Eulers Gem

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691191999
Total Pages : 336 pages
Book Rating : 4.97/5 ( download)

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Download or read book Euler's Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691191379
Total Pages : 336 pages
Book Rating : 4.79/5 ( download)

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Download or read book Euler's Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691154570
Total Pages : 331 pages
Book Rating : 4.72/5 ( download)

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Download or read book Euler's Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2012-04-15 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David Richeson
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.58/5 ( download)

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Download or read book Euler's Gem written by David Richeson and published by . This book was released on 2012 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Paul J. Nahin
Publisher : Princeton University Press
ISBN 13 : 0691175918
Total Pages : 416 pages
Book Rating : 4.11/5 ( download)

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Download or read book Dr. Euler's Fabulous Formula written by Paul J. Nahin and published by Princeton University Press. This book was released on 2017-04-04 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691218722
Total Pages : 450 pages
Book Rating : 4.24/5 ( download)

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Download or read book Tales of Impossibility written by David S. Richeson and published by Princeton University Press. This book was released on 2021-11-02 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : George F. Simmons
Publisher : MAA
ISBN 13 : 9780883855614
Total Pages : 386 pages
Book Rating : 4.15/5 ( download)

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Download or read book Calculus Gems written by George F. Simmons and published by MAA. This book was released on 2007-08-02 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates the profound connections that join mathematics to the history of philosophy.

Author : Julia Cooke
Publisher : Seal Press
ISBN 13 : 1580055311
Total Pages : 250 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Other Side of Paradise written by Julia Cooke and published by Seal Press. This book was released on 2014-04-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Change looms in Havana, Cuba's capital, a city electric with uncertainty yet cloaked in cliché, 90 miles from U.S. shores and off-limits to most Americans. Journalist Julia Cooke, who lived there at intervals over a period of five years, discovered a dynamic scene: baby-faced anarchists with Mohawks gelled with laundry soap, whiskey-drinking children of the elite, Santería trainees, pregnant prostitutes, university graduates planning to leave for the first country that will give them a visa. This last generation of Cubans raised under Fidel Castro animate life in a waning era of political stagnation as the rest of the world beckons: waiting out storms at rummy hurricane parties and attending raucous drag cabarets, planning ascendant music careers and black-market business ventures, trying to reconcile the undefined future with the urgent today. Eye-opening and politically prescient, The Other Side of Paradise offers a deep new understanding of a place that has so confounded and intrigued us.

Author : William Dunham
Publisher : American Mathematical Society
ISBN 13 : 147046618X
Total Pages : 185 pages
Book Rating : 4.83/5 ( download)

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Download or read book Euler written by William Dunham and published by American Mathematical Society. This book was released on 2022-01-13 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Marcelo Aguilar
Publisher : Springer Science & Business Media
ISBN 13 : 0387224890
Total Pages : 499 pages
Book Rating : 4.93/5 ( download)

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Download or read book Algebraic Topology from a Homotopical Viewpoint written by Marcelo Aguilar and published by Springer Science & Business Media. This book was released on 2008-02-02 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any student who knows some topology, providing a useful method to quickly learn this novel homotopy-theoretic point of view of algebraic topology.