Talk:Centroid

Mathematics C‑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
C	This article has been rated as C-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

Archives

1

This page has archives. Sections older than 365 days may be automatically archived by when more than 10 sections are present.

Smallest circle problem

I was wondering if someone can find a reputable source for the problem of finding the smallest circle which inscribes a polygon in general? I have heuristically worked out a solution for triangles, but that would count as original research, so this cannot go into the article! Just to satiate anyone's curiosity the triangle problem can be solved as follows.

First, determine if 2 or 3 points of the triangle will be on the circle's parameter. Two edges will be on the parameter when the second longest edge is shorter than half the longest edge. This can be clearly seen by selecting the midpoint of the longest edge, producing a circle with radius =1/2 the longest edge. This will inscribe the third vertex since the second longest edge is less than or equal to radius. Otherwise all three vertices will be on the circle's parameter. When that is the case you can analytically solve for some point (x,y) which produces the same distance from all three vertices, provided the triangle is not degenerate. Simply algebraically solve (y-y1)^2+(x-x1)^2=(y-y2)^2+(x-x2)^2=(y-y3)^2+(x-x3)^2 for x and y (although the solution is a bit ugly so I'm not going to post it here). Mouse7mouse9 20:31, 23 April 2013 (UTC)

See Smallest-circle problem. There are known algorithms that solve the problem in linear time for arbitrary polygons. —David Eppstein (talk) 20:38, 23 April 2013 (UTC)[reply]

Thank you! Mouse7mouse9 20:44, 23 April 2013 (UTC)

For an acute triangle, all three vertices will lie on the circle. So draw a circle centred on the point where the perpendicular bisectors of the sides meet. For an obtuse triangle, only two vertices will lie on the circle: draw a circle centred on the midpoint of the longest side. Maproom (talk) 21:11, 23 April 2013 (UTC)[reply]

Coding for centroid

I have moved the following coding here because it wasn't explained in the article. What language is it?

       public static function getCentroid(vertices:Array):Point
       {
           var i:int, j:int;
           var A:Number = 0;
           var Cx:Number = 0;
           var Cy:Number = 0;
           for(i=0;i<vertices.length;i++){
               j = (i+1)%vertices.length;
               A += (vertices[i].x * vertices[j].y) - (vertices[j].x * vertices[i].y);
               Cx += (vertices[i].x + vertices[j].x)*((vertices[i].x * vertices[j].y) - (vertices[j].x * vertices[i].y));
               Cy += (vertices[i].y + vertices[j].y)*((vertices[i].x * vertices[j].y) - (vertices[j].x * vertices[i].y));
           }
           A /= 2;
           Cx /= (6*A);
           Cy /= (6*A);
           return new Point(Cx,Cy); //it may be placed out of polygon
       }

Any comments about whether it should be included (with explanation and perhaps collapsed)? Dbfirs 17:37, 13 June 2013 (UTC)[reply]

I don't see the need for code here at all. There is a simple formula for this that can be expressed much more concisely in mathematical notation than in code, and there is nothing to code beyond implementing the formula. —David Eppstein (talk) 17:45, 13 June 2013 (UTC)[reply]

That's what I thought, but I didn't want to discourage the anon editor who added it by just reverting. Dbfirs 17:47, 13 June 2013 (UTC)[reply]

'Barycenter' redirects here

But there is no mention of celestial mechanics or orbits in the Centroid article. Lori (talk) 02:48, 15 October 2013 (UTC)[reply]

Yes, you are correct; it's a valid criticism. I've now redirected both Barycenter and Barycentre to the more appropriate Center of mass article. Would it be better to redirect to the subsection Center of mass#Astronomy where there is a further link to astronomical applications? Dbfirs 11:18, 15 October 2013 (UTC)[reply]

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)[reply]

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. Dbfirs 06:53, 21 September 2015 (UTC)[reply]

Divisor in calculation of centroid.

@193.17.42.129: If there are n vertices, numbered from 0 to (n-1) then the divisor should be n should it not? Dbfirs 12:37, 6 June 2016 (UTC)[reply]

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. Dbfirs 07:09, 7 June 2016 (UTC)[reply]

External links modified

Hello fellow Wikipedians,

I have just modified 2 external links on Centroid. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{Sourcecheck}}).

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 13:32, 18 November 2016 (UTC)[reply]

"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)[reply]

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)[reply]

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)[reply]

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)[reply]

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

"The arithmetic mean position of all the points in the figure"

Arithmetic mean is only defined for a finite number of quantities.— Pingku^dimmi 12:09, 27 December 2020 (UTC)[reply]

@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)[reply]

Proposed merge of Locating the center of mass into Centroid

overlapping content fgnievinski (talk) 15:16, 4 April 2022 (UTC)[reply]

Support. Some of Center of mass § Locating the center of mass might need to be reworked or merged here as well. -Apocheir (talk) 21:58, 4 April 2022 (UTC)[reply]
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)[reply]