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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, 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 paperwe see how M. C. Escher used geometric progressions in his artand 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 na

Trigonometry. --- Trigonométrie --- Trigonometry --- #WWIS:AGGR --- Geometry --- Mathematics --- goniometrie --- driehoeksmeting --- geometrie --- Trigonométrie --- Trig (Trigonometry)

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By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most math-phobic students. Well over four hundred proofs are known to exist, including ones by a twelve-year-old Einstein, a young blind girl, Leonardo da Vinci, and a future president of the United States. Here--perhaps for the first time in English--is the full story of this famous theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years before him. He may have been the first to prove it, but his proof--if indeed he had one--is lost to us. Euclid immortalized it as Proposition 47 in his 'Elements', and it is from there that it has passed down to generations of students. The theorem is central to almost every branch of science, pure or applied. It has even been proposed as a means to communicate with extraterrestrial beings, if and when we discover them. And, expanded to four-dimensional space-time, it plays a pivotal role in Einstein's theory of relativity. In this book, Eli Maor brings to life many of the characters that played a role in the development of the Pythagorean theorem, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.

Pythagorean theorem --- History. --- Pythagoras' theorem --- Pythagorean proposition --- Theorem, Pythagorean --- Geometry, Plane --- History --- Pythagore, théorème de --- Histoire

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e (The number) --- Number theory --- Napier, John --- e [The number ] --- E (The number). --- Musique. --- Music. --- Bernoulli, Johann --- Bernoulli, Jean, --- Exponential functions. --- Fonctions exponentielles. --- Bernoulli, Jakob, --- Bernoulli, Jacques --- Euler, Leonhard --- Euler, Leonhard, --- Logarithms. --- Logarithmes. --- Fonctions exponentielles --- Histoire des mathematiques --- E (le nombre) --- Musique --- Theorie --- 18e siecle

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The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

e (The number) --- Napier number --- Number, Napier --- Logarithmic functions --- Transcendental numbers