Euler S Gem
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Euler S Gem
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Author : David S. Richeson
language : en
Publisher: Princeton University Press
Release Date : 2019-07-23
Euler S Gem written by David S. Richeson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Mathematics categories.
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
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Author : David S. Richeson
language : en
Publisher: Princeton University Press
Release Date : 2019-07-23
Euler S Gem written by David S. Richeson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Mathematics categories.
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
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Author : David S. Richeson
language : en
Publisher: Princeton University Press
Release Date : 2012-04-15
Euler S Gem written by David S. Richeson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-15 with Mathematics categories.
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.
Euler S Gem
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Author : David Richeson
language : en
Publisher:
Release Date : 2012
Euler S Gem written by David Richeson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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
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Author : Paul Nahin
language : en
Publisher: Princeton University Press
Release Date : 2017-04-04
Dr Euler S Fabulous Formula written by Paul Nahin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-04 with Mathematics categories.
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
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Author : David S. Richeson
language : en
Publisher: Princeton University Press
Release Date : 2021-11-02
Tales Of Impossibility written by David S. Richeson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-02 with Mathematics categories.
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.
Calculus Gems
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Author : George Finlay Simmons
language : en
Publisher: McGraw-Hill Science, Engineering & Mathematics
Release Date : 1992
Calculus Gems written by George Finlay Simmons and has been published by McGraw-Hill Science, Engineering & Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Biography & Autobiography categories.
The first half of Calculus Gems is a biographical history of mathematics from the earliest times to the late nineteenth century. The author shows how science - and mathematics in particular - is something that people do, and not merely a mass of observed data and abstract theory. He demonstrates the profound connections that join mathematics to the history of philosophy and also to the broader intellectual and social history of Western civilization. The second half contains nuggets that Simmons has collected from number theory, geometry, science, etc., which he has used in his mathematics classes, meaning that it can be used as a supplement in a Calculus course, or a History of Mathematics course. The overall aim of this book is to answer the question, 'What is mathematics for?' and with its inevitable answer, 'To delight the mind and help us understand the world.'
The Universe In Zero Words
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Author : Dana Mackenzie
language : en
Publisher: Princeton University Press
Release Date : 2013-08-25
The Universe In Zero Words written by Dana Mackenzie and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-25 with Mathematics categories.
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.
Proofs From The Book
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Proofs From The Book written by Martin Aigner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added.