Talk:Pappus's centroid theorem
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Proof without calculus[edit]
does there exist a proof not involving calculus of the first theorem? I have never seen a proof of this without calculus 70.19.103.56 (talk) 01:46, 25 June 2007 (UTC)
- Probably not. At least I didn't hear about the (general) surface area definition or the (general) curve arc length definition which would not involve calculus. Both surface and curve are approximated with the sum of small parts, then we use the limit of the infinite sum of infinitesimal terms (parts areas or lengths, resp.) to get a final value. That is called integration, and is a central concepts of calculus. :) --CiaPan (talk) 16:19, 1 April 2010 (UTC)
I have always understood that the formula for the volume of a conical solid, with the base as any closed figure in a plane; one third the area of the base times the altitude, was attributed to Pappas. Can anyone confirm or refute this? Alexselkirk1704 (talk) 23:24, 14 December 2008 (UTC)
Surely these theorems are more general than rotation about an axis ? For any movement which keeps the curves orientation in space constant and does not make "any overlaps" the volume will be the area of the curve times the distance the center of gravity moved. Feynman mentions it in "Lectures on Physics part I", section 19-2. (And it is not unreasonable: Any 'nice' curve can be approximated by sequence of linear and circular segments, right?). I believe this is a proof http://www.utgjiu.ro/conf/8th/S1/15.pdf ClausVind (talk) 18:42, 13 August 2011 (UTC)
About long footnotes[edit]
I think it's strange, though.--61.23.114.146 (talk) 13:28, 9 May 2017 (UTC)