Dr Eulers Fabulous Formula

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.

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.

Accessible to any reader with the equivalent of the first two years of college mathematics, this is the story behind one of the world's most influential mathematical equations. 2 halftones. 77 line illustrations.

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.

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.

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, eiπ + 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.

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.

Math—the application of reasonable logic to reasonable assumptions—usually produces reasonable results. But sometimes math generates astonishing paradoxes—conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than any other day? Or that cones can roll unaided uphill? In Nonplussed!—a delightfully eclectic collection of paradoxes from many different areas of math—popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas. Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs. Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.

"For centuries, mathematicians have tried, and failed, to solve the zeta-3 problem. This problem is simple in its formulation, but remains unsolved to this day, despite the attempts of some of the world's greatest mathematicians to solve it. The problem can be stated as follows: is there a simple symbolic formula for the following sum: 1+(1/2)^3+(1/3)^3+(1/4)^3+...? Although it is possible to calculate the approximate numerical value of the sum (for those interested, it's 1.20205...), there is no known symbolic expression. A symbolic formula would not only provide an exact value for the sum, but would allow for greater insight into its characteristics and properties. The answers to these questions are not of purely academic interest; the zeta-3 problem has close connections to physics, engineering, and other areas of mathematics. Zeta-3 arises in quantum electrodynamics and in number theory, for instance, and it is closely connected to the Riemann hypothesis. In In Pursuit of zeta-3, Paul Nahin turns his sharp, witty eye on the zeta-3 problem. He describes the problem's history, and provides numerous "challenge questions" to engage readers, along with Matlab code. Unlike other, similarly challenging problems, anyone with a basic mathematical background can understand the problem-making it an ideal choice for a pop math book"--