Eulers Gem

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Euler's Gem

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691191999
Total Pages : 336 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Euler's Gem by : David S. Richeson

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.

Euler's Gem

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691191379
Total Pages : 336 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Euler's Gem by : David S. Richeson

Euler's Gem

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691154570
Total Pages : 331 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Euler's Gem by : David S. Richeson

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.

Euler's Gem

Author : David Richeson
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Euler's Gem by : David Richeson

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.

Dr. Euler's Fabulous Formula

Author : Paul J. Nahin
Publisher : Princeton University Press
ISBN 13 : 0691175918
Total Pages : 416 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Dr. Euler's Fabulous Formula by : Paul J. Nahin

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.

Tales of Impossibility

Author : David S. Richeson
Publisher : Princeton University Press
ISBN 13 : 0691218722
Total Pages : 450 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Tales of Impossibility by : David S. Richeson

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.

Calculus Gems

Author : George F. Simmons
Publisher : MAA
ISBN 13 : 9780883855614
Total Pages : 386 pages
Book Rating : 4.8/5 (556 download)

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Book Synopsis Calculus Gems by : George F. Simmons

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.

Euler

Author : William Dunham
Publisher : American Mathematical Society
ISBN 13 : 147046618X
Total Pages : 185 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Euler by : William Dunham

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.

Mathematicians

Author : Mariana Cook
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Mathematicians by : Mariana Cook

Download or read book Mathematicians written by Mariana Cook and published by . This book was released on 2009-06-21 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Photographs accompanied by autobiographical text written by each mathematician.

Algebraic Topology from a Homotopical Viewpoint

Author : Marcelo Aguilar
Publisher : Springer Science & Business Media
ISBN 13 : 0387224890
Total Pages : 499 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Algebraic Topology from a Homotopical Viewpoint by : Marcelo Aguilar

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.

Objects of Desire

Author : Clare Sestanovich
Publisher : Vintage
ISBN 13 : 0593318102
Total Pages : 224 pages
Book Rating : 4.5/5 (933 download)

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Book Synopsis Objects of Desire by : Clare Sestanovich

Download or read book Objects of Desire written by Clare Sestanovich and published by Vintage. This book was released on 2021-06-29 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: “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

Author : Dana Mackenzie
Publisher : Princeton University Press
ISBN 13 : 0691160163
Total Pages : 224 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Universe in Zero Words by : Dana Mackenzie

Download or read book The Universe in Zero Words written by Dana Mackenzie and published by Princeton University Press. This book was released on 2013-08-25 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Brief Introduction to Theta Functions

Author : Richard Bellman
Publisher : Courier Corporation
ISBN 13 : 0486492958
Total Pages : 100 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Brief Introduction to Theta Functions by : Richard Bellman

Download or read book A Brief Introduction to Theta Functions written by Richard Bellman and published by Courier Corporation. This book was released on 2013-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Rinehart and Winston, 1961.

The Other Side of Paradise

Author : Julia Cooke
Publisher : Seal Press
ISBN 13 : 1580055311
Total Pages : 250 pages
Book Rating : 4.5/5 (8 download)

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Book Synopsis The Other Side of Paradise by : Julia Cooke

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.

Duelling Idiots and Other Probability Puzzlers

Author : Paul J. Nahin
Publisher : Princeton University Press
ISBN 13 : 0691155003
Total Pages : 300 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Duelling Idiots and Other Probability Puzzlers by : Paul J. Nahin

Download or read book Duelling Idiots and Other Probability Puzzlers written by Paul J. Nahin and published by Princeton University Press. This book was released on 2012-07-22 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds. If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly," for example, is a clever variation of a "random walk" problem, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions. Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.

Leonhard Euler

Author : Ronald S. Calinger
Publisher : Princeton University Press
ISBN 13 : 0691196400
Total Pages : 689 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Leonhard Euler by : Ronald S. Calinger

Download or read book Leonhard Euler written by Ronald S. Calinger and published by Princeton University Press. This book was released on 2019-12-03 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Proofs from THE BOOK

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3662223430
Total Pages : 194 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Proofs from THE BOOK by : Martin Aigner

Download or read book Proofs from THE BOOK written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.