Initialization

You need to find and load the LiveGraphics3D package:

SetDirectory["c:\documents and settings\paul\my documents"];
Needs["LiveGraphics3D`"];

Hyperboloid of one sheet

We use the ParametricPlot3D command to make the surface:

surface = ParametricPlot3D[{Sqrt[1+z^2] Cos[theta], 
                            Sqrt[1+z^2] Sin[theta],
                            z}, 
                       {theta, 0, 2 Pi},
                       {z, -3, 3}];

Execute this command if you want to see Mathematica's internal description of the surface. This description is what you will dump into a file to be read by the Java applet.

FullForm[surface]

This command performs the dump. You can use any file extension that you want, but I've found that it is handy to have an extension that tells you what's in the file.

WriteLiveForm["MAA_NES_Project_NeXT.math3Dgraphics",  
      surface]

After you have the file, you need to make an html file that tells the Java applet to load the graphic from the appropriate file. Use the view source command in your brouser to see the format of a typical html file of this sort. Take a look at circular_hyperboloid_1.html in the same directory where you found this Mathematica notebook.