  We prove a gluing theorem which allows to construct an ample divisor on a
rational surface from two given ample divisors on simpler surfaces. This
theorem combined with the Cremona action on the ample cone gives rise to an
algorithm for constructing new ample divisors. We then propose a conjecture
relating continued fractions approximations and Seshadri-like constants of line
bundles over rational surfaces. By applying our algorithm recursively we verify
our conjecture in many cases and obtain new asymptotic estimates on these
constants. Finally, we explain the intuition behind the gluing theorem in terms
of symplectic geometry and propose generalizations.
