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The double-differential production cross-section of positive pions, d 2 σ π + /dpdΩ, measured in the HARP experiment is presented. The incident particles are 8.9 GeV/c protons directed onto a beryllium target with a thickness of 5% of a nuclear interaction length. The measured cross-section has a direct impact on the prediction of neutrino fluxes for the MiniBooNE and SciBooNE experiments at Fermilab. After cuts, 13 million protons on target produced about 96,000 reconstructed secondary tracks which were used in this analysis. Cross-section results are presented in the kinematic range 0.75 GeV/c ≤ pπ ≤ 6.5 GeV/c and 30 mrad ≤ θπ ≤ 210 mrad in the laboratory frame.PACS. PACS-key discribing text of that key -PACS-key discribing text of that key

We derive an asymptotic formula for the difference of the volumes of a smooth convex body and its inscribed polytopes of maximum volume s the number of vertices tends to infinity. A similar result is proved for circumscribed polytopes. In addition, step-by-step approximation results are presented. The proofs are based on Delone triangulations, resp. Dirichlet -Voronoi tilings and make use of a generalized Version of Blaschke's "Sch ttelung"; they are quite involved.

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