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on February 25, 2000
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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on October 15, 2009
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.
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on May 1, 2012
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.
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