Math 223, Spring 2014
Various and sundry items that might amuse or inform you will appear below at random intervals
To get started with Mathematica, you might start here: "Get Started with Mathematica 9". Give it a whirl and tell me what you think. You can post your reactions in our "Course Lounge" Moodle forum.
Here are some web pages and toys pertaining to some of the course material. (Many of these use Java.)
HTML versions of Mathematica renderings of the parameterized curves and surfaces associated with Problem 13-1-26 and Problem 13-1-36 in Stewart (an earlier text).
Check out some Lissajous curves. When I look at these I observe optical illusions. You?
- A LiveGraphics3D demo of
curvature on a helix and an animated demo of
curvature on some dopey curve.
- A LiveGraphics3D demo of
TNB frames on a helix and an animated demo of
TNB frames on the dopey curve.
- Two-dimensional parallel paths.
Here's a "ruled surface" --- a doubly ruled surface, to be more precise. Ruled saddle.
- LiveGraphics3D demos of basic quadric surfaces:
- Speaking of saddles, here's a "5-saddle" for you.
- (LiveGraphics3D) Check out the envelope of this figure. How is an envelope formed? You'll officially meet the surface represented here when we discuss quadric surfaces. See the details of the problem HERE.
The projection and reflection in a plane of a simple figure. We want to be able to manipulate objects in 3D, to become Masters of Space.
- A flapping dodecahedron, just for your amusement. It's all simple geometry (of pentagons) and rotations (about lines).
- Solve this problem: calculate the angle between the planes (faces) of a regular dodecahedron. (This is the closed figure in the animation above.)
- Here is a HINT for finding the angle between the faces of a dodecahedron.
- My entire menagerie of flapping polyhedra, including the isocahedron and dodecahedron. I need to make the rest of the Archimedean solids one day. The web is teeming with all manner of polyhedral art and discussion.
- A Mathematica demo of some 3D vector stuff (from 2001).
- A LiveGraphics3D version of one of the figures in the above demo.
- A LiveGraphics3D version of the other figure in the above demo.
- A surface concave up at a point in two directions, but with no max or min at the point: the 4-saddle.
- From a few years ago, some pictures and discussion pertaining to a a basic problem concerning max and min values (from a different text).
- Old tests. Your tests might bear no resemblance to these.
You might want to check the Web for Calculus stuff. You could start at the
site below, but you'll probably need to dig around awhile before
finding something you like. (Hey --- no heavy surfing until you've
done your homework.) If you find something you like, send me the link and a brief description, so I can add it here.
(The above site is part of the more general site below.)
Math Forum Internet Math Library