Talk:Sphere

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WikiProject Mathematics
This article is within the scope of WikiProject Mathematics.
Mathematics grading: B Class Top Importance  Field: Geometry and topology

seems much too brief, there plenty more which could be said about the sphere.

Contents

[edit] stuff that was unheadered

I'm thinking there is some bug with the new wiki software, I saw the text went away that Zundark is talking about, but couldn't figure out how to bring it back. I'm using internet explorer 5, and had no problems with the old software. Either that, or my dog ate it. <grin> -- BenBaker

There was such a bug on the first day. Should be long gone. For old version, you'll have to wait for the promised http://old.wikipedia.com --Magnus Manske

Does anyone have any objections to the following text being added...?

A sphere can also be defined as a sphericon that is based on a polygon approaching a circle.

Proberts2003 19:31, 10 Apr 2004 (UTC)


I do Tosha 00:42, 11 Apr 2004 (UTC)

Which are...? Proberts2003 01:45, 12 Apr 2004 (UTC)

Ok, I think it is not directly relevent, one can mention sphere in sphericon, but not other way arround. (Otherwise you should include in this article ref to all geometric topics) Yet an other thing: yes it can be defined this way but it would be most wierd way to define sphere. Tosha 05:15, 12 Apr 2004 (UTC)

The article currently says "water drops (in the absence of gravity) are spheres". I changed this to simply "small water drops are spheres" because photographs of rain show small spheres (see http://www.ems.psu.edu/~fraser/Bad/BadRain.html ). -- DavidCary 23:33, 27 Jun 2004 (UTC)

I believe the claim that the topological convention is "the most common" is NPOV, as I believe it's a true statement. (Of course, people who work in the fields using the other definition will feel differently...I don't directly work in either field, so I'm going by my own experience. The topological definition is the only definition I've ever seen or heard; until today I wasn't aware there was another convention.) It would be good if the actual fields of research that use this convention were spelled out. (I honestly have no idea what these are.) I strongly object to the use of the term "geometrical definition" or "geometrical convention", because "geometry" is too broad a word; also, it conflicts with the convention used by differential geometers, who most certainly consider themselves to study "geometry". Revolver 00:08, 12 Jul 2004 (UTC)

Unless someone can provide at least one example of a peer-reviewed mathematical paper that uses the term "n-sphere" to mean (n-1)-sphere, then I'm going to remove all this stuff about different conventions. There is only one convention, as far as I'm aware. --Zundark 09:35, 23 Dec 2004 (UTC)

Can we split this up into two sections — Geometry and Topology — as I did for Ball (mathematics)? In the Geometry section have the metric-space definition (locus of points a radius from the center; boundary of a ball), the Eulcidean examples, the current Equations subsection, and all that jazz; and under Topology have

A sphere is any space homeomorphic to the Euclidean sphere described above under Geometry.

, definition of n-sphere, the fact that the boundary of a ball is a sphere one dimension down (for n>0), and definitions of homology sphere. —msh210 21:17, 27 Oct 2004 (UTC)

the prove that a n-sphere is compact is not complete?

  • needs why complement has only innerpoints
  • why is it bounded?? (maybe due it's definition Sn = {xεRn + 1 | d(x,0) = 1})

Shouldn't there be links to proofs of claims made on math pages? For instance, the claim that the sphere is the smallest shape enclosing a particular volume may seem obvious, but it would be good to see a proof.

Also, I added the word "locally" to the claim that "surface tension minimizes surface area", since there are actually examples of surface tension creating locally minimum, but not globally minimum, surface area. Flarity 06:33, 22 July 2006 (UTC)

[edit] Split article?

Currently the material on n-spheres is split between this article and hypersphere. The situation is somewhat unsatisfactory. I propose separating the material along logical lines

  • the sphere article should focus the ordinary 2-sphere in Euclidean 3-space. This is probably what people expect when they type sphere into the search box.
  • the n-sphere article should discuss the general case, with sections on both geometry and topology. We can have a redirect from hypersphere to there (I prefer it this way since the term hypersphere is not in common usage in mathematics).

I'm happy to do this split if no one objects. Comments? -- Fropuff 02:29, 2005 Apr 16 (UTC)

Iff sphere has a link to n-sphere at its top (not just {{otheruses}}), I agree. That is, it should say something like For higher-dimensional spheres in mathematics, see n-sphere; for other spheres see Sphere (disambiguation). —msh210 13:50, 17 Apr 2005 (UTC)

[edit] Perfect symmetry

Seems to me that the sphere is not perfectly symmetrical. For example, punctured 3-space is also self-similar under radial contractions, and so is more symmetrical. Ideas of perfection led to a lot of wrong-headed ideas about e.g. planetary motion. Maybe they are worth mentioning, but in my opinion putting "perfection" up front doesn't help. --JahJah 02:50, 22 August 2005 (UTC)

[edit] Convoluted

Definition number one from http://www.tfd.com/sphere It's succinct, accurate, and readable. It accomplishes in one sentence what Wikipedia's entire article fails. To whom are you trying to explain a sphere? Who is your audience? If your son or daughter asked you what a sphere is, how would you describe it?

Also, ease up on the passive voice.192.165.166.4

[edit] finding the surface area of part of a sphere

I think it would be very useful to have either a derivation for, or simply the integral one needs to use to find the surface area of part of a sphere. Also perhaps it would also be useful to do the same thing for the volume of part of a sphere. 68.6.112.70 18:22, 10 May 2006 (UTC)

[edit] colouring

Yesterday I assumed that a sphere could obviously be coloured with 4 colours. Then I realized I didn't actually know this, and it wasn't obvious. Can anyone confirm it by adding a bit to the article?

Maybe you mean the Four color theorem? --Abdull 09:29, 30 May 2006 (UTC)

[edit] Removal of "Jade Sphere" Graphic

It seems to me that this graphic is irrelevent and adds nothing to the article. It seems more suited to an article concerning digital graphics/photoshop/layers/aqua. Therefore, I am removing it from the sphere article.

[edit] Differential equation

A sphere of any radius centered at the origin is described by the following differential equation:

x \, dx + y \, dy + z \, dz = 0.

What is a sphere of any radius? --Abdull 09:46, 30 May 2006 (UTC)

What is meant is all spheres, regardless of radius satisfy the equation if they are centered at the origin. So
x2 + y2 + z2 = R2
satisfies the above equation, for all R. ❝Sverdrup❞ 10:37, 30 May 2006 (UTC)

[edit] other usage

does S^n only mean a N sphere or does it have any other meaning? thanks --I got scammed 09:12, 6 September 2006 (UTC)


[edit] spherical triangle picture

i couldn't figure out how to take the picture out temporarily but, the spherical triangle picture is incorrect. see the discussion of the image.

I've moved it here. --agr 13:49, 29 September 2006 (UTC)
A spherical triangle (red).
A spherical triangle (red).

[edit] 2-sphere as 3-dim object

I think it's unnecessary to say that the 2-sphere is a 3-dimensional object. Given the logic (ie. that it can be embedded in R3), a loop, a point, etc. are 3-dimensional objects. But they are also 4, 5, and 6(etc)-dimensional objects as they can be embedded there as well.

[edit] Removed vandalism

just removed some vandalism from the page (says "removed filth" in the edit log). I am not sure as to whether anything was deleted to put it in and I am not sure how to check. It would be helpful for someone to either do this for me or point me in the direction of instructions, so I know what to do in future. I just had the immediate response of removing the vandalism at the time. Aphswarrior 23:15, 10 January 2007 (UTC)

You got it right - you can check by looking at the page history. For help on reverting vandalism (or anything else that needs reverting), see Help:Reverting. --Zundark 09:27, 11 January 2007 (UTC)

[edit] Number of points to define a sphere?

What is the minimum number of point needed to define the surface of a unique sphere? Such as 2 points define a line, 3 points define a plane and a unique circle, my guess is that you need at least a fourth point not in the plane of the other three, but are more required?66.202.7.218 14:28, 30 March 2007 (UTC)

Yep. One could think of a one parameter family of spheres which each contain the circle, a fourth point would define one memer of the family. Its a strangly high number consider as you only need 4 numbers center and radius to uniquely define a sphere. --Salix alba (talk) 22:03, 30 March 2007 (UTC)
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