Is there a good program for drawing geometric figures, such as ellipses and hyperbolas; in particular, I'd like to type in the equations, and have it generate a picture that I can save as a bmp file. Once I have a bmp file, I can use Acrobat to generate a pdf, then use that in LaTex. --Bill C. -----Original Message----- From: math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com [mailto:math-fun-bounces+cordwell=sandia.gov@mailman.xmission.com]On Behalf Of Fred lunnon Sent: Tuesday, March 07, 2006 10:59 AM To: math-fun Subject: Re: [math-fun] sudoku, uniqueness, proofs On 3/7/06, Henry Baker <hbaker1@pipeline.com> wrote:

The basic idea is to reverse the logic of Tarski's decision procedure for geometry, which converts geometry into analytic geometry. Since the mapping is obviously not 1-1, you need a clever way to map questions about polynomials back into questions about lines, planes, circles, etc.

I skimmed over Gary's proof (literally for 2 seconds) and was unable to follow it; then pictured the problem mentally, saw the solution immediately, skimmed the proof again and realised it was saying the same thing as I had pictured. Pondering this chain of events, I wondered how does one teach people to think geometrically like this in the first place? [And when that's out of the way, is there a decent way to get 2-D or 3-D geometrical diagrams into TeX yet?] Fred Lunnon _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun