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

Science & Math

Livio, Mario

History & Philosophy

Crown

Advance Praise for The Accelerating Universe"The Accelerating Universe is not only an informative book about modern cosmology. It is rich storytelling and, above all, a celebration of the human mind in its quest for beauty in all things." —Alan Lightman, author of Einstein's Dreams
"This is a wonderfully lucid account of the extraordinary discoveries that have made the last years a golden period for observational cosmology. But Mario Livio has not only given the reader one clear explanation after another of what astronomers are up to, he has used them to construct a provocative argument for the importance of aesthetics in the development of science and for the inseparability of science, art, and culture." —Lee Smolin, author of The Life of the Cosmos
"What a pleasure to read! An exciting, simple account of the universe revealed by modern astronomy. Beautifully written, clearly presented, informed by scientific and philosophical insights." —John Bahcall, Institute for Advanced Study
"A book with charm, beauty, elegance, and importance. As authoritative a journey as can be taken through modern cosmology." —Allan Sandage, Observatories of the Carnegie Institution of Washington

The Accelerating Universe: Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos

Astronomy & Space Science

John Wiley&Sons, Inc.

The Most Beautiful Number

Humor & Entertainment

Puzzles & Games

wiley

Advance Praise for The Accelerating Universe
""""The Accelerating Universe"" is not only an informative book about modern cosmology. It is rich storytelling and, above all, a celebration of the human mind in its quest for beauty in all things."" --Alan Lightman, author of Einstein's Dreams
""This is a wonderfully lucid account of the extraordinary discoveries that have made the last years a golden period for observational cosmology. But Mario Livio has not only given the reader one clear explanation after another of what astronomers are up to, he has used them to construct a provocative argument for the importance of aesthetics in the development of science and for the inseparability of science, art, and culture."" --Lee Smolin, author of ""The Life of the Cosmos""
""What a pleasure to read! An exciting, simple account of the universe revealed by modern astronomy. Beautifully written, clearly presented, informed by scientific and philosophical insights."" --John Bahcall, Institute for Advanced Study
""A book with charm, beauty, elegance, and importance. As authoritative a journey as can be taken through modern cosmology."" --Allan Sandage, Observatories of the Carnegie Institution of Washington

Trade Paper Press

Traces the four-thousand-year-old mathematical effort to discover and define the laws of symmetry in nature and the arts, citing the achievements of doomed geniuses Niels Henrick Abel and Evariste Galois to solve the quintic equation and give birth to group theory. By the author of The Golden Ratio. 50,000 first printing.

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

Mathematics

Simon&Schuster

What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. 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. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. 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.

Explores the plausibility of mathematical answers to puzzles in the physical world, in an accessible exploration of the lives and thoughts of such figures as Archimedes, Galileo, and Newton. By the author of The Golden Ratio. 50,000 first printing.

Is God a Mathematician?

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. Is God a Mathematician? investigates why mathematics is as powerful as it is. 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. 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. 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. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

Politics & Social Sciences

Philosophy

What do the Parthenon in Greece, crosses in graveyards, the ratio of the height of the navel to a woman's total height, sunflowers and Leonardo da Vinci's "Mona Lisa" have in common? The answer is that these disparate elements share a geometrical proportion of ancient origin, commonly known as the 'Golden Ratio', or expressed numerically as phi. In a captivating journey through art and architecture, botany and biology, taking in fractals and DNA on the way, Livio takes us into the heart of this extraordinary number, and gives an account of the phi-obsessed individuals who devoted their lives to discovering its secrets - from the Pythagoreans who believed that the study of the Golden Ratio would reveal the hand of God, to the great astronomer Johannes Kepler who felt that phi was the greatest treasure of geometry, to the modern day scientists who are discovering ever more remarkable ramifications of this strange, almost mystical, number. It is a journey into the heart of beauty itself.

The Golden Ratio : The Story of Phi, the Extraordinary Number of Nature, Art and Beauty

Review

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. 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. 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. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, 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, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

The Golden Ratio: The Story of Phi, the World's Most Astonishing Number

Broadway

See the best price to sell, buy, or rent books by Livio, Mario. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Livio, Mario

See the best price to sell, buy, or rent books by Livio, Mario. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

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

The Accelerating Universe: Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos

The Most Beautiful Number

The Accelerating Universe: Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos

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

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

Is God a Mathematician?

Is God a Mathematician?

The Golden Ratio : The Story of Phi, the Extraordinary Number of Nature, Art and Beauty

The Golden Ratio: The Story of Phi, the World's Most Astonishing Number