A collection of inter-connected topics in areas of mathematics which particularly interest the author, ranging over the two millennia from the work of Archimedes to the "Werke" of Gauss. The book is intended for those who love mathematics, including undergraduate students of mathematics, more experienced students and the vast unseen host of amateur mathematicians. It is equally a useful source of material for those who teach mathematics.

Archimedes to Hawking takes the reader on a journey across the centuries as it explores the eponymous physical laws--from Archimedes' Law of Buoyancy and Kepler's Laws of Planetary Motion to Heisenberg's Uncertainty Principle and Hubble's Law of Cosmic Expansion--whose ramifications have profoundly altered our everyday lives and our understanding of the universe. Throughout this fascinating book, Clifford Pickover invites us to share in the amazing adventures of brilliant, quirky, and passionate people after whom these laws are named. These lawgivers turn out to be a fascinating, diverse, and sometimes eccentric group of people. Many were extremely versatile polymaths--human dynamos with a seemingly infinite supply of curiosity and energy and who worked in many different areas in science. Others had non-conventional educations and displayed their unusual talents from an early age. Some experienced resistance to their ideas, causing significant personal anguish. Pickover examines more than 40 great laws, providing brief and cogent introductions to the science behind the laws as well as engaging biographies of such scientists as Newton, Faraday, Ohm, Curie, and Planck. Throughout, he includes fascinating, little-known tidbits relating to the law or lawgiver, and he provides cross-references to other laws or equations mentioned in the book. For several entries, he includes simple numerical examples and solved problems so that readers can have a hands-on understanding of the application of the law. A sweeping survey of scientific discovery as well as an intriguing portrait gallery of some of the greatest minds in history, this superb volume will engage everyone interested in science and the physical world or in the dazzling creativity of these brilliant thinkers.

Many of the things you know about science began with Archimedes. What was so unusual about a man who spent almost his whole life on one small island, more than two thousand years ago? Many things about Archimedes were unusual. His mind was never still, but was always searching for something that could be added to the sum of things that were known in the world. No fact was unimportant; no problem was dull. Archimedes worked not only in his mind, but he also performed scientific experiments to gain knowledge and prove his ideas.

Many of us know little about Archimedes other than his "Eureka" exclamation upon discovering that he could immerse an object in a full tub of water and measure the spillage to determine the object's weight. That seemingly simple observation not only proved to King Hieron II of Syracuse that a certain amount of silver had been used in what was supposed to be his solid-gold crown, it established the key principles of buoyancy that govern the flotation of hot-air balloons, ships, and denizens of the sea. Archimedes had a profound impact on the development of mathematics and science: from square roots to irrigation devices; planetariums to the stability of ships; polyhedra to pulleys; number systems to levers; the value of pi to the size of the universe. Yet this same cerebral man developed machines of war so fearsome, they might have sprung from a devil's darkest imagination - indeed, weapons that held at bay the greatest army of antiquity. Ironically, Archimedes' reputation swelled to mythic proportions in the ancient world for his feats of engineering: the hand-cranked irrigation device, commonly known as "Archimedes' screw," and his ingenuous use of levers, pulleys, and ropes to pull, single-handedly, a fully laden ship! His treatises, rediscovered after a thousand years of collective amnesia in Europe, guided nascent thinkers out of the Dark Ages and into the Renaissance. Indeed, Archimedes' cumulative record of achievement-both in breadth and sophistication-places him among the exalted ranks of Aristotle, Leonardo da Vinci, Isaac Newton, and Albert Einstein. Eureka Man brings to life for general readers the genius of Archimedes, offering succinct and understandable explanations of some of his more important discoveries and innovations.

This classic study by the eminent Dutch historian of science E. J. Dijksterhuis (1892-1965) presents the work of the Greek mathematician and mechanical engineer to the modern reader. With meticulous scholarship, Dijksterhuis surveys the whole range of evidence on Archimedes' life and the 2000-year history of the manuscripts and editions of the text, and then undertakes a comprehensive examination of all the extant writings. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

​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.

At a moment of great discovery, one Big Idea can change the world... The greatest mathematician of his time, Archimedes transformed the development of early maths. But it is his revolutionary insights into mechanical science for which he is so revered, inventing the fulcrum and lever, pulley and water pump, among other technological advances that changed the course of history. Archimedes & the Fulcrum is a captivating and easily digestible investigation into the legendary life and work of the greatest mathematical mind the world had seen, up until his tragic death at the hands of the Romans. Single-handedly launching a 4,000 ton ship, calculating volumes and perfect spirals, laying the foundations of theoretical physics and inventing military weaponry as a seventy-year-old, Archimedes' Big Idea was so much more than his famed leap from his bath, shouting 'Eureka!' The Big Idea series is a fascinating look at the greatest advances in our scientific history, and at the men and women who made these fundamental breakthroughs.