Saturday, May 16, 2009

Vocab Level E Unit 4-6 Review

Presentations on Foucault pendulum

I never understood the call Coriollis force, I thought that physicists were getting me fingers to his mouth with his elaborate explanation. But like everything else, this can be seen as an elementary geometric result of Newton's law.
This article (download here ) is an interesting presentation on Foucault's pendulum, which uses spherical coordinates and the basic notion of holonomy, and it really clear how the phenomenon depends on the position. The article is very interesting, can be read with arithmetic and is a gateway to the beautiful world of differential geometry.
Please if your exposure is on the Foucault pendulum, be sure to read this article. If you understood the phenomenon as satisfatoria using another source, as I am eager to listen.

Fasion Without Clothes

Exhibition on game theory.

There are two options, one is present the proof of the theorem of Nash that appears in the article by Milnor. The other is to present the usual demonstration using fixed-point theorem of Kakutani.
Presentations should focus on the Pueba Nash's theorem, as already some examples.

Japanese Grope Doctor

For fixed-point presentations on hex. DEMONSTRATION ELEMENTARY

To avoid repeating the presentations and to be more specific, I suggest you supplement your information in the article by Gale (download here ).
The idea is to demonstrate the fixed-point theorem using hex game properties in the article is 2-dimensional case and the n-dimensional focus on the 2-dimensional case, that is short and elegant.
The property that the game is always a winner, is also shown in the article, but a simpler and more natural demostraciĆ³m, is in this article (download here ).
The other issue is the demonstration of Milnor's fixed point theorem, which can be downloaded from a previous post.
Another option is the demonstration of Peter Lax's fixed point theorem, as a result of his demonstration of the change of variables theorem. (Download article here ).