

U(1)=2
U(2)=pi;
for n=3:15
   U(n) = U(n-2)*2*pi/n
end
return


N=1000000;
nmax=15;
e=.01;
V=zeros(nmax,1);
S=zeros(nmax,1);
for n=1:nmax
   x = 2*rand(n,N)-1;
   normsqx=sum(x.*x,1);
   V(n)= 2^n * mean (normsqx <=1);
   S(n)= 2^n * mean (((1-e)^2 <= normsqx ).*(normsqx < 1.0));
   F(n)=S(n)/V(n);
end 
return




