Legacy and influence in Mathematics -- An Archimedean Research Theme: The Calculation of the Volume of Cylindrical Groins -- On Archimedean Roots in Torricelli’s Mechanics -- Rational Mechanics and Science Rationnelle Unique -- Archimedes and Caustics: A Twofold Multimedia and Experimental Approach -- Archimedes’ Quadratures -- On Archimedes’ Pursuit Concerning Geometrical Analysis -- Legacy and influence in Engineering and Mechanisms Design -- Simon Stevin and the Rise of Archimedean Mechanics in the Renaissance -- Archimedes’ Cannons Against the Roman Fleet? -- V-Belt Winding Along Archimedean Spirals During the Variator Speed Ratio Shift -- Ancient Motors for Siege Towers -- From Archimedean Spirals to Screw Mechanisms – A Short Historical Overview -- The Mechanics of Archimedes Towards Modern Mechanism Design -- Archimedean Mechanical Knowledge in 17th Century China -- Archimedes Arabicus. Assessing Archimedes’ Impact on Arabic Mechanics and Engineering -- Legacy and influence in Hydraulics -- The Golden Crown: A Discussion -- The Heritage of Archimedes in Ship Hydrostatics: 2000 Years from Theories to Applications -- Notes on the Syrakosia and on Archimedes’ Approach to the Stability of Floating Bodies -- What Did Archimedes Find at “Eureka” Moment? -- Floatability and Stability of Ships: 23 Centuries after Archimedes -- The “Syrakousia” Ship and the Mechanical Knowledge between Syracuse and Alexandria -- Legacy and influence in Philosophy -- Browsing in a Renaissance Philologist’s Toolbox: Archimedes’ Rule -- The Mystery of Archimedes. Archimedes, Physicist and Mathematician, Anti-Platonic and Anti-Aristotelian Philosopher -- Archimedes to Eratosthenes: “Method for Mechanical Theorems” -- Archimedes in Seventeenth Century Philosophy -- Legacy and influence in Science and Technology -- Cross-Fertilisation of Science and Technology in the Time of Archim?d?s -- Archimedes in Ancient Roman World -- Archimedes: Russian Researches -- Archimedean Science and the Scientific Revolution -- Archimedes’ Burning Mirrors: Myth or Reality? -- The Influence of Archimedes in the Machine Books from the Renaissance to the 19th Century -- Archimedes Influence in Science and Engineering -- Legacy and influence in teaching and history aspects -- The Founder-Cult of Hieron II at Akrai: The Rock-Relief from Intagliatella’s Latomy -- Archimedes: Russian Editions of Works -- Archimedes in Program on History of Mechanics in Lomonosov Moscow St. University -- Archimedes Discovers and Inventions in the Russian Education -- Archimedes in Secondary Schools: A Teaching Proposal for the Math Curriculum -- Mechanical Advantage: The Archimedean Tradition of Acquiring Geometric Insight form Mechanical Metaphor -- The Death of Archimedes: A Reassessment.

Archimedes is held in high esteem by mathematicians, physicists and engineers as one of the most brilliant scientists of all time. These proceedings contain original, unpublished papers with the primary emphasis on the scientific work of Archimedes and his influence on the fields of mathematics, science, and engineering. There are also papers dealing with archaeological aspects and the myths and legends about Archimedes and about the Archimedes Palimpsest. Papers on the following subjects form part of the book: Hydrostatics (buoyancy, fluid pressure and density, stability of floating bodies); Mechanics (levers, pulleys, centers of gravity, laws of equilibrium); Pycnometry (measurement of volume and density); Integral Calculus (Archimedes as the father of the integral calculus, method of exhaustion, approximation of pi, determination of areas and volumes); Mathematical Physics (Archimedes as the father of mathematical physics, Law of the Lever, Law of Buoyancy, Axiomatization of Physics); History of Mathematics and Mechanics (Archimedes’ influence in antiquity, the middle ages, the Renaissance, and modern times; his influence on Leonado da Vinci, Galileo, Newton, and other giants of science and mathematics); Ancient Machines and Mechanisms (catapults, water screws, iron hands, compound pulleys, planetaria, water clocks, celestial globes, the Antikythera Mechanism); Archimedean Solids (their rediscovery in the Rennaisance and their applications in materials science and chemistry); Archimedean Legends (how stories of golden crowns, eureka moments, naked runs, burning mirrors, steam cannons, etc., have influenced us through the ages, whether true or not); The Cattle Problem (how its 18th century rediscovery inspired the study of equations with integer solutions); Teaching the Ideas of Archimedes (how his life and works have influenced the teaching of science, mathematics, and engineering).