Archimedes: What Did He Do Beside Cry Eureka? (Classroom Resource Materials) by Sherman Stein (PDF)

Description

Many people have heard two things about Archimedes: he was the greatest mathematician of antiquity, and he ran naked from his bath crying ‘Eureka!’. However, few people are familiar with the actual accomplishments upon which his enduring reputation rests, and it is the aim of this book to shed light upon this matter. Archimedes’ ability to achieve so much with the few mathematical tools at his disposal was astonishing. He made fundamental advances in the fields of geometry, mechanics, and hydrostatics. No great mathematical expertise is required of the reader, and the book is well illustrated with over 100 diagrams. It will prove fascinating to students and professional mathematicians alike.

User’s Reviews

Editorial Reviews: Review Highly recommended to anyone interested in mathematics and its history, as it is an eye-opening and a great read. — Choice Magazine, March 2000

The author’s writing style is elegant yet logical… In short, the book is eminently readable… Highly recommended for all teachers of mathematics. –The Australian Mathematics TeacherThe book is most timely, appearing, as it does, so soon after the October 1998 auction for $2 million of the Archimedes Palimpsest, and in fact, while the Palimpsest was on exhibition at the Walters Art Gallery in Baltimore. By the end of 155 pages, the reader is convinced that Archimedes deserves his position on Gauss’ pedastal. More books like Stein’s book on Archimdes would be welcome. –Ed SandifurThe topics in this volume are treated caraefully clearly, and with many illustrations. –AAAS, Science Books and Films/May-June 2000 Book Description This book looks carefully at Archimedes’ fundamental advances in the fields of geometry, mechanics, and hydrostatics. Book Description Archimedes’ enduring reputation rests upon his ability to achieve so much with the few mathematical tools at his disposal. He made fundamental advances in the fields of geometry, mechanics, and hydrostatics, and this book is devoted to his work. It will prove fascinating to students and professional mathematicians alike. About the Author Sherman Stein received his Ph.D. from Columbia University. After a one-year instructorship at Princeton University, he joined the faculty at the University of California, Davis, where he taught until 1993. His main mathematical interests are in algebra, combinatorics, and pedagogy. He has been the recipient of two MAA awards: the Lester R. Ford Award for Mathematical Exposition, and the Beckenbach Book Prize for Algebra and Tiling (with Sándor Szabó, published by MAA). He has also received The Distinguished Teaching Award from the University of California, Davis, and an honorary Doctor of Humane Letters from Marietta College. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Archimedes is one of the greatest mathematicians to have lived. He worked in geometry, physics, and ballistics. His work has spanned the ages. What’s more, he did his work without the tools we have today. With tools I don’t mean calculators, or computers. I mean without the descriptive mathematical language of equations and the number systems of today. Archimedes held his ideas in total within his mind and was able to solve problems that would take calculus today. And he didn’t have calculus either.This book describes many of the problems Archimedes solved and how he approached the problems. We find center of gravity and buoyancy, for example. Each chapter is a thorough discussion of the problems, Archimedes’s solution, and, at times, the importance of the problem. The book is slim and handy to take with you for reading whenever you find a few minutes. In that sense, the chapters are short enough to read quickly (although you’ll want to spend time going through the equations) so that you get a good view of the approach taken.Finally, the author takes you on a few tangents to explain how Archimedes viewed mathematics and here, too, you see the greatness of Archimedes. He was meticulous and precise in his work. He didn’t publish his methods until he was certain of them and he corresponded with other mathematicians to work out problems and discuss various topics. What a good insight into the past and, for us, a good place to draw lessons for our own work.

⭐Flipping through the pages quickly you will see over 120 illustrations! We know what geometry textbooks look like, over 120 illustrations. Well fear not, unlike a textbook the author, Sherman Stein, articulates Archimedes’ thoughts, assumptions, theorems, proofs, and correspondences as if the great mathematician was assisting you, over-the-shoulder. The theories build upon each other, connecting each major contribution linking chapters. A basic understanding of math (9th grade equivalent) will allow a seamless understanding and appreciation for Archimedes and his contributions to mechanics, naval architecture, and mathematics. Great for math teachers who want to explore the early geometric proofs to surface area and volume of circles, spheres, and cylinders. Also covers the lever (mathematically), center of gravity, floating bodies, and mechanical method to finding volume of a paraboloid. Will keep this book on the book shelf, not the old textbook pile.

⭐The author’s aim is to make what he views “as Archimedes’ most mathematically significant discoveries accessible to the busy people of the mathematical community.” In this he succeeds admirably. The book is not only understandable by anyone who “recognizes the equation of a parabola,” but is also very well written in a style that brings out the beauty of the mathematical ideas discussed, as well as the power of Archimesdes’ creativity. As the author points out, the book treats most of Archimedes’ mathematical discoveries. The presentation cleverly integrates Archimedes’ own writing with the author’s modern explanation of the ancient discoveries. Frequently, before a main idea is introduced, a quotation from Archimedes’ own writing is presented in which the master reveals his thinking about what he had accomplished in that particular topic.In addition to providing the scientific community with a detailed account of Archimedes’ main mathematical discoveries and an insight into the ancient master’s thinking, this book, I believe, can be useful in the classroom in a variety of ways. The most obvious use, of course, would be in designating it as a textbook or a reference in courses on the history of calculus or, more generally, on the history of mathematics. But it would also make an excellent textbook for a course on axiomatic mathematics: the book starts with a few axioms from which Archimedes had developed the theory of center of gravity and used it throughout a good part of the material covered in the book, including the development of the volumes of a paraboloid and a sphere and the theory of floating bodies.In sum, this is an excellent book that should be within reach of any person interested in mathematics or science.

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