Talk:Centroid

Calculation of centroid of cone
My calculations for the centroid of cone differ from the results stated. For the solid cone I get H/cuberoot(2) and for the surface I get H/root(2). This is ~0.2 and ~0.3 the distance from the base plane to the apex, not the 1/4 and 1/3 stated in the article. — Preceding unsigned comment added by 92.2.78.233 (talk) 14:32, 20 September 2015 (UTC)


 * Sorry you are having trouble with your calculations. The article is correct.  You might like to consult a standard mathematical text for the correct choice of elemental slice and method of integration.  If you can't find one, ask again here and we can find an on-line link to the method.    D b f i r s   06:53, 21 September 2015 (UTC)

Divisor in calculation of centroid.
If there are n vertices, numbered from 0 to (n-1) then the divisor should be n should it not?  D b f i r s   12:37, 6 June 2016 (UTC)
 * Sorry, yes it was just 6 for the divisor, regardless of the number of vertices. Perhaps we were both thinking of the centroid of the vertices themselves, rather than of the area.  I'm pleased to see that 192.189.128.13 has put the original back again with a reference.  I should have found one myself but was busy yesterday.  Here is another that doesn't use a hexagon as an example.    D b f i r s   07:09, 7 June 2016 (UTC)

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"Of a triangle" section: redundant?
In the section Of a triangle, part of the first paragraph is repeated in the subsection === Of a triangle ===, of the section Locating, and the later paragraphs seem to be irrelevant. The former section and latter subsection also have identical names, making it difficult to refer to the latter. I suggest merging the former section into the latter subsection and removing irrelevant material.—Anita5192 (talk) 05:50, 11 February 2019 (UTC)


 * I think of the ==-headed section as of a welcome example-section, illustrating the rather terse (for this kind of concept) formulated ==-section on properties. So I can also imagine to (1)blow up the ==-section with non-triangle, illustrative chops, e.g., a preview on "plumb line" or "decomposition", (2)moving out most of the simple triangle results to the ===-section, and (3)rename the ==-section accordingly (-> "Illustrations"?). I just stumbled into this, and will not object to any solution of the acknowledged equivocation problem. Purgy (talk) 08:15, 11 February 2019 (UTC)


 * I have renamed the first "Of a triangle" section to "Examples" for now. This may not be the best choice of name and may not be permanent, but at least we can link and refer to the sections unequivocally.—Anita5192 (talk) 19:01, 11 February 2019 (UTC)

Centroids and Bisectors of 3d Objects
It is not clear that Centroid is taken universally by the mathematical community to be the point, such that only hyperplanes it lies on, can be equal volume bisectors of a compound object and no hyperplane it lies on cannot be.

It is not clear:-

https://byjus.com/maths/centroid/ defines a property of a centroid thusly: It should always lie inside the object.

Wikipedia states: For an object of uniform composition, the centroid of a body is also its center of mass. https://en.wikipedia.org/wiki/List_of_centroids and: The center of mass may be located outside the physical body. https://en.wikipedia.org/wiki/Center_of_mass

orbital1337 YouTube as of 29/09/20, writes: " For a convex body of uniform density you can get up to 1 - 1/e on one side of a hyperplane through the center of mass (in the limit as the dimension goes to infinity)".

We need mathematicians to state explicitly what a centroid is and to then furnish a proof.

My interest concerns the Ham Sandwich Theorem and whether each of three objects can be considered as centroids (points) for the purpose of equal volume bisection. After finding out what is meant (consensually); it only remains to find out if it is true. 82.29.184.92 (talk) 12:54, 15 November 2020 (UTC)

82.29.184.92 (talk) 13:33, 29 September 2020 (UTC)

"The arithmetic mean position of all the points in the figure"
Arithmetic mean is only defined for a finite number of quantities.— Pingkudimmi 12:09, 27 December 2020 (UTC)


 * @Pingku Doesn't the arithmetic mean become an integral in the case of an infinite number of points (if bounded in a region of space)? Or at least can be generalized to it? Ron van den Burg (talk) 10:15, 9 July 2023 (UTC)
 * Well, yes, but (at least in the article Arithmetic mean) it's then called mean of the probability distribution. That article explicitly defines AM in terms of a finite set of points. The function version is mentioned as a generalisation, more properly one of weighted mean than arithmetic mean. My point is that, according to Wikipedia, arithmetic mean only means the finite version.— Pingkudimmi 11:32, 9 July 2023 (UTC)

Proposed merge of Locating the center of mass into Centroid
overlapping content fgnievinski (talk) 15:16, 4 April 2022 (UTC)


 * Support. Some of might need to be reworked or merged here as well. -Apocheir (talk) 21:58, 4 April 2022 (UTC)
 * Sure, there was hardly anything at Locating the center of mass that wasn't already here. I've done it. JBL (talk) 20:57, 13 June 2022 (UTC)

Suggestion to disambiguate.
If we have a convex polygon in R^2 then we could average the vertices (vertex centroid= sum of vertices/n). Or we could average the edges (edge centroid / boundary centroid). Or we could average the enclosed area (plane centroid / solid centroid).

All can be considered centers of mass for resp. collection of points, boundary of polygon and plane polygon.

For triangles, they are the same. But for other polygons they are not!

The problem is that in the Petr-Douglas-Neumann (PDN) page, centroid is implicitly referring to the vertex centroid. But most of the wiki articles refer to centroid as the plane centroid.

My suggestion is to explicitly name them here; and to change references from e.g. the PDN to the deeplink of the specific type of centroid.

In higher dimensions we can generalize to "k-face centroid" for polytopes or "n-volume centroid" and "n-1 dim. boundary centroid" for generic objects in R^n. Ron van den Burg (talk) 10:38, 9 July 2023 (UTC)

Proposed merge of Centre (geometry) into Centroid
same concept. fgnievinski (talk) 23:40, 22 August 2023 (UTC) fgnievinski (talk) 23:40, 22 August 2023 (UTC) also notice Geometric center already redirects here, not to Centre (geometry). fgnievinski (talk) 00:14, 23 August 2023 (UTC)


 * Please explain what you mean by "same concept". As mentioned on pages such as Centre (geometry) and Triangle center, there are many concepts of a "center" in geometry, of which the centroid is one. It seems more like "overarching concept" to me. Apocheir (talk) 00:36, 23 August 2023 (UTC)
 * These seem largely unrelated to me. I'd like to see both articles improved, but there's barely any content/scope overlap between these (the centroid is one type of "center"). If you want to redirect geometric center to centre (geometry) that seems fine with me though. –jacobolus (t) 17:19, 25 August 2023 (UTC)

Suggested addition
1st moment of area links here saying it can be used to find the centroid so maybe good to have the method?


 * By first moment of area
 * In pure bending the neutral axis of a beam passes through the centroid. The first moment of area is zero at the neutral axis and therefore, starting at an arbitrary $$y=0$$ axis, the y value that satisfies the integral $$\int_A y dA=0$$ is how far the neutral axis is from the original $$y=0$$. This repeated for the x axis giving the centroid point.
 * The centroid of a composite shape can be determined using the fact that the sum of the first moments of area for each shape totals to the first moment of area for the composite.

OagreDove (talk) 18:04, 17 January 2024 (UTC)


 * First moment of area is the same as center of mass (a.k.a. first moment of mass) for a shape of uniform density. It seems worth wikilinking first moment of area from this article or explicitly calling the center of mass a "moment", but the part about bending beams seems somewhat irrelevant. Composite shapes are discussed at . –jacobolus (t) 18:53, 17 January 2024 (UTC)