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A work of morality, politics, criticism will be more elegant, other things being equal, if it is shaped by the hand of geometry.
Preface sur l'Utilite des Mathematiques et de la Physique, 1729.
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Consortium's Historical Notes
Consortium's Historical Notes: Mathematics Through the Ages, COMAP, 1992. 90pp.,$13.00, paper. ISBN 0-912843-24-1. COMAP, Inc., 57 Bedford Street, Suite 210, Lexington, MA 02173.(800)-772-6627, email@example.com.
Consortium is one of the few existing periodicals in mathematics education which has maintained a regular column on the history of mathematics. Historical Notes is composed of twenty-six of those articles published between Spring 1985 and Summer 1992. Each article is two to six pages long. There is an index on the last page of the collection. Eleven of the articles were contributed by Joseph W. Dauben of the CUNY Graduate Center. His articles were written in a fairly casual style, highly accessible to the layman. However, none contain a bibliography. They cover basic topics such as simple geometry, counting, and the calendar. His last five articles introduce the idea of infinity, concentrating primarily on the work of Georg Cantor. Dauben is acknowledged as an expert on this mathematician. I can think of few people more qualified to discuss Cantor and his work.
Eight articles are by Richard L. Francis. All but one of these contains a bibliography. The articles themselves vary in mathematical level and interest appeal. They include topics as mundane as Inauguration days and as important as solving higher degree equations. As with the Dauben selection, Francis finally settles down to focus on his particular mathematical hero of choice, Karl Gauss. In part, Francis’s articles were written with Gauss in mind. His final article on the three great problems of antiquity is well written and highly recommendable. Both Dauben and Francis have served as editors for the historical feature in Consortium.
The remaining seven articles were contributed by: Karen Doyle Watson (2), Kaila Katz, John P. Pommersheim, William Simpson, Frank Swetz, with one co-authored by Stephanos Gialamas and Miriam K. McCann. Watson, in her wonderful article on Non-Euclidean geometry, supplies a nice bibliography. The articles written by Simpson on quaternions and Swetz on Chinese mathematics provide excellent introductions to those topics. The other articles range in quality from average to uninspiring. This is, in fact, the major problem with the collection as a whole. All the articles are included for the sake of completeness but one wonders about the selection process, which accepted work of such varying quality and importance. One strength of the collection is the emphasis on vocabulary and notational development. At the modest price of $13 this collection can be a good resource for teachers who already have some knowledge of the history of mathematics.
Jim Kiernan, Adjunct Professor, Brooklyn College, CUNY