Talk:Parametric surface

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A parametric surface is a surface defined by a parametric equation, involving two parameters. Are parametric surfaces limited to two parameters? I could imagine that it is possible to come up with parametric surfaces that have more (or maybe even less) parameters. What about parametric curves? Can they be thought of as parametric surfaces limited to one parameter? --Abdull 15:50, 30 May 2006 (UTC)

In the contex used here, they do require two parameters (or variables). The defining equation f:R^2->R^3 ,f:x,y->f(x,y) has two dimensions for the source, hence two parameters is needed. There are other ways of defining surfaces (algebraic surfaces), with a different type of defining equation.

In terms of manifolds parametric surfaces can be though of as local charts on 2-manifolds. In general they cannot be used to define a complete close surface, in such cases you would need to join two or more surfaces together.

I supose you could use three parameters, but in that case the equations would be degenerate in some way. --Salix alba (talk) 17:09, 30 May 2006 (UTC)

[edit] Uniformizing notation

While its true that calculus textbooks may use any pair of variables as parameters for a general parametrized surface, I think that it's a really bad idea to mix up the notation within the same article; forget the article — within the same paragraph even! This is totally schizophreniac. Most modern differential geometry books use u and v, why not stick to them throughout? Arcfrk (talk) 05:01, 11 March 2008 (UTC)