The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number

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Broadway Books #ad - It tells the human story of numerous phi-fixated individuals, bartok, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, and physicist Roger Penrose.

Since then it has shown a propensity to appear in the most astonishing variety of places, sunflower florets, from mollusk shells, and rose petals to the shape of the galaxy. It is believed to feature in works of art from leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works.

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number #ad - Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it.

. Wherever his quest for the meaning of phi takes him, beauty, Mario Livio reveals the world as a place where order, and eternal mystery will always coexist. In this fascinating book, mario Livio tells the tale of a number at the heart of that mystery: phi, or 1. 6180339887.

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The Golden Ratio:The Divine Beauty of Mathematics

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Race Point Publishing #ad - The golden ratio examines the presence of this divine number in art and architecture throughout history, animals, as well as its ubiquity among plants, and even the cosmos. Author gary meisner shares the results of his twenty-year investigation and collaboration with thousands of people across the globe in dozens of professions and walks of life.

The evidence will close the gaps of understanding related to many claims of the golden ratio’s appearances and applications, and present new findings to take our knowledge further yet. Whoever you are, you’ll find something new, interesting, and informative in this book, apply, and whatever you may know about this topic, and may find yourself challenged to see, and share this unique number of mathematics and science in new ways.

The Golden Ratio:The Divine Beauty of Mathematics #ad - This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of giza, to the proportions of the human face, to quasicrystals, the golden ratio has an infinite capacity to generate shapes with exquisite properties.

This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book.

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Is God a Mathematician?

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Simon & Schuster #ad - Is mathematics ultimately invented or discovered? if, as einstein insisted, mathematics is “a product of human thought that is independent of experience, ” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world.

More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world.

Is God a Mathematician? #ad - Is god a mathematician? investigates why mathematics is as powerful as it is. Bestselling author and astrophysicist mario livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world.

Nobel laureate eugene wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

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The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

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Simon & Schuster #ad - Their incredible labor, however, produced the origins of group theory. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

What do bach's compositions, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, Rubik's Cube, the way we choose our mates, which elegantly unify scientific and artistic principles. These geniuses, a norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young.

The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry #ad - Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula.

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The Golden Section: Nature's Greatest Secret

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Wooden Books #ad - Small books, big ideas. Stunning" new yorK TIMES. Rich and artful" THE LANCET. Genuinely mind-expanding" FORTEAN TIMES. Fascinating" finanCIAL TIMES. What was the golden secret known to leonardo da vinci, plato and the ancient magicians? can there really be a key to nature and life itself? In this small but compact volume internationally renowned divine proportion supersleuth Dr Olsen unravels perhaps the greatest mystery of all time, a pattern we instinctively recognise as beautiful, a code that seems to underly life, Kepler, the universe and everything, and which nature herself uses at every scale.

Excellent" new sCIENTIST. Wooden books are small but packed with information. Designed for artists and scientists alike, this is the smallest, densest and most beautiful book on the golden section ever produced. Beautiful" london review OF BOOKS.

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Zero: The Biography of a Dangerous Idea

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Penguin Books #ad - Zero has pitted east against west and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Zero is really something"-Washington PostA New York Times Notable Book. The babylonians invented it, the Hindus worshiped it, the Greeks banned it, and the Church used it to fend off heretics.

For zero, infinity's twin, is not like other numbers. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Now it threatens the foundations of modern physics. Popular math at its most entertaining and enlightening. It is both nothing and everything.

Zero: The Biography of a Dangerous Idea #ad - In zero, its rise and transcendence in the west, science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, and its ever-present threat to modern physics. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.

Here are the legendary thinkers—from pythagoras to Newton to Heisenberg, science, mathematics, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, and religion.

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Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe - Brilliant Blunders: From Darwin to Einstein

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Simon & Schuster #ad - Astrophysicist fred hoyle dismissed the idea of a “Big Bang” origin to the universe ironically, the caustic name he gave to this event endured long after his erroneous objections were disproven. Darwin’s theory of natural selection shouldn’t have worked, according to the prevailing beliefs of his time.

. And albert einstein speculated incorrectly about the forces of the universe—and that speculation opened the door to brilliant conceptual leaps. Thoughtful, and beautifully written” the washington Post, well-researched, Brilliant Blunders is a wonderfully insightful examination of the psychology of five fascinating scientists—and the mistakes as well as the achievements that made them famous.

Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe - Brilliant Blunders: From Darwin to Einstein #ad - As mario livio luminously explains in this “thoughtful meditation on the course of science itself” The New York Times Book Review, the evolution of the earth, and the evolution of the universe, these five scientists expanded our knowledge of life on earth, despite and because of their errors. Linus pauling, the world’s premier chemist, constructed an erroneous model for DNA in his haste to beat the competition to publication.

Lord kelvin gravely miscalculated the age of the earth. Drawing on the lives of five great scientists, this “scholarly, insightful, and beautifully written book” Martin Rees, author of From Here to Infinity illuminates the path to scientific discovery. Charles darwin, linus pauling, william thomson Lord Kelvin, Fred Hoyle, and Albert Einstein all made groundbreaking contributions to their fields—but each also stumbled badly.

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A History of Pi

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St. Martin's Griffin #ad - The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

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The Fabulous Fibonacci Numbers

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Prometheus Books #ad - Turning to botany, through illustrative diagrams, sunflowers, the unbelievable connections between Fibonacci numbers and natural forms pineapples, the authors demonstrate, and daisies are just a few examples. Far from being just a curiosity, this sequence recurs in structures found throughout nature?from the arrangement of whorls on a pinecone to the branches of certain plant stems.

All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, math educators Alfred Posamentier and Ingmar Lehmann take us on a fascinating tour of the many ramifications of the Fibonacci numbers. In art, the stock market, they point out numerous examples of the Fibonacci sequence as well as its derivative, and other areas of society and culture, architecture, the "golden ratio.

And of course in mathematics, number theory, there are almost boundless applications in probability, geometry, as the authors amply demonstrate, algebra, and Pascal?s triangle, to name a few. Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

The Fabulous Fibonacci Numbers #ad - The authors begin with a brief history of their distinguished Italian discoverer, among other accomplishments, who, was responsible for popularizing the use of Arabic numerals in the West. The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it 1, 3, 13, 21, 2, 5, 8, 1, ad infinitum.

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An Imaginary Tale: The Story of √-1

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Princeton University Press #ad - In an imaginary tale, the square root of minus one, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, also known as i. 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.

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. 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.

An Imaginary Tale: The Story of √-1 #ad - 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. 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, including the application of complex numbers and functions to important problems, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, such as Kepler's laws of planetary motion and ac electrical circuits.

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.

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e: The Story of a Number

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Princeton University Press #ad - Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science. The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St.

. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number.

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