Search Loci: Convergence:
Whoever ... proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured.
J Heidrich (ed.) Albrecht Durer's schriftlicher Nachlass Berlin, 1920.
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Great Moments in Mathematics Before 1650
Great Moments in Mathematics Before 1650, Howard Eves, 1983, 270 pages, $30.95 ($25.95 if MAA member) paper, ISBN 0-88385-310-8, The Mathematical Association of America, 800-331-1622, www.maa.org .http://www.maa.org
If you teach at the secondary level and are interested in using material about the history of mathematics in your classroom, Howard Eves’ Great Moments in Mathematics Before 1650 would be a great addition to your bookshelf. The book consists of 20 chapters each dedicated to a “Great Moment in Mathematics”. These moments range from the origins of counting at the dawn of civilization to the invention of analytic geometry in 1637. Each moment is described in some detail and includes many interesting facts about the people involved. They are very readable accounts of the mathematics at a level that a good high school senior could understand. Each moment is accompanied by a comprehensive problem set. Many of the great moments relate to what is currently being taught in schools today. For example, there are chapters which focus on the origins of the Pythagorean Theorem, the creation of Euclid’s Elements, Ptolemy’s construction of a table of chords which led to what we know now as trigonometry, the development of algebra as we know it, and the union of geometry and algebra in the form of analytic geometry. The problem sets are extensive and there is a collection of hints for the more difficult ones. These problems are a great source of interesting non-routine exercises related to what we currently teach. They also can be used as a source of interesting problems supported by the use of technology. For example, Eves’ description of the development of algebraic solutions for cubic and quartic equations suggests good problems that can be explored using a computer algebra system, such as that found on the TI-89 calculator or in software packages such as Mathematica and Maple. This book is not just for teachers but also for anyone who enjoys mathematics and is interested in how many of the important ideas were developed. After finishing reading this I am sure that, like I did, you will jump right into Eves’ Great Moments in Mathematics Since 1850.
Jon Choate, Co-Head Mathematics Dept., Groton School, Groton, MA