Catenary

2002-03-30 10:28 PM

Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2000 by Xah Lee. (http://xahlee.org/)

Packages and Initializations

Needs["ParaPlot`"]

Needs["PlaneCurveFormulas`"]

Needs["Graphics`SurfaceOfRevolution`"]

$HistoryLength = 5;

minimal surface

Surface of revolution of catenary is a mimimal surface.
Consider the ends of a right circular cylinder as two parallel circles. If we were to connect these two circles with a surface with the criterion that the resulting surface must have a mimimal area, the solution is the surface of revolution of catenary. The surface of any soap bubbles films are minimal surfaces.

Clear[gp];
gp = 
        First[SurfaceOfRevolution[Catenary[][t], {t, -1.5, 1.5}, 
            RevolutionAxis -> {1, 0, 0}, 
            DisplayFunction -> Identity]];
Show[
        Graphics3D[{EdgeForm[{GrayLevel[ .6], Thickness[ .002]}], gp}, 
          Boxed -> False]];
Clear[gp]