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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.

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.

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.

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.

Euler s Gem

Euler s Gem Author David S. Richeson
ISBN-10 0691126771
Release 2008
Pages 317
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Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to giant all-carbon molecules. "Euler's Gem" tells the illuminating story of this indispensable mathematical idea. Line drawings and tables throughout.

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

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.

The Little Big Number

The Little Big Number Author Dirk Philipsen
ISBN-10 9781400865529
Release 2015-05-26
Pages 416
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In one lifetime, GDP, or Gross Domestic Product, has ballooned from a narrow economic tool into a global article of faith. As The Little Big Number demonstrates, this spells trouble. While economies and cultures measure their performance by it, GDP only measures output. It ignores central facts such as quality, costs, or purpose. Sustainability and quality of life are overlooked. Losses don't count. The world can no longer afford GDP rule—GDP ignores real development. Dirk Philipsen demonstrates how the history of GDP reveals unique opportunities to fashion smarter goals and measures. The Little Big Number explores a possible roadmap for a future that advances quality of life rather than indiscriminate growth.

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.

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.

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.

Life on a Young Planet

Life on a Young Planet Author Andrew H. Knoll
ISBN-10 9781400866045
Release 2015-03-22
Pages 288
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Australopithecines, dinosaurs, trilobites--such fossils conjure up images of lost worlds filled with vanished organisms. But in the full history of life, ancient animals, even the trilobites, form only the half-billion-year tip of a nearly four-billion-year iceberg. Andrew Knoll explores the deep history of life from its origins on a young planet to the incredible Cambrian explosion, presenting a compelling new explanation for the emergence of biological novelty. The very latest discoveries in paleontology--many of them made by the author and his students--are integrated with emerging insights from molecular biology and earth system science to forge a broad understanding of how the biological diversity that surrounds us came to be. Moving from Siberia to Namibia to the Bahamas, Knoll shows how life and environment have evolved together through Earth's history. Innovations in biology have helped shape our air and oceans, and, just as surely, environmental change has influenced the course of evolution, repeatedly closing off opportunities for some species while opening avenues for others. Readers go into the field to confront fossils, enter the lab to discern the inner workings of cells, and alight on Mars to ask how our terrestrial experience can guide exploration for life beyond our planet. Along the way, Knoll brings us up-to-date on some of science's hottest questions, from the oldest fossils and claims of life beyond the Earth to the hypothesis of global glaciation and Knoll's own unifying concept of ''permissive ecology.'' In laying bare Earth's deepest biological roots, Life on a Young Planet helps us understand our own place in the universe--and our responsibility as stewards of a world four billion years in the making. In a new preface, Knoll describes how the field has broadened and deepened in the decade since the book's original publication.

Strange Glow

Strange Glow Author Timothy J. Jorgensen
ISBN-10 9781400880522
Release 2016-02-23
Pages 512
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More than ever before, radiation is a part of our modern daily lives. We own radiation-emitting phones, regularly get diagnostic x-rays, such as mammograms, and submit to full-body security scans at airports. We worry and debate about the proliferation of nuclear weapons and the safety of nuclear power plants. But how much do we really know about radiation? And what are its actual dangers? An accessible blend of narrative history and science, Strange Glow describes mankind's extraordinary, thorny relationship with radiation, including the hard-won lessons of how radiation helps and harms our health. Timothy Jorgensen explores how our knowledge of and experiences with radiation in the last century can lead us to smarter personal decisions about radiation exposures today. Jorgensen introduces key figures in the story of radiation—from Wilhelm Roentgen, the discoverer of x-rays, and pioneering radioactivity researchers Marie and Pierre Curie, to Thomas Edison and the victims of the recent Fukushima Daiichi nuclear power plant accident. Tracing the most important events in the evolution of radiation, Jorgensen explains exactly what radiation is, how it produces certain health consequences, and how we can protect ourselves from harm. He also considers a range of practical scenarios such as the risks of radon in our basements, radiation levels in the fish we eat, questions about cell-phone use, and radiation's link to cancer. Jorgensen empowers us to make informed choices while offering a clearer understanding of broader societal issues. Investigating radiation's benefits and risks, Strange Glow takes a remarkable look at how, for better or worse, radiation has transformed our society.

Number Crunching

Number Crunching Author Paul J. Nahin
ISBN-10 1400839580
Release 2011-08-08
Pages 408
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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.