# [Maxima] How understanding is Maxima?

Jaime Villate villate at fe.up.pt
Mon Mar 17 19:44:57 CDT 2008

```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

```