for n = 6:5:41,
   x = linspace(0,2*pi,n+1)';
   y = sin(x);
   V = zeros(n+1);
   for i = 1:n+1,
      V(:,i) = x.^(i-1);
   end
   a = V \ y;
   
   xmany = linspace(0,2*pi,500)';
   plot(xmany,horner(a,xmany),'b-',x,y,'rx');
   makelarge
   pause
end