Q: Mathematica & minimal surfaces
- To: mathgroup at christensen.cybernetics.net
- Subject: [mg1675] Q: Mathematica & minimal surfaces
- From: Zorro <berriz at husc.harvard.edu>
- Date: Tue, 11 Jul 1995 05:57:20 -0400
- Organization: Harvard University, Cambridge, Massachusetts
Hi. This is a simple question for those more familiar with Mathematica's capabilities and/or differential geometry than I am. I've seen many examples of minimal surfaces drawn using Mathematica, but it seems that Mathematica is of little help if all one starts with is the parametrization of the curve, without an explicit parametrization for the corresponding minimal surface. (Here's where my total ignorance of differential geometry shines through: I'm assuming that there is no straightfoward way of computing the parametrization of the minimal surface given the parametrization of the generating curve). It seems that if one wants to have Mathematica draw a given curve's minimal surface, one must first somehow figure out, basically "by hand", the parametrization of this surface and feed it to Mathematica, which then plots it like any other parametrized surface. Is this correct? Or is it the case that given a parametrization t -> f(t) of an arbitrary curve living in R^3, there's a "simple way" (i.e. either built-in or package functions) in Mathematica to display the minimal surface corresponding to this curve? (Note that I'm not interested in a functional parametrization of the minimal surface in question, only in an image on the screen, therefore numerical solutions are fine for my purposes.) Thanks for your help, Z.