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 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.
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.
Dr Euler S Fabulous Formula
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Author : Paul J. Nahin
language : en
Publisher: Princeton University Press
Release Date : 2017-04-04
Dr Euler S Fabulous Formula written by Paul J. 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.
Euler
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Author : William Dunham
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-13
Euler written by William Dunham and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-13 with Mathematics categories.
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.
Proofs From The Book
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
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 2013-06-29 with Mathematics categories.
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Leonhard Euler S Letters To A German Princess
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Author : Ronald S Calinger
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2019-06-28
Leonhard Euler S Letters To A German Princess written by Ronald S Calinger and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-28 with Science categories.
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.
That S Maths
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Author : Peter Lynch
language : en
Publisher: Gill & Macmillan Ltd
Release Date : 2016-10-14
That S Maths written by Peter Lynch and has been published by Gill & Macmillan Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-14 with Mathematics categories.
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!
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.
Leonhard Euler
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Author : Ronald S. Calinger
language : en
Publisher: Princeton University Press
Release Date : 2019-12-03
Leonhard Euler written by Ronald S. Calinger 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 2019-12-03 with Biography & Autobiography categories.
"This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment."--Publisher's description.