Math 21 a Math21a, Fall 2000
Course Head: Prof. Clifford H. Taubes
Dini surface: surface of constant negative curvature, Picture by O.Knill (with Mathematica 4.0, Povray 3.1 on Linux), Fall 2000 Math21a

Mainpage Syllabus Calendar Homework Exams Supplements Comput. assigns Links

Mathematica Assignments

To download the third Mathematica notebook (the third lab is due December 20), click on the link "lab3.nb" below while holding down the shift key. Save the notebook on your computer and open this notebook in Mathematica (on a Mac or PC start up Mathematica and read in "lab3.nb" like in other software applications, on Unix just type "mathematica lab2.nb" in a terminal). Consult the Mathematica at Harvard page for instructions on how to get Mathematica on your own computer, how to get documentation etc. The labs in the basement of the Science center (Unix, PC and Mac) have Mathematica installed. Getting started with the computer assignments will probably be the biggest challenge. Start early and network around to find the best solution for you. Instructions, on how to use the notebooks and how to get credit can be found in the first notebook . When stuck, the FAQ page might help. Good luck!
A selection of surfaces from the second Mathematica assigmnent is now posted here! A selection of curves from the first Mathematica assigmnent.
Download
lab1.nb (Notebook) lab2.nb (Notebook) lab3.nb (Notebook)

Dini surface: surface of constant negative curvature
The Mathematica command which produces this picture of the Dini surface (also animated above) is 

 f[u_,v_]:={Cos[u]*Sin[v],Sin[u]*Sin[v],Cos[v]+Log[Tan[v/2]]+u/5};
     ParametricPlot3D[f[u,v],{u,0,4*Pi},{v,1/20,1}]

(v,u) -> f(u,v) is an object in multivariable calculus, the topic of this course Math 21a.

Move interactively the Dini surface (proceed only with a computer having some muscle and if Java is enabled in your browser).
Last update, 9/24/2000