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