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Trigonometry (Gelfand Mathematical Seminar) (Englisch) Taschenbuch – 4. Oktober 2013

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"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..."


"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


Trigonometry, a basic course in high school which follows algebra and geometry, entails the study of the Pythagorean theorem, right triangles and the ratios within triangles. It is a fundamental pre-calculus topic.


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Amazon.com: HASH(0x9d226e60) von 5 Sternen 15 Rezensionen
66 von 68 Kunden fanden die folgende Rezension hilfreich
HASH(0x9cfd7c90) von 5 Sternen A fascinating treatment of trigonometry. 24. September 2004
Von N. F. Taussig - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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).
56 von 59 Kunden fanden die folgende Rezension hilfreich
HASH(0x9cfdb084) von 5 Sternen Terrific! 6. Oktober 2006
Von LimehouseBlues - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
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!
53 von 60 Kunden fanden die folgende Rezension hilfreich
HASH(0x9cfe7564) von 5 Sternen Outstanding Math Text 14. Juni 2006
Von L. D. Rafey - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
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).
19 von 19 Kunden fanden die folgende Rezension hilfreich
HASH(0x9cfd7cd8) von 5 Sternen Good geometrical approach to trigonometry 7. August 2009
Von sluggo77 - Veröffentlicht auf Amazon.com
Format: Taschenbuch
This book is a very nice change away from the overly analytical approach that most trigonometry texts take nowadays. In my view something is lost when the geometric aspects are not emphasized. There is some fantastic geometry in this book, and I especially liked the connection between the sine addition formula and Ptolemy's theorem for quadrilaterals inscribed in a circle. Those kinds of connections are not only neat in themselves, but I think they help to understand the material better. I think they can spark students' interest more than the dull plug-in-the-numbers types of exercises in most books.

Speaking of the exercises, many of them are excellent. As some other reviewers have mentioned, it's nice to see a book at this level not insult the intelligence of its readers. I wish more elementary math textbooks were like this.

The only criticism I have is that there are lots of errors and typos in the book, enough to make me give it only 4 stars instead of 5. For instance, in Exercise 8 on p.147 it asks the reader to prove that (cos a)^2 <= cos(2a). Of course, that inequality should be reversed. And there are many more annoying little errors like that, which makes me believe that no one actually proofread the book.
12 von 13 Kunden fanden die folgende Rezension hilfreich
HASH(0x9cfe78d0) von 5 Sternen Innovative, clear, well written trigonomety textbook 7. April 2007
Von George C. Johnson - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
I enjoyed this textbook, especially the way some subjects were so well explained. Not only does this text cover a good bit of material, but it also reveals the way in which the author thinks about this subject. I have noticed, both with this text and the previous two which I have commented on, that certain aspects of the subject become much more transparent or understandable when reexamined with a keener mathematical ability than, at least I possessed, when I was first exposed to these subjects in high school. I had no special interest in math at that time. The limited reexposure one has to trigonomety and geometry as one learns new areas of mathematics in college doesn't seem to do justice to these foundation areas of math.
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