function out = ratio(k)
    function gO = g(dx,dy)
        function fO = f(x,y)
            fO = sin(x.*x.*y);
        end

        gO = (1./(2.*dx.*dx.*dy)).*(f(dx,dy)-2.*f(0,dy)+f(-dx,dy)-f(dx,-dy)+2.*f(0,-dy)-f(-dx,-dy));

    end

    out = (2.0-g(k,k))./(2.0-g(k./2.0,k./2.0));

end