Trigonometric Delights

Author : Eli Maor, Department of Mathematics and Statistics, Loyola University, Chicago
ISBN : 0-691-05754-0
Pages : 256
Publication Date : March 1998
Publisher : Princeton University Press

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Book Excerpts:

Trigonometry has always been the black sheep of mathematics. It has a reputation as a dry and difficult subject, "a glorified form of geometry complicated by tedious computation". In this book, author Eli Maor tries to dispel that view. Rejecting the usual descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and an account of its vital contribution to science and social development.

This book begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. It shows how Greek astronomers developed the first true trigonometry. It traces the slow emergence of modern, analytical trigonometry, recounting its origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, readers will see trigonometry at work in, for example, the struggle of the mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; how M. C. Escher used geometric progressions in his art; and how the toy Spirograph uses epicycles and hypocycles.

This book also sketches the lives of some of the figures who have shaped four thousand years of trigonometric history. Readers will meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor -- but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name "the witch of Agnesi." The book is richly illustrated, including rare prints from the author's own collection.

The first nine chapters require only basic algebra and trigonometry; the remaining chapters rely on some knowledge of calculus (no higher than Calculus II). Much of the material should thus be accessible to high school and college students. Aiming for this audience, this book limited the discussion to plane trigonometry, avoiding spherical trigonometry altogether (although historically it was the latter that dominated the subject at first). Some additional historical material -– often biographical in nature -- is included in eight "sidebars" that can be read independently of the main chapters.

Review(s):

Amazon.com

"Anyway, if you're a fairly gifted high school trig student, this book will certainly liven up the subject for you. If you're a college math major, it will be easy reading, and certainly interesting. If you're a teacher, you might find something interesting to entertain your students."

"For all readers, this book offers a fresh perspective. You will see the practical applications; and you will truly learn the purpose of a trigonometric function. If you appreciate graphical representations, you will appreciate this author's approach."

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