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