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A part of a circle or a disk?
editIn German and Russian the sector is a part of a disk (2-dimentional object) rather than merely a circular arc. I think that en.wp mistakes, as other languages which align to this article. Incnis Mrsi (talk) 10:21, 17 April 2010 (UTC)
Center of Mass
editThe expression given in this section describes the center of mass of a half-disc, not a general circular sector.--84.108.213.97 (talk) 07:34, 15 June 2011 (UTC)
The current paragraph that replaced the incorrect expression is neither comprehendible nor referenced, and not very useful at any rate because it gives no actual mathematical expression. Unless we have something concrete to say about the center of mass of a circular sector, there's really no point in having this section. — Preceding unsigned comment added by 84.108.213.97 (talk) 08:41, 18 July 2011 (UTC)
Agreed. — Preceding unsigned comment added by 67.142.176.25 (talk) 04:18, 11 July 2012 (UTC)
logical circles
editEhrenpreis used to point out this logical circle in most calculus texts. The Wikipedia article on the proof of the derivative of sine references this article. Now, the issue is, how does one prove that the area of a circular sector is proportional to the angle subtended? The answer is, you can't. Unless you use integral calculus, there is no proof using geometry alone....in fact, there is no way to "measure" an angle in Euclidean geometry, i.e., no way to associate a real number to it. One could develop a theory of proportion, perhaps, but I do not see any reference to a source on this.
So it seems to me that only the explanation using integrals here is valid. But in that case, it cannot be used for the other Wikipedia article that refers to this one.
I would like to see a source for the claim that one can prove that the area is proportional to the subtended angle.98.109.232.157 (talk) 05:53, 1 September 2014 (UTC)
- Interesting observation. I don't have a source, and it may be hard to find one because authors might tend to assume it's "obvious", on grounds of symmetry: If you have a sector, then rotate the circle by theta, then you have a sector congruent to the first one and hence with the same area. Together the two sectors have twice the angle and twice the area, and by symmetry they're in the same circle. Since the sector is infinitely divisible into sub-sectors, and all of them can be rotated the same way to be adjacent to the original sector, you get proportionality of the area to the angle subtended. Loraof (talk) 18:20, 17 January 2015 (UTC)