I gather that your answer to my question is, solving this problem without being given a solution method would make Maxima a different kind of system, and that kind of system would be called a geometric theorem prover (although I haven't really stated a theorem to be proven, I've just asked for an area). I'll try looking at your references to see what's been done in getting a computer to reason about geometry problems.
Thanks,
Bob Baker
From: fateman at cs.berkeley.eduTo: b_baker at hotmail.comCC: maxima at math.utexas.eduSubject: RE: [Maxima] How understanding is Maxima?Date: Mon, 17 Mar 2008 19:32:34 -0700
Typically you would have to translate these English statements into algebraic equations and then solve them; then translate the solution back into English, if necessary.
There is a fairly large literature on geometric and algebraic theorem proving, e.g. a book by Steven Chou; also translation from English to math by Daniel Bobrow's classic STUDENT program, also physics problems by a professor at Texas.
Also look up OTTER, and that should give you lots of bibliographic references to the rest of the field.
RJF
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Bob BakerSent: Monday, March 17, 2008 3:26 PMTo: maxima at math.utexas.eduSubject: How understanding is Maxima?
I have a question about systems like Maxima I would like to ask members of this group. I posted it in the Maple forum and didn't generate much discussion, but I think this is a more suitable group. I will start by posing a problem: Let C be a unit circle and let P be a point on C. Draw a bigger circle B with P as center which crosses C at two diametrically opposed points of C. What is the area of the crescent-shaped region inside C and outside B? This problem has a simple answer, but whether the solution is simple depends on the solution method chosen. I can solve the problem in my head without even a pocket calculator if I choose the right solution method. Now here is my real question. Is there a "neutral" way to pose this problem to Maxima? By that I mean to pose it as I have to you, without presupposing a particular solution method. Or, would that make Maxima a different kind of system from what it is, and if so, what do you call that kind of system? Thanks,Bob Baker