you. Generalcp702 18:31, 31 March 2007 (UTC)

types of cone

"There are four types of cones: circular, elliptical, right, and oblique, all of which are conic solids."

These seem not to be mutually exclusive types. e.g. a "right circular" is a valid cone type. Is there some way this could be better explained.

"All pyramids are also cones"

Which type are they? or are they a 5th type? In my head saying that a cone is just a n = ∞ cone makes sense, but I am aware that standard terminolgy is not always logical. The pyramid page just says

"[a pyramid]is a conic solid with polygonal base"

So is conic solid the parent class to which cone and pyramid belong? --130.88.20.10 09:56, 8 May 2007 (UTC)

"In general, a cone is a pyramid with a circular cross section." http://mathworld.wolfram.com/Cone.html --130.88.20.10 10:08, 8 May 2007 (UTC)

We should state the generalization but also include a pyramid as a conic Nicholas SL Smith 17:35, 7 June 2007 (UTC)

All cones are pyramids. Not all pyramids are cones. Specifically, cones are pyramids with circular bases, i.e. a special case. This is sourced here [1]. If necessary, I have a source that indicates this source is not just reliable but published by a highly respected source in the mathematical community.

• Last month I found an error in that "highly respected source", so there. 8-)
  Anyway, there is hardly ever *the* definition of a math concept; there are usually many definitions. Even such a basic thing like natural number has two definitions, both still in use.
  Normally each author (including mathworld's) picks one definition and pretends the others do not exist. But Wikipedia cannot do that; it must record all definitions and not try to make value judgements.
  The use of "cone" for shapes with non-circular section is actually common. Just google "non circular cone" or "elliptical cone" to get an idea. In particular I liked this example which shows that non-circular cones are not only popular but even legal! 8-)
  All the best, --Jorge Stolfi (talk) 09:56, 8 February 2010 (UTC)
  • I have no objection to calling a cone a fruitcake, so long as it comes from a reliable source. Since this is a subject in the academic field of geometry, all assertions should be come from reliable, academic sources. I've provided an academic source that defines a cone. If you wish to contradict or expand this, please use another reliable source. A patent registration firm is not equal to an academic source when it comes to defining mathematical terms. Ultimately, this article needs much better sourcing, as it had none at all until today. Rklawton (talk) 13:48, 8 February 2010 (UTC)

Speaking of which "google it and you will see" is not a substitute for reliable sources. Rklawton (talk) 17:27, 8 February 2010 (UTC)

• Hi Rklawton, first please note that this article is about a concept of "(geometry)", not "(academic geometry)". Geometry is widely used outside academia — by engineers, builders, technicians, and even by lawyers it seems. Also, Google is a good way to *find* sources; in this case we are tryng to establish "what do people understand by 'cone' as a geometric shape", so the search should not be confined to academic sources. That, by the way, is what dictionary makers (the OED specifically) do when they want to know what words mean.

As for that, Here are some sources that apparently assume "elliptic cone" is a known concept:

• A formula handbook (2001)
• A website with math formulas
• An applied geometry journal paper (2009)
• "elliptic+cone"+formulas&hl=en&gl=br&sig=AHIEtbSjw1-KHZXoHkbeSSVc-loxGG9oUw A math course lecture by a Colorado State University teacher
• A paper by W.R. Hamilton of Hamiltonian and qaternions fame (ca. 1845)

And finally (I wouldn't have guessed, Google found it for me)

• "Elliptic Cone" article on Wolfram's MathWorld!

So, well, I still defend my sentence. All the best, --Jorge Stolfi (talk) 23:49, 8 February 2010 (UTC)

I'm not against elliptical cones. I'm in favor of using sources throughout the article so that people using it can be reassured the article wasn't authored by an eight-grader. I also prefer viewing a cone as special case pyramid and not the other way around, but would be pleased to present a reliably sourced, differing view. Rklawton (talk) 03:09, 9 February 2010 (UTC)

Other Mathematical Meanings

I'm no math wiz, but it seems to me that the definitions given using lines and half-lines passing through a common point are lacking some fundemental constraint. It is possible to have an infinite variety of lines passing through a single point that have nothing to do with the cone - for example, the cone's axis will also pass through this point and yet is not part of the set that defines the cone.

Pleah (talk) 17:37, 9 February 2010 (UTC)