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e The Story of a Number

 e   The Story of a Number Author Eli Maor
ISBN-10 9781400832347
Release 2011-10-12
Pages 248
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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.



An Imaginary Tale

An Imaginary Tale Author Paul J. Nahin
ISBN-10 1400833892
Release 2010-02-22
Pages 296
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Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.



Music by the Numbers

Music by the Numbers Author Eli Maor
ISBN-10 9781400889891
Release 2018-05-15
Pages 176
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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.



Dr Euler s Fabulous Formula

Dr  Euler s Fabulous Formula Author Paul J. Nahin
ISBN-10 1400838479
Release 2011-04-25
Pages 416
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In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.



Beautiful Geometry

Beautiful Geometry Author Eli Maor
ISBN-10 9781400848331
Release 2014-01-19
Pages 208
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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.



The Pythagorean Theorem

The Pythagorean Theorem Author Eli Maor
ISBN-10 9780691148236
Release 2010-08-15
Pages 280
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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.



Number Theory and Its History

Number Theory and Its History Author Oystein Ore
ISBN-10 9780486136431
Release 2012-07-06
Pages 400
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Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.



A Source Book in Mathematics

A Source Book in Mathematics Author David Eugene Smith
ISBN-10 9780486158297
Release 2012-05-07
Pages 736
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The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.



A Natural History of Shells

A Natural History of Shells Author Geerat J. Vermeij
ISBN-10 0691001677
Release 1995
Pages 207
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Geerat Vermeij wrote this "celebration of shells" to share his enthusiasm for these supremely elegant creations and what they can teach us about nature. Most other popular books on shells emphasize the identification of species, but Vermeij uses shells as a way to explore major ideas in biology. How are shells built? How do they work? How did they evolve? With these questions in mind, the author lucidly - and charmingly - demonstrates how shells give us insights into the lives of animals in our own day as well as in the distant geological past. As snails, clams, and other molluscs enlarge their shells, they inscribe a detailed record of the everyday events and unusual circumstances that mark their lives. Moreover, the fossil record that chronicles the history of life is replete with shells of extinct species. Vermeij draws on comparisons of shells from different parts of the world and from successive geological periods to argue that predators have played a decisive role in the evolution of shells. Architectural specialization, he argues, is dictated by the risks, rewards, costs, and benefits imposed by predators and competitors on shell-builders living in a dangerous world. This book will be of interest both to amateur shell collectors and to scholars, and its lively review of evolutionary history should prove especially appealing to a general audience.



T rex and the Crater of Doom

 T  rex  and the Crater of Doom Author Walter Alvarez
ISBN-10 9781400847402
Release 2013-06-25
Pages 208
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Sixty-five million years ago, a comet or asteroid larger than Mount Everest slammed into the Earth, inducing an explosion equivalent to the detonation of a hundred million hydrogen bombs. Vaporized detritus blasted through the atmosphere upon impact, falling back to Earth around the globe. Disastrous environmental consequences ensued: a giant tsunami, continent-scale wildfires, darkness, and cold, followed by sweltering greenhouse heat. When conditions returned to normal, half the plant and animal genera on Earth had perished. This horrific chain of events is now widely accepted as the solution to a great scientific mystery: what caused the extinction of the dinosaurs? Walter Alvarez, one of the Berkeley scientists who discovered evidence of the impact, tells the story behind the development of the initially controversial theory. It is a saga of high adventure in remote locations, of arduous data collection and intellectual struggle, of long periods of frustration ended by sudden breakthroughs, of friendships made and lost, and of the exhilaration of discovery that forever altered our understanding of Earth's geological history.



The Irrationals

The Irrationals Author Julian Havil
ISBN-10 9781400841707
Release 2012-07-22
Pages 312
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The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.



To Infinity and Beyond

To Infinity and Beyond Author Eli Maor
ISBN-10 0691025118
Release 1991
Pages 284
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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



A History of pi pi

A History of  pi   pi Author Petr Beckmann
ISBN-10 0880294183
Release 1989
Pages 200
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Documents the calculation, numerical value, and use of the ratio from 2000 B.C. to the modern computer age, detailing social conditions in eras when progress was made.



A Certain Ambiguity

A Certain Ambiguity Author Gaurav Suri
ISBN-10 1400834775
Release 2010-07-01
Pages 296
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While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.



Single Digits

Single Digits Author Marc Chamberland
ISBN-10 9781400865697
Release 2015-06-02
Pages 240
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In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? And, are there really "six degrees of separation" between all pairs of people? Chamberland explores these questions and covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, the number of guards needed to protect an art gallery, problematic election results and so much more. The book's short sections can be read independently and digested in bite-sized chunks—especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem. Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.



The Meaning of the Library

The Meaning of the Library Author Alice Crawford
ISBN-10 9781400865741
Release 2015-06-23
Pages 336
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From Greek and Roman times to the digital era, the library has remained central to knowledge, scholarship, and the imagination. The Meaning of the Library is a generously illustrated examination of this key institution of Western culture. Tracing what the library has meant since its beginning, examining how its significance has shifted, and pondering its importance in the twenty-first century, notable contributors—including the Librarian of Congress and the former executive director of the HathiTrust—present a cultural history of the library. In an informative introduction, Alice Crawford sets out the book's purpose and scope, and an international array of scholars, librarians, writers, and critics offer vivid perspectives about the library through their chosen fields. The Meaning of the Library will appeal to all who are interested in this vital institution's heritage and ongoing legacy.



Trigonometric Delights

Trigonometric Delights Author Eli Maor
ISBN-10 9781400846757
Release 2013-03-13
Pages 256
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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.