On Tue, 18 Mar 2008 Jaime Villate wrote: > On Mon, 2008-03-17 at 15:26 -0700, Bob Baker wrote:> > 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?> > > Now here is my real question. Is there a "neutral" way to pose this> > problem to Maxima?> Depends on what you mean by neutral. Would this be neutral enough?:> > (%i1) display2d:false$> (%i2) C: x^2 + y^2 = 1$> (%i3) B: x^2 + (y+1)^2 = 2$> (%i4) f: solve(C, y);> (%o4) [y = -sqrt(1-x^2),y = sqrt(1-x^2)]> (%i5) g: solve(B, y);> (%o5) [y = -sqrt(2-x^2)-1,y = sqrt(2-x^2)-1]> (%i6) q: solve([B,C], [x,y]);> (%o6) [[x = -1,y = 0],[x = 1,y = 0]]> (%i7) integrate(rhs(f[2])-rhs(g[2]),x,rhs(q[1][1]),rhs(q[2][1]));> (%o7) 1> > or if you wanted Maxima to find out that the radius of B was sqrt(2),> you could do:> (%i2) B: x^2 + (y+1)^2 = r^2$> (%i3) B, x=1, y=0;> (%o3) 2 = r^2> > Cheers,> Jaime Villate
Is that neutral enough? Not really. It presupposes that the best solution method is to solve an integration problem. Clearly, that is not the method that lets me solve the problem in my head from looking at the picture.
Bob Baker