Trigonometric Delights

Trigonometric Delights, by Eli Maor, Princeton University Press, Princeton,    NJ , 1998, xiv + 236 pp. 104 figures, $18.95. ISBN 0-691-05754-0; softcover; http://pup.princeton.edu

Professor Maor has written several books with a slant towards the history of mathematics.  Trigonometric Delights is one of these.   Throughout this book, Maor weaves a fascinating story that combines history, anecdotes, applications, and theory (explained at a non-threatening level).  Sprinkled among the book’s fifteen short chapters are six informative mini-biographies. Every chapter and each mini-biography ends with a list of notes and sources.  The notes are just as interesting to read as the text itself!

In the first three chapters, Professor Maor, introduces the reader to the Ahmes Papyrus and the ancient Egyptian measurement of the seked , which is equivalent to what we now call the cotangent of the angle between the base of a pyramid and its face.  From ancient Egypt , he takes the reader to ancient Greece and Ptolemy’s table of chords found in the great work, the Almagest.  Since the chord of an angle is fundamentally equivalent to the sine of half the angle, the reader has met the first trigonometric table.  Along the way, the reader encounters the influences of the ancient Babylonian astronomical studies and several other ancient Greek mathematicians.  Next the reader travels to sixth century India to meet Aryabhata who first used the sine function.  Almost a thousand years later, the reader becomes acquainted with John Müller, a.k.a. Regiomontanus, who wrote the first comprehensive work in Europe on trigonometry.   The origin of the words degree, radian, and all of the six trigonometric functions are included in these three chapters.   This information is more than sufficient for a brief introduction to the history of trigonometry.

The reader should not stop there, however. The rest of the book provides ample motivation for the past and ongoing importance of trigonometry.  In particular, the fifth and thirteenth chapters deal with the historical squabbles over the shape of the earth and the development of useful maps for navigational purposes.  In these chapters, Maor uses historical context to make an indisputable argument for the indispensability of trigonometry and he accomplishes this in an extremely reader-friendly manner.

Trigonometric Delights is appropriate for supplemental reading in a History of Mathematics class, especially for a group project on the history of trigonometry. At the secondary level, it provides teachers with an interesting source of stories to use as they teach trigonometry to their students. 

Dorothee Jane Blum,  Associate Professor of Mathematics,  Millersville University of Pennsylvania

See also the MAA Review by Sean Bradley.