Geometry Civilized: History, Culture, & Technique

Geometry Civilized: History, Culture and Technique, J.L. Heilbron, 2000. 309 pages, illustrations, problems and exercises, $54.50 paperbound. ISBN 0 19 850690 2. Oxford University Press, 198 Madison Avenue, New York, NY 10016. (800) 451-7556.  www.oup.com/us/

It has been said that the most reproduced pieces of literature in human history are the Bible, the Koran and Euclid’s Elements.  Unlike the first two “otherworldly” texts, the third owes its longevity to a series of authors who kept “trying to get it right.”  To perpetrate knowledge of Euclid’s Elements and make it understandable to a large audience has been a difficult task.  But this time, J. L. Heilbron has “gotten it right.”  His Geometry Civilized is visually appealing, historically informative and mathematically rigorous.  Entertainingly written and beautifully illustrated, this is certainly an enjoyable and satisfying book to both read and work through.  The classical geometry considered covers the material of the Elements: books I – IV and some of book VI.  Both theoretical and applied aspects of plane geometry and trigonometry are considered.  Heilbron includes a wide selection of problems and exercises that span cultures and historical periods.

As the title indicates, the focus of this book is to affirm that geometry is an integral part of human civilization, of human experience both intellectually and aesthetically.  Historical insights provide an understanding of the evolution of the learning and teaching of geometry from that of a mental discipline “worthy of every gentleman” to a haphazard collection of definitions, terms and applied problems.  Along this journey, a reader encounters the 17th century belief that the study of geometry improved morals; A. M. Legendre’s break with tradition in his user-friendly text of 1784; and John Perry’s condemnation of 19th century British geometry teaching as “soul-destroying.”  The journey is enlightening.

Heilbron’s scope of information is impressive.  His writing style is appealing and his problem selection excellent.  This book provides a wonderful example of how history can enliven and reinforce mathematics teaching.  Although the price may be prohibitive for individual purchase, school libraries should obtain a copy.  I highly recommend the reading of this book to all instructors of geometry and trigonometry.

Frank J. Swetz. Professor Emeritus, The Pennsylvania State University