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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 becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.
With this fun romp through the world of equations we encounter in our everyday lives, you’ll find yourself flipping through the stories of fifty-two formulas faster than a deck of cards. John M. Henshaw’s intriguing true accounts, each inspired by a different mathematical equation, are both succinct and easy to read. His tales come from the spheres of sports, business, history, the arts, science, and technology. Anecdotes about famous equations, like E=mc 2, appear alongside tales of not-so-famous—but equally fascinating—equations, such as the one used to determine the SPF number for sunscreen. Drawn from the breadth of human endeavor, Henshaw's stories demonstrate the power and utility of math. He entertains us by exploring the ways that equations can be used to explain, among other things, Ponzi schemes, the placebo effect, "dog years," IQ, the wave mechanics of tsunamis, the troubled modern beekeeping industry, and the Challenger disaster. Smartly conceived and fast paced, his book offers something for anyone curious about math and its impacts.
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.
The universe is a mathematical hologram. It’s made of ontological mathematics. It’s a living, thinking, self-optimising holographic organism composed of immortal, indestructible, ontological mathematical units called monads, defined by the most powerful and beautiful equation in the whole of mathematics: Euler’s Formula. Monads have a much more resonant name: souls. We all inhabit Soul World, a wondrous immaterial Singularity outside space and time. Our souls are individual mathematical singularities: autonomous, uncaused, uncreated, dimensionless frequency domains. Via Fourier mathematics, these imperishable, immaterial monadic souls can collectively create the spacetime domain of the material world. Where each soul is a single frequency domain, the material world of space and time is their collective Fourier output. What is “matter”? It’s simply dimensional energy: energy existing in the Fourier spacetime domain rather than in the Fourier dimensionless frequency domain. Welcome to Soul World.
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.
This book is about beautiful mathematical concepts and creations. Mathematical ideas have an aesthetic appeal that can be appreciated by those who have the time and dedication to investigate. Mathematical topics are presented in the categories of words, images, formulas, theorems, proofs, solutions, and unsolved problems. Readers will investigate exciting mathematical topics ranging from complex numbers to arithmetic progressions, from Alcuin's sequence to the zeta function, and from hypercubes to infinity squared.Do you know that a lemniscate curve is the circular inversion of a hyperbola? That Sierpinski's triangle has fractal dimension 1.585….? That a regular septagon can be constructed with straightedge, compass, and an angle trisector? Do you know how to prove Lagrange's theorem that every positive integer is the sum of four squares? Can you find the first three digits of the millionth Fibonacci number? Discover the keys to these and many other mathematical problems. In each case, the mathematics is compelling, elegant, simple, and beautiful.Who should read this book? There is something new for any mathematically-minded person. High school and college students will find motivation for their mathematical studies. Professional mathematicians will find fresh examples of mathematical beauty to pass along to others. Within each chapter, the topics require progressively more prerequisite knowledge. An appendix gives background definitions and theorems, while another gives challenging exercises (with solutions).
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.
Euler’s Formula is the most beautiful equation in mathematics. Yet it’s much more. It the governs the universe and defines the soul! Euler’s Formula perfectly complements Leibniz’s Monadology. They form the most powerful intellectual combination ever, capable of establishing a true grand unified theory of everything, including religion. It provides a rational explanation of near-death and out-of-body experiences, and homeopathy. It overturns Einstein’s principle of relativity, providing the same results via an absolute framework that restores the reality principle. In this groundbreaking book, we provide the solution to the Cartesian mind-body problem via the Fourier transform – which has the Euler Formula as its engine. We present the Riemann sphere, which works in perfect harmony with the Euler Formula, as the ideal working model of the human soul. And we give the first ever technical explanation of the process of reincarnation. The Euler equation is everything you thought – and more. It’s divine.
Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Third Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations, the use of Euler’s formula to study the five Platonic solids, the use of prime numbers to encode and decode secret information, and the theory of how to compare the sizes of two infinite sets. New to the Third Edition The third edition of this popular text contains three new chapters that provide an introduction to mathematical analysis. These new chapters introduce the ideas of limits of sequences and continuous functions as well as several interesting applications, such as the use of the intermediate value theorem to prove the existence of nth roots. This edition also includes solutions to all of the odd-numbered exercises. By carefully explaining various topics in analysis, geometry, number theory, and combinatorics, this textbook illustrates the power and beauty of basic mathematical concepts. Written in a rigorous yet accessible style, it continues to provide a robust bridge between high school and higher level mathematics, enabling students to study further courses in abstract algebra and analysis.