Leonhard Euler

Author: Ronald S. Calinger
Publisher: Princeton University Press
ISBN: 9781400866632
Release Date: 2015-11-24
Genre: Biography & Autobiography

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. Some images inside the book are unavailable due to digital copyright restrictions.

Leonhard Euler

Author: R. Calinger
Publisher:
ISBN: 0691119279
Release Date: 2015-08
Genre: Biography & Autobiography

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.

Leonhard Euler and the Bernoullis

Author: M. B. W. Tent
Publisher: CRC Press
ISBN: 9781439865484
Release Date: 2009-09-18
Genre: Mathematics

"Leonhard Euler and the Bernoullis is a fascinating tale of the Bernoulli family and Euler's association with them. Successful merchants in the 16th and 17th centuries, the Bernoullis were driven out of Antwerp during the persecution of the Huguenots and settled first in Frankfurt, and then in Basel, where one of the most remarkable mathematical dynasties evolved with Jacob, Johann, and Daniel Bernoulli the most prominent among them. Euler, fortunate to have had Johann Bernoulli as a tutor, quickly rose to prominence in the academies of Berlin and St. Petersburg, and became the most prolific and profound mathematician that ever lived. The story of these remarkable men, their great ambitions and dedication to their science-often against parental authority-is skillfully told by the author. Refreshing fictional dialogue is interspersed throughout into an otherwise accurate historical scenario. The book is intended for the young adult audience of middle school and early high school ages, but surely will also appeal to a general audience, with or without mathematical background." --Walter Gautschi, Purdue University

Euler

Author: William Dunham
Publisher: MAA
ISBN: 0883853280
Release Date: 1999-03-04
Genre: Mathematics

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.

Gottfried Wilhelm Leibniz

Author: M. B. W. Tent
Publisher: CRC Press
ISBN: 9781439892220
Release Date: 2011-10-17
Genre: Mathematics

Gottfried Wilhelm Leibniz: The Polymath Who Brought Us Calculus focuses on the life and accomplishments of one of the seventeenth century’s most influential mathematicians and philosophers. The book, which draws on Leibniz’s written works and translations, and reconstructs dialogues Leibniz may have had based on the historical record of his life experiences, portrays Leibniz as both a phenomenal genius and a real person. Suitable for middle school age readers, the book traces Leibniz’s life from his early years as a young boy and student to his later work as a court historian. It discusses the intellectual and social climate in which he fought for his ideas, including his rather contentious relationship with Newton (both claimed to have invented calculus). The text describes how Leibniz developed the first mechanical calculator that could handle addition, subtraction, multiplication, and division. It also examines his passionate advocacy of rational arguments in all controversial matters, including the law, expressed in his famous exclamation calculemus: let us calculate to see who is right. Leibniz made groundbreaking contributions to mathematics and philosophy that have shaped our modern views of these fields.

Euler Through Time

Author: V. S. Varadarajan
Publisher: Harper Collins
ISBN: 0821835807
Release Date: 2006
Genre: Mathematics

Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at the center of today's mathematics. It is of great interest therefore to examine his work and its relation to current mathematics. This book attempts to do that. In number theory the discoveries he made empirically would require for their eventual understanding such sophisticated developments as the reciprocity laws and class field theory. His pioneering work on elliptic integrals is the precursor of the modern theory of abelian functions and abelian integrals. His evaluation of zeta and multizeta values is not only a fantastic and exciting story but very relevant to us, because they are at the confluence of much research in algebraic geometry and number theory today (Chapters 2 and 3 of the book). Anticipating his successors by more than a century, Euler created a theory of summation of series that do not converge in the traditional manner. Chapter 5 of the book treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics. The last chapter contains a brief treatment of Euler products. Euler discovered the product formula over the primes for the zeta function as well as for a small number of what are now called Dirichlet $L$-functions. Here the book goes into the development of the theory of such Euler products and the role they play in number theory, thus offering the reader a glimpse of current developments (the Langlands program).

Euler s Gem

Author: David S. Richeson
Publisher: Princeton University Press
ISBN: 9780691154572
Release Date: 2008-09-08
Genre: 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 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.

A Contextual History of Mathematics

Author: Ronald Calinger
Publisher: Pearson College Division
ISBN: 0023182857
Release Date: 1999
Genre: Mathematics

Tracing the roots of mathematics, this fascinating survey covers the ancient beginnings and subsequent branches of growth in this rich, diverse, and rapidly expanding scientific field, with discussions that progress from the theoretical mathematics in ancient Mesopotamia and Egypt to the emergence of higher analysis mathematics in the late seventeenth century. Well-documented, it presents both established and promising emerging theses, with careful consideration throughout to the remappings, redivisions, and renarrations presented by each new body of historians. Reflects on the nature and roots of mathematics, and a look at some of our more important historiographical issues. Considers mathematics before civilization, with examinations of the Neolithic Revolution and writing and metrology in ancient Sumer, and tracks the science from proto- to theoretical mathematics. Provides a broad survey of mathematics progression in the Islamic world, Latin West, and Maya America from the Middle Ages to 1500, and contain discussions on such topics as the age of absolutism, the culture of science, inventions of differential and fluxional calculus, as well as algebra, number theory, and probability.

Euler s Pioneering Equation

Author: Robin Wilson
Publisher: Oxford University Press
ISBN: 9780192514066
Release Date: 2018-02-22
Genre: Mathematics

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence". What is it that makes Euler's identity, e]iPi + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

Dr Euler s Fabulous Formula

Author: Paul J. Nahin
Publisher: Princeton University Press
ISBN: 1400838479
Release Date: 2011-04-25
Genre: Mathematics

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.

A Most Elegant Equation

Author: David Stipp
Publisher: Basic Books
ISBN: 9780465093786
Release Date: 2017-11-07
Genre: Mathematics

An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

The Prince of Mathematics

Author: M. B. W. Tent
Publisher: A K Peters, Ltd.
ISBN: 9781568814551
Release Date: 2008-10-23
Genre: Juvenile Nonfiction

Now in Paperback! The author narrates the life of Carl Friedrich Gauss, the 18th century mathematician, from his prodigious childhood to his extraordinary achievements that earned him the title Prince of Mathematics. Along the way, the author introduces her young readers to a different culture, the era of small states in Germany where advancement on merits, such as Gauss, was supported by enlightened rulers, competing for intellectual excellence and economic advantage through scientific progress in their small states.Based on extensive research of original and secondary sources, the author has created a historical narrative that will inspire young readers and even curious adults with a story full of human touch and personal achievement.

An Imaginary Tale

Author: Paul J. Nahin
Publisher: Princeton University Press
ISBN: 1400833892
Release Date: 2010-02-22
Genre: Mathematics

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.