Euler S Gem

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Euler's Gem

David S. Richeson
Euler s Gem Book PDF

Author : David S. Richeson
Publisher : Princeton University Press
Page : 336 pages
File Size : 52,5 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9780691191379

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Euler's Gem by David S. Richeson Pdf

How a simple equation reshaped mathematics 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 theorem is so simple it can be explained to a child. 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. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’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. This paperback edition contains a new preface by the author.

Euler's Gem

David S. Richeson
Euler s Gem Book PDF

Author : David S. Richeson
Publisher : Princeton University Press
Page : 336 pages
File Size : 55,7 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9780691191997

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Euler's Gem by David S. Richeson Pdf

How a simple equation reshaped mathematics 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 theorem is so simple it can be explained to a child. 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. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’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. This paperback edition contains a new preface by the author.

Euler's Gem

David Richeson
Euler s Gem Book PDF

Author : David Richeson
Publisher : Unknown
Page : 336 pages
File Size : 55,6 Mb
Release : 2012
Category : Mathematics
ISBN : OCLC:1105789358

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Euler's Gem by David Richeson Pdf

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.

Dr. Euler's Fabulous Formula

Paul J. Nahin
Dr Euler s Fabulous Formula Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 416 pages
File Size : 51,7 Mb
Release : 2017-04-04
Category : Mathematics
ISBN : 9780691175911

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Dr. Euler's Fabulous Formula by Paul J. Nahin Pdf

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.

Tales of Impossibility

David S. Richeson
Tales of Impossibility Book PDF

Author : David S. Richeson
Publisher : Princeton University Press
Page : 450 pages
File Size : 41,7 Mb
Release : 2021-11-02
Category : Mathematics
ISBN : 9780691218724

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Tales of Impossibility by David S. Richeson Pdf

A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

Euler

William Dunham
Euler Book PDF

Author : William Dunham
Publisher : American Mathematical Society
Page : 185 pages
File Size : 40,8 Mb
Release : 2022-01-13
Category : Mathematics
ISBN : 9781470466183

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Euler by William Dunham Pdf

Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

Mathematicians

Mariana Cook
Mathematicians Book PDF

Author : Mariana Cook
Publisher : Unknown
Page : 212 pages
File Size : 49,7 Mb
Release : 2009-06-21
Category : Mathematics
ISBN : UOM:39076002867351

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Mathematicians by Mariana Cook Pdf

Photographs accompanied by autobiographical text written by each mathematician.

Birds and Frogs

Freeman J Dyson
Birds and Frogs Book PDF

Author : Freeman J Dyson
Publisher : World Scientific Publishing Company
Page : 375 pages
File Size : 54,7 Mb
Release : 2015-03-25
Category : Mathematics
ISBN : 9789814602877

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Birds and Frogs by Freeman J Dyson Pdf

This book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990–2014. The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity — Is a Graviton Detectable? Various possible graviton-detectors are examined. This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world.

Objects of Desire

Clare Sestanovich
Objects of Desire Book PDF

Author : Clare Sestanovich
Publisher : Vintage
Page : 224 pages
File Size : 43,7 Mb
Release : 2021-06-29
Category : Fiction
ISBN : 9780593318102

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Objects of Desire by Clare Sestanovich Pdf

“A debut story collection of the rarest kind ... you wish that every single entry could be an entire novel." —Entertainment Weekly Fresh, intimate stories of women’s lives from an extraordinary new literary voice, laying bare the unexpected beauty and irony in contemporary life A college freshman, traveling home, strikesup an odd, ephemeral friendship with the couple next to her on the plane. A mother prepares for her son’s wedding, her own life unraveling as his comes together. A long-lost stepbrother’s visit to New York prompts a family’s reckoning with its old taboos. A wife considers the secrets her marriage once contained. An office worker, exhausted by the ambitions of the men around her, emerges into a gridlocked city one afternoon to make a decision. In these eleven powerful stories, thrilling desire and melancholic yearning animate women’s lives, from the brink of adulthood to the labyrinthine path between twenty and thirty, to middle age, when certain possibilities quietly elapse. Tender, lucid, and piercingly funny, Objects of Desire is a collection pulsing with subtle drama, rich with unforgettable scenes, and alive with moments of recognition each more startling than the last—a spellbinding debut that announces a major talent.

The Universe in Zero Words

Dana Mackenzie
The Universe in Zero Words Book PDF

Author : Dana Mackenzie
Publisher : Princeton University Press
Page : 224 pages
File Size : 47,5 Mb
Release : 2013-08-25
Category : Mathematics
ISBN : 9780691160160

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The Universe in Zero Words by Dana Mackenzie Pdf

Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics--the universal language of science--keep the masterpieces of the subject hidden behind a veil? The Universe in Zero Words tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called "a popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives. Illustrated in color throughout, the book tells the human and often-surprising stories behind the invention or discovery of the equations, from how a bad cigar changed the course of quantum mechanics to why whales (if they could communicate with us) would teach us a totally different concept of geometry. At the same time, the book shows why these equations have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human expression can match. The Universe in Zero Words is the ultimate introduction and guide to equations that have changed the world.

Leonhard Euler's Letters to a German Princess

Ronald S Calinger,Ekaterina (Katya) Denisova,Elena N Polyakhova
Leonhard Euler s Letters to a German Princess Book PDF

Author : Ronald S Calinger,Ekaterina (Katya) Denisova,Elena N Polyakhova
Publisher : Morgan & Claypool Publishers
Page : 215 pages
File Size : 40,5 Mb
Release : 2019-06-28
Category : Science
ISBN : 9781643271927

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Leonhard Euler's Letters to a German Princess by Ronald S Calinger,Ekaterina (Katya) Denisova,Elena N Polyakhova Pdf

Leonhard Euler's Letters to a German Princess: A Milestone in the History of Physics Textbooks and More is a milestone in the history of physics textbooks and the instruction of women in the sciences. It also covers views of its author on epistemology, religion, and innovations in scientific equipment, including telescopes and microscopes. Today, 250 years later, we study this work of Euler's as a foundation for the history of physics teaching and analyze the letters from an historical and pedagogical point of view.

Gamma

Julian Havil
Gamma Book PDF

Author : Julian Havil
Publisher : Princeton University Press
Page : 292 pages
File Size : 50,5 Mb
Release : 2017-10-31
Category : Mathematics
ISBN : 9780691178103

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Gamma by Julian Havil Pdf

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, 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.

That's Maths

Peter Lynch
That s Maths Book PDF

Author : Peter Lynch
Publisher : Gill & Macmillan Ltd
Page : 328 pages
File Size : 42,9 Mb
Release : 2016-10-14
Category : Mathematics
ISBN : 9780717169566

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That's Maths by Peter Lynch Pdf

From atom bombs to rebounding slinkies, open your eyes to the mathematical magic in the everyday. Mathematics isn't just for academics and scientists, a fact meteorologist and blogger Peter Lynch has spent the past several years proving through his Irish Times newspaper column and blog, That's Maths.Here, he shows how maths is all around us, with chapters on the beautiful equations behind designing a good concert venue, predicting the stock market and modelling the atom bomb, as well as playful meditations on everything from coin-stacking to cartography. If you left school thinking maths was boring, think again!

A Beautiful Math

Tom Siegfried
A Beautiful Math Book PDF

Author : Tom Siegfried
Publisher : National Academies Press
Page : 272 pages
File Size : 45,5 Mb
Release : 2006-09-21
Category : Science
ISBN : 9780309133807

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A Beautiful Math by Tom Siegfried Pdf

Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

Calculus Gems: Brief Lives and Memorable Mathematics

George F. Simmons
Calculus Gems Brief Lives and Memorable Mathematics Book PDF

Author : George F. Simmons
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 45,9 Mb
Release : 2020-03-17
Category : Education
ISBN : 9781470451288

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Calculus Gems: Brief Lives and Memorable Mathematics by George F. Simmons Pdf

Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices ("Biographical Notes" and "Variety of Additional Topics") found in Simmons' 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The text is suitable as a supplement for a calculus course and/or a history of mathematics course, The overall aim is bound up in the question, "What is mathematics for?" and in Simmons' answer, "To delight the mind and help us understand the world". The essays are independent of one another, allowing the instructor to pick and choose among them. Part A, "Brief Lives", is a biographical history of mathematics from earliest times (Thales, 625–547 BC) through the late 19th century (Weierstrass, 1815–1897) that serves to connect mathematics to the broader intellectual and social history of Western civilization. Part B, "Memorable Mathematics", is a collection of interesting topics from number theory, geometry, and science arranged in an order roughly corresponding to the order of most calculus courses. Some of these sections have a few problems for the student to solve. Students can gain perspective on the mathematical experience and learn some mathematics not contained in the usual courses, and instructors can assign student papers and projects based on the essays. The book teaches by example that mathematics is more than computation. Original illustrations of influential mathematicians in history and their inventions accompany the brief biographies and mathematical discussions.