Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: area of surface of revolution of 3D curve Date: Fri, 15 Apr 2011 19:06:05 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 10 Message-ID: <ioa4ut$b3m$1@fred.mathworks.com> References: <io8rdg$5bb$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: www-06-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1302894365 11382 172.30.248.38 (15 Apr 2011 19:06:05 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Fri, 15 Apr 2011 19:06:05 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:722130 "Prakhar" wrote in message <io8rdg$5bb$1@fred.mathworks.com>... > How do you calculate area of surface of revolution of 3D curve? Though using integration I am able to calculate the area, but I would like to know a simpler method such as Pappus theorem for 2D curve. > > Is the Pappus theorem limited to 2D curve or is the generalisation of Pappus theorem for 3D curve available? > > I would also like to know that is there a theorem which says that the line about which surface of revolution of a given curve has minimum area should pass through the centroid of the curve? - - - - - - - - - - Given the axis of revolution, transform curve point coordinates to cylindrical coordinates using that axis as the z-axis. Then the curve of z and r (regarding r as always positive,) and ignoring azimuth, would constitute a two-dimensional curve and the Pappus centroid theorem would apply to that. However it means finding the 2D centroid and the total 2D arc-length along this 2D curve which would surely require some kind of integration. This 2D arc-length is not the same as the original curve's 3D arc-length. At least a one-dimensional integration seems inevitable. Roger Stafford