"e:" The Story of a Number

The Story of a Number

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 1400832349

Category: Mathematics

Page: 248

View: 4997

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.
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To Infinity and Beyond

A Cultural History of the Infinite

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 9780691025117

Category: Mathematics

Page: 284

View: 1911

Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates."--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama."--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics."--Science
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The Pythagorean Theorem

A 4,000-Year History

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 0691148236

Category: Mathematics

Page: 280

View: 9219

The author presents a complex history of the Pythagorean Theorem, examining the earliest evidence of knowledge of the theorem to Einstein's theory of relativity.
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The Joy of x

Die Schönheit der Mathematik

Author: Steven Strogatz

Publisher: Kein & Aber AG

ISBN: 3036992693

Category: Mathematics

Page: 352

View: 444

Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.
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Music by the Numbers

From Pythagoras to Schoenberg

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 1400889898

Category: Mathematics

Page: 176

View: 5552

How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system. Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.
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Venus in Transit

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 9780691048741

Category: Science

Page: 186

View: 3930

For previous sky-watchers, though, transits afforded the only chance to determine the all-important astronomical unit: the mean distance between earth and sun.".
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Gamma

Exploring Euler's Constant

Author: Julian Havil

Publisher: Princeton University Press

ISBN: 1400832535

Category: Mathematics

Page: 296

View: 3252

Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.
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Beautiful Geometry

Author: Eli Maor,Eugen Jost

Publisher: Princeton University Press

ISBN: 1400848334

Category: Mathematics

Page: 208

View: 498

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.
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Trigonometric Delights

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 1400846757

Category: Mathematics

Page: 256

View: 1289

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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Puppets of Nostalgia

The Life, Death, and Rebirth of the Japanese "Awaji Ningyō" Tradition

Author: Jane Marie Law

Publisher: Princeton University Press

ISBN: 1400872952

Category: Social Science

Page: 338

View: 6230

Puppets of Nostalgia is the first major work in any Western language to examine the ritual origins and religious dimensions of puppetry in Japan. In a lucid and engaging style accessible to the general reader, Jane Marie Law describes the "life, death, and rebirth" of awaji ningyo shibai, the unique form of puppet theater of Awaji Island that has existed since the sixteenth century. Puppetry rites on Awaji helped to maintain rigid ritual purity codes and to keep dangerous spiritual forces properly channeled and appeased. Law conducted fieldwork on Awaji, located in Japan's Inland Sea, over a ten-year period. In addition to being a detailed history and ethnography of this ritual tradition, Law's work is, at a theoretical level, a study of the process and meaning of tradition formation, reformation, invention, and revitalization. It will interest scholars in a number of fields, including the history of religions, anthropology, cultural studies, ritual and theater studies, Japanese studies, and social history. Focusing on the puppetry tradition of Awaji Island, Puppets of Nostalgia describes the activities of the island's ritual puppeteers and includes the first English translation of their performance texts and detailed descriptions of their rites. Because the author has lived on Awaji during extended periods of research, the work includes fine attention to local detail and nuanced readings of religious currents in Japan that affect popular religious expression. Illustrated throughout with rare photographs, the book provides an in-depth view of a four-hundred-year-old tradition never so thoroughly revealed to Western readers. Originally published in 1997. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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Symmetry

Author: Hermann Weyl

Publisher: Princeton University Press

ISBN: 9780691023748

Category: Science

Page: 168

View: 9901

Defines symmetry through a discussion of its many uses in a wide variety of fields both academic and natural
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Eine kurze Geschichte der Menschheit

Author: Yuval Noah Harari

Publisher: DVA

ISBN: 364110498X

Category: History

Page: 528

View: 2067

Krone der Schöpfung? Vor 100 000 Jahren war der Homo sapiens noch ein unbedeutendes Tier, das unauffällig in einem abgelegenen Winkel des afrikanischen Kontinents lebte. Unsere Vorfahren teilten sich den Planeten mit mindestens fünf weiteren menschlichen Spezies, und die Rolle, die sie im Ökosystem spielten, war nicht größer als die von Gorillas, Libellen oder Quallen. Vor 70 000 Jahren dann vollzog sich ein mysteriöser und rascher Wandel mit dem Homo sapiens, und es war vor allem die Beschaffenheit seines Gehirns, die ihn zum Herren des Planeten und zum Schrecken des Ökosystems werden ließ. Bis heute hat sich diese Vorherrschaft stetig zugespitzt: Der Mensch hat die Fähigkeit zu schöpferischem und zu zerstörerischem Handeln wie kein anderes Lebewesen. Anschaulich, unterhaltsam und stellenweise hochkomisch zeichnet Yuval Harari die Geschichte des Menschen nach und zeigt alle großen, aber auch alle ambivalenten Momente unserer Menschwerdung.
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Number-Crunching

Taming Unruly Computational Problems from Mathematical Physics to Science Fiction

Author: Paul J. Nahin

Publisher: Princeton University Press

ISBN: 9781400839582

Category: Mathematics

Page: 408

View: 3551

How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions. Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.
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Mathematics in Ancient Iraq

A Social History

Author: Eleanor Robson

Publisher: Princeton University Press

ISBN: 9780691091822

Category: History

Page: 441

View: 1647

"This work is an enormously significant contribution to the history of mathematics. No other work surveys the vast landscape of Mesopotamian mathematics from a position of the modern understanding of the past, incorporating the latest scholarship and yet still managing to be so accessible to nonspecialists. Robson's book is an outstanding guide that can be consulted by anyone interested in the field."--Duncan J. Melville, St. Lawrence University "A very significant contribution to the history of ancient mathematics, and to the history of mathematics in general. I anticipate this book will be very, very useful to readers outside the field and general readers, because it is very clearly and incisively written, it gives clear indications about where to find the primary sources, and it summarizes previous historiography very effectively. There is no comparable book."--Serafina Cuomo, Birkbeck College, London "A truly exciting and highly readable intellectual history of ancient Iraq. Eleanor Robson's "Mathematics in Ancient Iraq" is destined to become a classic. The book will have a wide readership among people interested in Near Eastern archaeology, the origins of writing, the history of education, and the history of science. This is truly a magnificent read."--Gary Urton, Harvard University "This is a wholly original work, the first to integrate all the recent work from the history of mathematics in this area with archaeological scholarship. The result is a remarkably rich portrayal of mathematics in ancient Iraq. The breadth of coverage is striking, both in chronological terms but also in broad intellectual ones. The book is very well written and handsomely illustrated."--Jeremy Gray, The Open University
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Euler's Gem

The Polyhedron Formula and the Birth of Topology

Author: David S. Richeson

Publisher: Princeton University Press

ISBN: 9781400838561

Category: Mathematics

Page: 336

View: 6277

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.
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Von Zeit und Macht

Herrschaft und Geschichtsbild vom Großen Kurfürsten bis zu den Nationalsozialisten

Author: Christopher Clark

Publisher: DVA

ISBN: 3641231639

Category: History

Page: 320

View: 7905

Worauf gründen sich Macht und Herrschaft? Wie entsteht Macht? Wie wird sie begründet und erhalten? Und in welchem Verhältnis stehen Macht und Zeit? Dies sind die großen Fragen, denen sich Christopher Clark hier widmet. Wer Macht hat, verortet sich in der Zeit. ‎Er begreift sich als Teil der Geschichte und schafft damit das Geschichtsbild seiner Epoche. Vier solcher Geschichtsbilder betrachtet dieses Buch: das des Großen Kurfürsten von Brandenburg, Friedrichs II. von Preußen, Bismarcks und der Nationalsozialisten. Geschrieben während der Brexit-Ereignisse, Trumps Präsidentschaft und Putins vierter Amtszeit ist dieses Buch nicht nur ein großes Geschichtswerk, sondern lehrt uns auch viel über unsere eigene Epoche und deren Strukturen von Selbstlegitimation, Machtverständnis und Machterhalt.
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Die Mühlen der Zivilisation

Eine Tiefengeschichte der frühesten Staaten

Author: James C. Scott

Publisher: Suhrkamp Verlag

ISBN: 3518761528

Category: Social Science

Page: 329

View: 2090

Uns modernen Menschen erscheint die Sesshaftigkeit so natürlich wie dem Fisch das Wasser. Wie selbstverständlich gehen wir und auch weite Teile der historischen Forschung davon aus, dass die neolithische Revolution, in deren Verlauf der Mensch seine nomadische Existenz aufgab und zum Ackerbauer und Viehzüchter wurde, ein bedeutender zivilisatorischer Fortschritt war, dessen Früchte wir noch heute genießen. James C. Scott erzählt in seinem provokanten Buch eine ganz andere Geschichte. Gestützt auf archäologische Befunde, entwickelt er die These, dass die ersten bäuerlichen Staaten aus der Kontrolle über die Reproduktion entstanden und ein hartes Regime der Domestizierung errichteten, nicht nur mit Blick auf Pflanzen und Tiere. Auch die Bürger samt ihren Sklaven und Frauen wurden der Herrschaft dieser frühesten Staaten unterworfen. Sie brachte Strapazen, Epidemien, Ungleichheiten und Kriege mit sich. Einzig die »Barbaren« haben sich gegen die Mühlen der Zivilisation gestemmt, sich der Sesshaftigkeit und den neuen Besteuerungssystemen verweigert und damit der Unterordnung unter eine staatliche Macht. Sie sind die heimlichen Helden dieses Buches, das unseren Blick auf die Menschheitsgeschichte verändert.
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Music and the Making of Modern Science

Author: Peter Pesic

Publisher: MIT Press

ISBN: 0262027275

Category: Music

Page: 360

View: 3638

In the natural science of ancient Greece, music formed the meeting place between numbers and perception; for the next two millennia, Pesic tells us in Music and the Making of Modern Science, "liberal education" connected music with arithmetic, geometry, and astronomy within a fourfold study, the quadrivium. Peter Pesic argues provocatively that music has had a formative effect on the development of modern science -- that music has been not just a charming accompaniment to thought but a conceptual force in its own right. Pesic explores a series of episodes in which music influenced science, moments in which prior developments in music arguably affected subsequent aspects of natural science. He describes encounters between harmony and fifteenth-century cosmological controversies, between musical initiatives and irrational numbers, between vibrating bodies and the emergent electromagnetism. He offers lively accounts of how Newton applied the musical scale to define the colors in the spectrum; how Euler and others applied musical ideas to develop the wave theory of light; and how a harmonium prepared Max Planck to find a quantum theory that reengaged the mathematics of vibration. Taken together, these cases document the peculiar power of music -- its autonomous force as a stream of experience, capable of stimulating insights different from those mediated by the verbal and the visual. An innovative e-book edition available for iOS devices will allow sound examples to be played by a touch and shows the score in a moving line.
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The Oxford Handbook of the History of Mathematics

Author: Eleanor Robson,Jacqueline Stedall

Publisher: OUP Oxford

ISBN: 0191607444

Category: Mathematics

Page: 926

View: 1968

This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
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