Trigonometry [Paperback]

I.M. Gelfand (Author), Mark Saul (Author)

Book Description

ISBN-10: 0817639144 | ISBN-13: 978-0817639143 | Publication Date: June 8, 2001 | Edition: 1

Trigonometry, a work in the collection of the Gelfand School Program, is the result of a collaboration between two experienced pre-college teachers, one of whom, I.M. Gelfand, is considered to be among our most distinguished living mathematicians. His impact on generations of young people, some now mathematicians of renown, continues to be remarkable. Trigonometry covers all the basics of the subject through beautiful illustrations and examples. The definitions of the trigonometric functions are geometrically motivated. Geometric relationships are rewritten in trigonometric form and extended. The text then makes a transition to the study of algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject. Like other I.M. Gelfand treasures in the program—Algebra, Functions and Graphs, and The Method of Coordinates—Trigonometry is written in an engaging style, and approaches the material in a unique fashion that will motivate students and teachers alike. From a review of Algebra, I.M. Gelfand and A. Shen, ISBN 0-8176-3677-3: "The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gel'fand and Shen. There are specific 'practical' problems but there is much more development of the ideas.... [The authors] have shown how to write a serious yet lively book on algebra." —R. Askey, The American Mathematics Monthly  

Editorial Reviews

Review

"Cover[s] all of the basic topics that a high school or beginning university student should be expected to know.... There are...some nice touches; for example, a nice informal discussion showing that the sine of an angle in a right triangle does not depend on whether the sides are measured in inches or centimeters..." —Choice "Covers all the basics of the subject through beautiful illustrations and examples…. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject." — L'enseignement Mathématique "As a teacher I enjoyed this book enormously and I will doubtless borrow many of the plums to spice up my lessons…. [For] that ideal student who is to be prepared to be challenged to think what the subject is really about, and has the patience to excavate the basic ideas for all they are worth before jumping on to the next chapter, it should prove to be a godsend." —The Mathematical Gazette "The authors tried to explain the results of trigonometry as simply as possible…. The exercises include a few problems of each routine type. Most of the problems exhibit a new aspect of the technique or object under discussion. One of the goals of this book is to prepare students for a course in calculus. We recommend it for teachers and students." —Publicationes Mathematicae

Product Details

• Paperback: 239 pages
• Publisher: Birkhäuser Boston; 1 edition (June 8, 2001)
• Language: English
• ISBN-10: 0817639144
• ISBN-13: 978-0817639143
• Product Dimensions: 8.9 x 6 x 0.5 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #226,021 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

54 of 55 people found the following review helpful:

5.0 out of 5 stars A fascinating treatment of trigonometry., September 23, 2004

By 

N. F. Taussig (Bronx, NY) - See all my reviews
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This review is from: Trigonometry (Paperback)

This text, which is designed as a supplement to a trigonometry course, is noteworthy for the clarity of its explanations, the connections it draws between trigonometry and other mathematical topics, its many challenging problems, and its numerous worked and illustrated examples. Of particular interest are the appendices to the later chapters in which the authors relate trigonometry to Pythagorean triples, use sequences of trigonometric functions to approximate pi, and introduce Fourier series.

After reviewing the geometry of the triangle, the authors cover right triangle trigonometry, the relationship between trigonometry and the geometry of the triangle, unit circle trigonometry, trigonometric formulas and identities, graphs of trigonometric functions, and inverse trigonometric functions. The authors make every effort to explain why the results hold and how to use them. Rather than presenting a self-contained treatment, the authors make every effort to connect trigonometry with other branches of mathematics, thereby providing the reader with many fascinating insights.

The problems are designed to be challenging. The reader who diligently studies the numerous worked examples in the text and works through the problems will acquire considerable knowledge of the subject. Solutions to the problems are not provided in the text.

I also highly recommend the other texts in the Gelfand School Outreach Program. They include The Method of Coordinates, Algebra, and Functions and Graphs (Dover Books on Mathematics).

39 of 42 people found the following review helpful:

5.0 out of 5 stars Terrific!, October 5, 2006

By 

Clifford Stoll (Berkeley, CA United States) - See all my reviews
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This review is from: Trigonometry (Paperback)

Finally - a trig book that doesn't talk down to students. Gelfand treats his readers as intellegent, curious, and competent. This goes far ... especially with kids.

Most other trig books are written by educational consultants who view the subject as a odorous swamp that you have to slog through. They distract the reader with glitzy graphics and useless photos. No such chartjunk here. It's from someone who loves the subject, and places the mathematics first.

I feel like an avuncular mathematician is showing me the delights of trig ... indeed, he seems to revel in sines, cosines, and tangents. Several of the problems have tickled my 10 year old son: "Dad! Did you know that the area under the first half of the sine curve is exactly 2?"

Aaah. Now *that's* a great trig book!

37 of 42 people found the following review helpful:

5.0 out of 5 stars Outstanding Math Text, June 14, 2006

By 

L. D. Rafey "math'nmore" (Ft. Walton Beach, FL) - See all my reviews
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This review is from: Trigonometry (Paperback)

I rarely compose reviews even if I happen to really appreciate a book. But THIS is one of those rare exceptions!Gelfand (who also happens to rank among the 20th Century's most renowned and prolific Mathematicians ... I noticed that no reviewer has mentioned this little fact) has written an exceptionally clear and concise, easy to read and to digest text concerning Trigonometry with advancement to higher education in mind. The perfectly logical format and development is novel, very inspiring, coaxing the reader to read on and on and one truly begins to learn right from the first sentence. The reader requires little in the way of prior knowledge and yet, I am convinced, will come away with an enthusiasm for this subject (and hopefully for Mathematics in general).
I am a member of a Mathematical Honor Society and of the Mathematical Association of America but I must confess that I was a poor math student, had some very poor teachers and, thanks to some inspiring individuals along the way, managed to discover the real magic and beauty of Math before it was too late (although I have spent the better portion of my professional life compensating for the failures of my former teachers!).
This text represents the way Math should be taught in schools. I believe that any frustrated math student will benefit from this text (and probably the other texts also by Gelfand).