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Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life--samurai, farmers, and merchants--inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan. Sacred Mathematics is the first book published in the West to fully examine this tantalizing--and incredibly beautiful--mathematical tradition.

Fukagawa Hidetoshi and Tony Rothman present for the first time in English excerpts from the travel diary of a nineteenth-century Japanese mathematician, Yamaguchi Kanzan, who journeyed on foot throughout Japan to collect temple geometry problems. The authors set this fascinating travel narrative--and almost everything else that is known about temple geometry--within the broader cultural and historical context of the period. They explain the sacred and devotional aspects of sangaku, and reveal how Japanese folk mathematicians discovered many well-known theorems independently of mathematicians in the West--and in some cases much earlier. The book is generously illustrated with photographs of the tablets and stunning artwork of the period. Then there are the geometry problems themselves, nearly two hundred of them, fully illustrated and ranging from the utterly simple to the virtually impossible. Solutions for most are provided.

A unique book in every respect, Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries.

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Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound Topics include curved space time as a higher dimension, special relativity and shape of space-time. Accessible to layman but also of interest to specialist. 141 illustrations.
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Price: $4.36 [Notify me when price goes down.]

By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most math-phobic students. Well over four hundred proofs are known to exist, including ones by a twelve-year-old Einstein, a young blind girl, Leonardo da Vinci, and a future president of the United States. Here--perhaps for the first time in English--is the full story of this famous theorem.

Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years before him. He may have been the first to prove it, but his proof--if indeed he had one--is lost to us. Euclid immortalized it as Proposition 47 in his Elements, and it is from there that it has passed down to generations of students. The theorem is central to almost every branch of science, pure or applied. It has even been proposed as a means to communicate with extraterrestrial beings, if and when we discover them. And, expanded to four-dimensional space-time, it plays a pivotal role in Einstein's theory of relativity.

In this book, Eli Maor brings to life many of the characters that played a role in the development of the Pythagorean theorem, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.

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Price: $15.79 [Notify me when price goes down.]

"Trigonometry", a work in the collection of the "Gelfand School Outreach Program", is the result of the successful collaboration between two experienced pre-college teachers, one of whom, I.M. Gelfand, is considered the most distinguished living mathematician. Gelfand's impact on generations of young people, some now mathematicians of renown, continues to be remarkable.

All basic topics in Trigonometry are covered with an emphasis on beautiful illustrations and examples that treat elementary trigonometry as an outgrowth of geometry, but stimulate the reader to think of all of mathematics as a unified subject. The definitions of the trigonometric functions are geometrically motivated. Geometric relationships are rewritten in trigonometric form and extended. The text then makes a transition to a study of the algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions.

Like other I.M. Gel'fand treasures in the program, Algebra, Functions and Graphs, and The Method of Coordinates, Trigonometry is written in an engaging style, and approaches the material in a unique fashion that will motivate students and teachers alike..
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The book is an English adaptation of a classical Russian grade school-level text in solid Euclidean geometry. It contains the chapters Lines and Planes, Polyhedra, Round Solids, which include the traditional material about dihedral and polyhedral angles, Platonic solids, symmetry and similarity of space figures, volumes and surface areas of prisms, pyramids, cylinders, cones and balls. The English edition also contains a new chapter Vectors and Foundations (written by A. Givental) about vectors, their applications, vector foundations of Euclidean geometry, and introduction to spherical and hyperbolic geometries. This volume completes the English adaptation of Kiselev's Geometry whose 1st part ( Book I. Planimetry ), dedicated to plane geometry, was published by Sumizdat in 2006 as ISBN 0977985202.

Both volumes of Kiselev's Geometry are praised for precision, simplicity and clarity of exposition, and excellent collection of exercises. They dominated Russian math education for several decades, were reprinted in dozens of millions of copies, influenced geometry education in Eastern Europe and China, and are still active as textbooks for 7-11 grades. The books are adapted to the modern US curricula by a professor of mathematics from UC Berkeley..
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Students will find all the information covered in the standard textbooks--and more--explained clearly and concisely in this powerful study tool. Unusually detailed, it elucidates all the most difficult-to-grasp concepts that class studies and texts sometimes gloss over. The hundreds of problems with fully explained solutions illuminate important points and teach students sound problem-solving skills. Ideal, also, for independent study..
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Over the years, the text has been shaped and adapted to meet the changing needs of both students and educators. As always, special care was taken to respond to the specific suggestions of users and reviewers through enhanced discussions, new and updated examples and exercises, helpful features, and an extensive package of supplements and study aids. The result is an easy-to-use, comprehensive text that is the best edition yet..
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This book is based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another. In teaching his readers a variety of problem solving techniques as well, the author succeeds in enhancing the readers' hands-on knowledge of mathematics and provides glimpses into the world of research and discovery. The connections between different techniques and areas of mathematics are emphasized throughout and constitute one of the most important lessons this book attempts to impart. This book is interesting and accessible to anyone with a basic knowledge of high school mathematics and a curiosity about research mathematics. The author is a professor at the University of Missouri and has maintained a keen interest in teaching at different levels since his undergraduate days at the University of Chicago. He has run numerous summer programs in mathematics for local high school students and undergraduate students at his university. The author gets much of his research inspiration from his teaching activities and looks forward to exploring this wonderful and rewarding symbiosis for years to come..
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