Talk:Infinite-dimensional optimization
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Minimizing the area of a surface connecting two parallel circles
The optimized surface for two parallel circles would be a cylinder, either right or oblique. Here's a paper that demonstrates this well: http://math.rice.edu/~zhmeng/SkewedCylinder.pdf
Mipchunk 06:49, 31 May 2006 (UTC)
- That paper you are referring to is assuming that the horizontal crosssections have constant area, so that's a different problem. Oleg Alexandrov (talk) 14:58, 31 May 2006 (UTC)
- Ah you're right. What then, is the surface of minimal area that would enclose two parallel circles? It must have a name. Or an equation. Mipchunk 22:21, 31 May 2006 (UTC)
- Yes it does have a name, the curve which rotated gives that surface is very famous, but I don't recall that name. A search on google on "minimal surface" or "calculus of variations" could give the answer. Oleg Alexandrov (talk) 00:25, 1 June 2006 (UTC)
- Ah you're right. What then, is the surface of minimal area that would enclose two parallel circles? It must have a name. Or an equation. Mipchunk 22:21, 31 May 2006 (UTC)
- Ah...yes...I should've known, with my knowledge of the catenary. The surface is the catenary's rotation, the catenoid.Mipchunk 01:33, 1 June 2006 (UTC)