Archimedes In The 21st Century

​This book is a collection of papers presented at the “Archimedes in the 21st Century” world conference, held at the Courant Institute of Mathematical Sciences in 2013. This conference focused on the enduring and continuing influence of Archimedes in our modern world, celebrating his centuries of influence on mathematics, science, and engineering. Archimedes planted the seeds for a myriad of seminal ideas that would grow over the ages. Each chapter surveys the growth of one or more of these seeds, and the fruit that they continue to bear to this day. The conference speakers contributing to this book are actively involved in STEM fields whose origins trace back to Archimedes, many of whom have conducted and published research that extends Archimedes’ work into the 21st century. The speakers are not historians, so while historical context is provided, this book is uniquely focused on the works themselves as opposed to their history. The breadth and depth of Archimedes’ influence will inspire, delight, and even surprise readers from a variety of fields and interests including historians, mathematicians, scientists, and engineers. Only a modest background in math is required to read this book, making it accessible to curious readers of all ages.

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 These proceedings contain original, unpublished papers with the primary emphasis on the scientific work of Archimedes and his influence on the fields of mathematics, science, and engineering.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).

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Known as the Father of Mathematics, Archimedes was the most important mathematician and inventor in ancient Greece. Many of the inventions he created as solutions to problems presented to him by King Hiero II are still in use today. Accomplished in both theoretical and practical mathematics, Archimedes is best known for mechanical inventions like Archimedes' screw, the Claw of Archimedes, and the heat ray as a weapon, as well as his discoveries using water displacement and buoyancy. But his contributions to pure mathematics, such as his approximation of pi, laid the groundwork for modern calculus.

Archimedes was one of the greatest mathematicians and inventors of the ancient world. His native city was Syracuse on the island of Sicily. When he was a young man, Archimedes was sent to study in Alexandria, which was the great intellectual center of the Mediterranean area during the Third Century B.C. There he met other brilliant mathematicians who became his friends. Even after they parted, when Archimedes returned to Syracuse, they wrote to each other sending the problems and theorems they were working on. Thanks to these letters we have many of Archimedes' theoretical writings. Back in Syracuse, King Hiero II, a friend and kinsman, asked Archimedes to use his mathematical genius to create practical solutions and inventions. The wonderful tools and weapons that Archimedes invented made him famous throughout the ancient world, and some such as levers and pulleys are still used today. Book jacket.

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).

Essays analyze the connections between science and technology and military power in the late medieval, Renaissance, and Enlightenment periods. The integration of scientific knowledge and military power began long before the Manhattan Project. In the third century BC, Archimedes was renowned for his research in mechanics and mathematics as well as for his design and coordination of defensive siegecraft for Syracuse during the Second Punic War. This collection of essays examines the emergence during the early modern era of mathematicians, chemists, and natural philosophers who, along with military engineers, navigators, and artillery officers, followed in the footsteps of Archimedes and synthesized scientific theory and military practice. It is the first collaborative scholarly assessment of these early military-scientific relationships, which have been long neglected by scholars both in the history of science and technology and in military history. From a historical perspective, this volume investigates the deep connections between two central manifestations of Western power, examining the military context of the Scientific Revolution and the scientific context of the Military Revolution. Unlike the classic narratives of the Scientific Revolution that focus on the theories of, and conflicts between, Aristotelian and Platonic worldviews, this volume highlights the emergence of the Archimedean ideal--in which a symbiosis exists between the supply of mechanistic science and the demand for military capability. From a security-studies perspective, this work presents an in-depth study of the central components of military power as well as their dynamic interactions in the political, acquisitional, operational, and tactical domains. The essays in this volume reveal the intellectual and cultural struggles to enhance the capabilities of these components--an exercise in transforming military power that remains relevant for today's armed forces. The volume sets the stage by examining the innovation of gunpowder weaponry in both the Christian and the Islamic states of the late medieval and Renaissance eras. It then explores such topics as the cultural resistance to scientific techniques and the relationship between early modern science and naval power--particularly the intersecting developments in mathematics and oceanic navigation. Other essays address the efforts of early practitioners and theorists of chemistry to increase the power and consistency of gunpowder. The final essays analyze the application of advanced scientific knowledge and Enlightenment ideals to the military engineering and artillery organizations of the eighteenth century. The volume concludes by noting the global spread of the Archimedean ideal during the nineteenth century as an essential means for resisting Western imperialism.