Talk:List of centroids

message: It should be noted that there is a more general formula for the x coordinate of the triangle's centroid, as illustrated here, but the present illustration does not allow for this. --Tarnjp 05:57, 16 November 2006 (UTC)
replies: text: That is correct, however, is it a practical method? DMZ 13:36, 17 November 2006 (UTC)
replies: text: The coordinate of the centroid along the line on which the base of the triangle lies is simply \frac{a + b}{3}, where b is the length of the base of the triangle, and a is the distance between the upper vertex and one of the lower vertices, along a line parallel to the base. The number so obtained is relative to the lower vertex used. In the simplest case, the base of the triangle lies on the x axis, and one of the vertices lies at the origin (as in the previously linked illustration). One then uses the length of the base and the x coordinate of the upper vertex for a and b. Given that both of the required quantities can be easily measured, it is a practical method.  --Tarnjp 01:35, 18 November 2006 (UTC)
replies: text: Fair enough. Feel free to add it, just make sure it's illustrated correctly in the figure.. DMZ 19:02, 18 November 2006 (UTC)
thread_title:  Triangle 

message: Based on the (slightly ambiguous) description of "Sector Area", it seems that "Sector Area" is a duplicate of "Circular Sector." The y coordinate of the centroid being zero suggests that the area described is symmetric about the origin, however the other formulae do not agree. In fact, with the given formula for area of a sector (A = \frac{2\pi^2 r^2}{\alpha}), area varies inversely as \alpha. Furthermore, the formula for the x coordinate of the centroid is negative for values of \alpha > \pi. Both of these discrepancies need justification. --Tarnjp 04:43, 21 November 2006 (UTC)
thread_title:  "Sector Area" vs. "Circular Sector" 

message: In order to be really usable, there need to be figures for all of these, not just some. You could tell from a figure what a parabolic spandrel is, for example.
Also, there is no consistency between labeling and shading of shapes. Some areas are not shaded, some are shaded grey, and one is shaded yellow. Sometimes the radius of a circle is R, sometimes r, and sometimes {\rho}. And for the circular arcs, the quantities listed under "Area" are actually lengths.  —Preceding unsigned comment added by Hermanoere (talk • contribs) 19:09, 22 April 2009 (UTC)
thread_title:  Consistency and Usability 

message: The main article starts:
The centroid of an object X in n-dimensional space is the intersection of all hyperplanes that divide X into two parts of equal moment about the hyperplane.
And goes on:
For an object of uniform composition, the centroid of a body is also its center of mass.
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Other sources state that it is possible for the 'centroid' of an object to be located outside of its geometric boundaries.
This may erroneously or otherwise facilitate a deduction allowing an object hyperplane bisector that does not pass through the object's centroid.
This may erroneously or otherwise facilitate a deduction allowing a hyperplane on which the centroid lies not bisecting the object to which the centroid belongs.  — Preceding unsigned comment added by 82.29.184.92 (talk) 12:42, 29 September 2020 (UTC)
thread_title:  Centroids and Bisectors of 3d Objects 

message: 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. 82.29.184.92 (talk) 12:16, 15 October 2020 (UTC)
thread_title:  Unambiguous Definition of Centroid