Talk:Area of a Circle

Beautiful! - are you going to do sector integration as well? Although it occurs to me we haven't formally defined polar co-ordinates yet, mea culpa, I couldn't find a graphics package that would put a pretty picture up without lots of work. Let alone polar calculus. --Matt Westwood 22:11, 1 May 2009 (UTC)

Interesting idea, but I think that might actually be circular. From my recollection of our one week discussing polar calculus and wikibooks article, I think that the formulas for polar calculus are tied to the area of a sector of a circle, which is based on the area of a circle. One of you might have a better idea from more advanced studies of calculus and topology. I was contemplating putting up a calculus proof with the area of the sectors approximated by triangles (which incidentally might help make polar calculus non-circular), but I think I'd need to find my notes on it (lord knows why I effectively discussed calculus in my freshman year of high school, but I did, and now I don't really remember it). --Cynic (talk) 00:09, 2 May 2009 (UTC)

Shell Integration

How do we know the area of the ring without knowing the area of the circle? Isn't each ring the limit of the area of a bigger circle minus the smaller one as $\Delta{area} \to 0?$ --GFauxPas 10:25, 20 November 2011 (CST)

Yes, that's one way to calculate it, but who said that was the way the area of the ring is calculated here? It isn't.--prime mover 10:11, 20 November 2011 (CST)

Thank you! --GFauxPas 10:25, 20 November 2011 (CST)