The genius of Archimedes-- 23 centuries of influence on mathematics, science and engineering : Proceedings of an International Conference held at Syracuse, Italy, June 8-10, 2010

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The Genius of Archimedes

23 Centuries of Influence on Mathematics, Science and Engineering; PREFACE; TABLE OF CONTENTS; 1. LEGACY AND INFLUENCE IN MATHEMATICS; AN ARCHIMEDEAN RESEARCH THEME: THE CALCULATION OF THE VOLUME OF CYLINDRICAL GROINS; 1. INTRODUCTION; 2. HOW ARCHIMEDES CALCULATED THE VOLUMES OF CYLINDRICAL WEDGES; 3. GIROLAMO SETTIMO AND HIS HISTORICAL CONTEST; 4. GROINS IN SETTIMO'S TREATRISE; 5. CONCLUSION; REFERENCES; ON ARCHIMEDEAN ROOTS IN TORRICELLI'S MECHANICS; 1. INTRODUCTION; 2. ARCHIMEDEAN THINKING; 3. ON PROOFS; 4. CONCLUSION; REFERENCES. RATIONAL MECHANICS AND SCIENCE RATIONNELLE UNIQUE1. INTRODUCTION; 2. FROM RENAISSANCE TO THE ECOLE POLYTECHNIQUE; 2.1. Simon Stevin's Wonder en is gheen Wonder; 2.2. From the Late Renaissance to Radical Enlightenment; 3. SCIENCE RATIONNELLE UNIQUE & NATURAL SHAPES; 3.1. Science Rationnelle Unique; 3.2. Universal Natural Shapes; 4. THE DIRICHLET PROBLEM FOR POISSON'S EQUATION IN A STARLIKE DOMAIN; 5. OUTLOOK; ACKNOWLEDGMENTS; REFERENCES; ARCHIMEDES AND CAUSTICS: A TWOFOLD MULTIMEDIA AND EXPERIMENTAL APPROACH; 1. INTRODUCTION; 2. CAUSTICS; 3. COMPUTATIONAL CAUSTIC EXPLORATION. 4. EXPERIMENTAL CAUSTIC EXPLORATION5. CONCLUSION; REFERENCES; ARCHIMEDES' QUADRATURES; 1. INTRODUCTION; 2. THE QUADRATURE AND THE METHOD: SOME FEATURES OF THE TWO TREATISES; 3. THE QUADRATURES OF THE PARABOLIC SEGMENT: A HISTORIOGRAPHICAL DISCUSSION; REFERENCES; ON ARCHIMEDES' PURSUIT CONCERNING GEOMETRICAL ANALYSIS; 1. INTRODUCTION; 2. PAPPUS' DISCUSSION OF GEOMETRICAL ANALYSIS; 3. GEOMETRICAL ANALYSIS IN ARCHIMEDES; 4. A CONJECTURE ON THE MISSING ANALYSIS OF PROBLEM 4 OF ARCHIMEDES' ON THE SPHERE AND CYLINDER, II; 5. CONCLUSION; ACKNOWLEDGMENTS; REFERENCES. 2. LEGACY AND INFLUENCE IN ENGINEERING AND MECHANISMS DESIGNSIMON STEVIN AND THE RISE OF ARCHIMEDEAN MECHANICS IN THE RENAISSANCE; 1. INTRODUCTION; 2. THE BACKGROUND; 3. THE SCIENCE OF WEIGHTS: DEFINITIONS AND POSTULATES; 4. THE SCIENCE OF WEIGHTS: THE FIRST PROPOSITIONS; 5. THE SCIENCE OF WEIGHTS: THE LAW OF THE LEVER AND THE LAW OF THE INCLINED PLANE; 6. STEVIN: FROM THE SCIENCE OF WEIGHTS TO THE PRINCIPLES OF THE ART OF WEIGHING AND THE PRACTICE OF WEIGHING; 7. THE GENESIS OF STEVIN'S STATICS; 8. STEVIN'S TREATMENT OF THE INCLINED PLANE: THE CRUCIAL PROOF. 9. THE PRINCIPLES OF THE ART OF WEIGHING10. A REMARK ON THE PRACTICE OF WEIGHING; 11. STEVIN'S ANALYSIS OF WINDMILLS; 12. CALCULATION OF THE WIND PRESSURE WITHOUTKNO WLEDGE OF AERODYNAMICS; 13. A BRILLIANT NEW DESIGN?; 14. HOW SUCCESSFUL WAS THE NEW DESIGN?; 15. CONCLUSION; REFERENCES; ARCHIMEDES' CANNONS AGAINST THE ROMAN FLEET?; 1. INTRODUCTION; 2. A RECONSTRUCTION OF THE ARCHIMEDES' STEAM CANNON; 3. ROUGH EVALUATION OF ENERGIES AND TRAJECTORIES; 3.1. The Projectile Muzzle Energy; 3.2. The Projectile Trajectory; 4. CONCLUSIONS; 5. APPENDIX; REFERENCES