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Trigonometric Delights (Princeton Science Library) [Englisch] [Taschenbuch]

Eli Maor

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15. März 2013 Princeton Science Library
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights. Maor, whose previous books have demystified the concept of infinity and the unusual number "e," begins by examining the "proto-trigonometry" of the Egyptian pyramid builders. He shows how Greek astronomers developed the first true trigonometry. He traces the slow emergence of modern, analytical trigonometry, recounting its colorful origins in Renaissance Europe's quest for more accurate artillery, more precise clocks, and more pleasing musical instruments. Along the way, we see trigonometry at work in, for example, the struggle of the famous mapmaker Gerardus Mercator to represent the curved earth on a flat sheet of paper; we see how M. C. Escher used geometric progressions in his art; and we learn how the toy Spirograph uses epicycles and hypocycles. Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We 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. Trigonometric Delights will change forever our view of a once dreaded subject.

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Trigonometric Delights (Princeton Science Library) + Beautiful Geometry + The Pythagorean Theorem: A 4,000-Year History (Princeton Science Library)
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"Maor's presentation of the historical development of the concepts and results deepens one's appreciation of them, and his discussion of the personalities involved and their politics and religions puts a human face on the subject. His exposition of mathematical arguments is thorough and remarkably easy to understand. There is a lot of material here that teachers can use to keep their students awake and interested. In short, Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it."--George H. Swift, American Mathematics Monthly "[Maor] writes enthusiastically and engagingly... Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, MAA Online "Maor clearly has a great love of trigonometry, formulas and all, and his enthusiasm shines through... If you always wanted to know where trigonometry came from, and what it's good for, you'll find plenty here to enlighten you."--Ian Stewart, New Scientist "This book will appeal to a general audience interested in the history of mathematics. I highly recommend [it] to teachers who would like to ground their lessons in the sort of mathematical investigations that were undertaken throughout history."--Richard S. Kitchen, Mathematics Teacher

Über den Autor und weitere Mitwirkende

Eli Maor teaches the history of mathematics at Loyola University in Chicago. He is the author of "To Infinity and Beyond", "e: The Story of a Number", "Venus in Transit", and "The Pythagorean Theorem: A 4,000-Year History".

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4.0 von 5 Sternen An ideal book for high school mathematics teachers 3. Januar 2014
Von Jordan Bell - Veröffentlicht auf
Trigonometry is the study of relations between angles and lengths. Indeed SOH CAH TOA and trigonometric identities are part of the subject, but there is much more to the subject than what you may have learned in high school. If you have trouble remembering whether sin(0)=0 or cos(0)=0, you can fix this either by using your calculator to find that sin(0)=0, or you can memorize sin(0)=0 (which at least stores something in your brain, and if the memorization is done severely enough it will indeed last your life), or finally by having such a comprehensive understanding of trigonometry that mixing up sin(0)=0 and cos(0)=0 would be like forgetting whether sugar or salt tastes sweet.

Learning the history of a subject along with learning the content of the subject itself helps you remember material and makes the material feel alive. It also helps with pacing the rate at which you absorb careful mathematical proofs. After reading even a page or two of a serious proof you need time to let the material settle before going on to the next proof. Many in the discipline of mathematics today think of theorems and proofs as real mathematics and anything else as motivation that one should learn to do without. This is wrong; things are true whether or not someone has written them down and things will wait for us to find them out. Anything that helps people absorb mathematics into their brains is real mathematics. (Thus using a calculator to calculate values of trigonometric functions is a skill but not a mathematical skill as it doesn't involve putting mathematics in your brain, any more than idly chatting while playing a video game is practice in public speaking.) Of course talking about the provenance of the Rhind Papyrus has no mathematical content. But it is fun to read about, and it gives you hooks in your mind to remember things about the papyrus. Likewise, learning the etymology of mathematical terms such as sine and degree gives us more ways to summon mathematics from our memory.

This is not a serious work of history like the works of T. L. Heath, D. T. Whiteside, D. H. Fowler, W. K. Bühler, J. E. Hofmann, André Weil, Lucio Russo or Clifford Truesdell, and a careful writer should not use this as a reference. But it is a fun book that shows the reader many different theorems in trigonometry they may not have seen before, and gives the reader an outline of the history of the subject that can be filled in by reading more detailed books.

If you just skim this book, I encourage you to at least read the chapter on Regiomantanus, which presents a problem posed by him: "At what point on the ground does a perpendicularly suspended rod appear largest?" Aside from being a question that doesn't seem contrived, it can involve the arithmetic mean-geometric mean inequality and calculus.
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