Talk:Centroid

Mathematics Start‑class Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

Centroid = center of mass?

From WordNet (r) 2.0 (August 2003) [wn]:
  centroid
      n : the center of mass of an object of uniform density

WordNet says, the center of mass is called centroid when the object has uniform density distribution. Is it ture?

Not exactly. When the object has an uniform density distribution, the centre of mass coincides with the object's geometric centre. Yet, the names of the concepts remain the same, which means that a centroid is still a centroid and a centre of mass is still a centre of mass --Maciel 11:35, 25 Sep 2004 (UTC)

I agree with both of you. On a very slightly different note I've never seen a text that equates the physical center of mass with its "centroid", unlike the current version of the introduction: "In physics, the words centroid and barycenter may mean either the center of mass or the center of gravity of an object, depending on context." Weisstein's physicsworld page partially supports this usage, but he cites no sources, and I'm more inclined to think he's just wrong. I'll change the intro to be more conservative. Melchoir 04:06, 19 April 2006 (UTC)[reply]

I have restored the more "liberal" physics definition, that admits "centroid"="barycenter" in some cases. While I have no textbook citation to support this alternative, it does seem to occur in many less formal documents found over the net [1] [2] [3]. Methinks that Wikipedia should inform readers of all common names and usages, not just the "officially correct" ones. (On the other hand, if all physics textbooks *do* define "centroid"

\neq

"barycenter", then the wording of the head parag should make it clear that "centroid"="barycenter" is only colloquial.) All the best, --Jorge Stolfi (talk) 15:43, 24 October 2008 (UTC)[reply]

Centroid = intersection of bisecting planes (NOT)

In geometry, the centroid or barycenter of an object

X

in

n

-dimensional space is the intersection of all hyperplanes that divide

X

into two halves of equal measure.

This is wrong. The line parallel to one side of a triangle that divides it in half is sqrt(1/2) from the opposite corner, not 2/3, which is where the centroid is. -phma 21:06, 26 Jul 2004 (UTC)

Oops! Thanks... Jorge Stolfi 23:26, 15 Sep 2004 (UTC)

==Of a finite set of points Casually flipping through, and I noticed that for this equation, there is no mention of what variable K is. Sum of masses? Size of left foot? Poor form, define your variables, people...

Centroid of a circle

Does anyone know what the formula for the centroid of a circle is? I tried to derive it, but it didn't work. I can't find it online, either. Can anyone tell me what it is?

--Gscshoyru 17:42, 17 September 2005 (UTC)[reply]

Isn't it just the center?.... and if it isn't just use the formula in the article, with the circle centered at the origin. the y value is given by int(1/2*f(x)^2 from a to b) divided by the area. Xunflash 04:28, 30 October 2005 (UTC)[reply]

Yes, at the center, compare Point_groups_in_three_dimensions#Center_of_symmetry.--Patrick 11:07, 30 October 2005 (UTC)[reply]

Programming the centroid computation

Just a minor edit how to calculate centroid of a triangle using programming. I am sure someone will find it useful. SnegoviK 12:22, 24 February 2006 (UTC)[reply]

Good try, but unfortunately that whole section seems quite pointless. The previous section already says that the centroid of a triangle is obtained by averaging the coordinates of the corners; that is all one needs to know in order to solve your programming exercise. Why would the reader want to know other (incorrect!) ways of doing it? Besides, this is a geometry article; computer language details do not belong here.
But please do not get discouraged, surely you will find many other ways to help Wikipedia.
All the best, Jorge Stolfi 17:06, 24 February 2006 (UTC)[reply]

I just realised that you are absolutely right! I am sorry I didn't manage to come with a resourceful article, I will try harder next time. Your comment is very helpful to me, thanks. ;) SnegoviK 19:33, 24 February 2006 (UTC)[reply]

Revision as of 21:29, 15 August 2006 (edit) 129.110.8.39 (Talk)

The formula for finding a polygon's centroid is not precise. It may give a negative where a positive is called for. For a better formula, see: http://tog.acm.org/resources/GraphicsGems/gemsiv/centroid.c

Centroids in GIS systems

In Geographic information systems, the term centroid may refer to other points than the geometric centre, primarily because of the desire that the centroid is inside the object. See for example [4]. Apus 08:24, 11 October 2006 (UTC)[reply]

Suspected Excessive Promotion of Herve Abdi

An anon at 129.110.8.39 (pc0839.utdallas.edu) added the reference:

==References==

*\{\{cite paper | author=Abdi, H | title = [5] ((2007). Centroid, center of gravity, center of mass, barycenter. In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage.| year = 2007 |\}\}

Someone might want to check whether this is a worthwhile addition. Lunch 22:32, 1 September 2006 (UTC)[reply]

Another reference to Herve Abdi! Inserted by an anonymous user with ip address 129.110.8.39 which seems to belong to the University of Texas at Dallas. Apparently the only editing activity so far has been to insert excessive references to publications by Herve Abdi (of the University of Texas at Dallas). The effect is that many Wikipedia articles on serious scientific topics currently are citing numerous rather obscure publications by Abdi et al, while ignoring much more influential original publications by others. I think this constitutes an abuse of Wikipedia. As a matter of decency, I suggest to 129.110.8.39 to remove all the inappropriate references in the numerous articles edited by 129.110.8.39 , before others do it. Truecobb 20:20, 14 April 2007 (UTC)[reply]

I have waited for several months; now I'll delete the obscure reference. Truecobb 21:23, 15 July 2007 (UTC)[reply]

missing pic

I didn't feel comfortable editing this page but felt I should point out that one image on this page does not appear for me.

The image Triangle_centroid_1.svg is on the page but appears not to contain anything. Clicking on the image yields http://en.wikipedia.org/wiki/Image:Triangle_centroid_1.svg which also appears not to contain anything. However, clicking on the image on that page yields a URL which does have a non-empty image http://upload.wikimedia.org/wikipedia/commons/8/85/Triangle_centroid_1.svg

--128.89.80.117 20:00, 29 October 2007 (UTC) Dan B.[reply]

I modified the svg file on commons to work better, I hope. It may take a while for the modified image to propagate back here through the various levels of caching we have. —David Eppstein 20:29, 29 October 2007 (UTC)[reply]

Proof that the centroid of a triangle divides each median in the ratio 2:1

This proof is not a proof. It is based on the statement that GBOC is a parallelogram, which is not proved.

Paolo.dL (talk) 09:38, 19 February 2008 (UTC)[reply]

I've fixed the hole in the proof. Occultations (talk) 02:57, 20 February 2008 (UTC)[reply]

Not to disparage the work, but Wikipedia math articles are not supposed to include proofs (except, of course, for articels on theorems and proofs). Perhaqps it can be moved to a textbook wiki? --Jorge Stolfi (talk) 03:49, 24 October 2008 (UTC)[reply]

 === Proof that the centroid of a triangle divides each median in the ratio 2:1 ===
 
 Let the medians AD, BE and CF of the triangle ABC intersect at G, the centroid of the triangle, and let the straight line   AD be extended up to the point O such that 
 : $AG=GO.\,$ 
 
 Then the triangles AGE and AOC are similar (common angle at A, AO is twice AG, AC is twice AE), and so OC is parallel to GE.  But GE is BG extended, and so OC is parallel to BG. Similarly, OB is parallel to CG.
 
 The figure GBOC is therefore a parallelogram. Since the diagonals of a parallelogram bisect one another, the point of intersection D between the diagonals GO and BC is such that GD = DO, and
 
 :  $GO=GD+DO=2GD.\,$ 
 
 So,  $AG=GO=2GD,\,$ 
 
 or  $AG:GD=2:1.\,$ 
 
 This is true for every other median.

Object which is a regular base?

there is no example of median in any object which is a regular base using object. —Preceding unsigned comment added by 59.94.188.39 (talk) 13:55, 4 January 2010 (UTC)[reply]
- I cannot understand the preceding comment. Can anyone clarify it? (From the way it was formatted, I suspect that ist was just a test edit.) Thanks, --Jorge Stolfi (talk) 15:36, 4 January 2010 (UTC)[reply]

Contradiction in article

The first section distinguishes, clearly, between "centroid" (also called "barycenter" in geometry), and "barycenter" as used in physics. Then the section "Locating the centroid" describes a method which finds not the centroid (as defined at the start of the article), but the physics-style barycenter.

I realise that different people use the term "centroid" in different ways. But the article ought to be consistent. It should not define "centroid" in one way then use it in another. Maproom (talk) 09:32, 9 July 2010 (UTC)[reply]

I agree. I've made a change in the "Locating the centroid" section that I hope addresses your concern. I don't think we need to specify a uniform gravitational field do we? The method can be extended, in theory, for any uniform solid, but the practicalities of recording lines through solids are questionable. Dbfirs 15:52, 9 July 2010 (UTC)[reply]

Your improvement certainly helps - but I was mistaken, I had missed the word "moment" in the first paragraph of the article. I am considering changing "average" to "mean" in that paragraph - what do you think? Maproom (talk) 16:40, 9 July 2010 (UTC)[reply]

Yes, I agree that arithmetic mean is the required average here, but we need to explain in simple words that can be understood by all. How about "average" (arithmetic mean)? Dbfirs 19:42, 9 July 2010 (UTC)[reply]

I think that would be an improvement. Maproom (talk) 08:23, 10 July 2010 (UTC)[reply]