Talk:List of centroids

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[edit] Triangle

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)

That is correct, however, is it a practical method? DMZ 13:36, 17 November 2006 (UTC)
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)
Fair enough. Feel free to add it, just make sure it's illustrated correctly in the figure.. DMZ 19:02, 18 November 2006 (UTC)

[edit] "Sector Area" vs. "Circular Sector"

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 α. Furthermore, the formula for the x coordinate of the centroid is negative for values of α > π. Both of these discrepancies need justification. --Tarnjp 04:43, 21 November 2006 (UTC)