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

Science & Math

Mario Livio

Mathematics

Souvenir Press Ltd.

<p>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 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!\nThe 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.\nFrom the Hardcover edition.</p>

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

Politics & Social Sciences

Philosophy

Review / Hodder Headline

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

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

Paw Prints 2008-06-05

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

We all make mistakes. Nobody’s perfect. Not even some of the greatest geniuses in history, as Mario Livio tells us in this marvelous story of scientific error and breakthrough.  Charles Darwin, William Thomson (Lord Kelvin), Linus Pauling, Fred Hoyle, and Albert Einstein were all brilliant scientists. Each made groundbreaking contributions to his field — but each also stumbled badly. Darwin’s theory of natural selection shouldn’t have worked, according to the prevailing beliefs of his time. Not until Gregor Mendel’s work was known would there be a mechanism to explain natural selection. How could Darwin be both wrong and right? Lord Kelvin, Britain’s leading scientific intellect at the time, gravely miscalculated the age of the earth. Linus Pauling, the world’s premier chemist (who would win the Nobel Prize in chemistry) constructed an erroneous model for DNA in his haste to beat the competition to publication. 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). And Albert Einstein, whose name is synonymous with genius, speculated incorrectly about the forces that hold the universe in equilibrium — and that speculation opened the door to brilliant conceptual leaps. These five scientists expanded our knowledge of life on earth, the evolution of the earth itself, and the evolution of the universe, despite and because of their errors. As Mario Livio luminously explains, the scientific process advances through error. Mistakes are essential to progress.  Brilliant Blunders is a singular tour through the world of science and scientific achievement — and a wonderfully insightful examination of the psychology of five fascinating scientists.

Simon&Schuster

Brilliant Blunders

Biographies & Memoirs

Professionals & Academics

BRILLIANCE AUDIO ^

Galileo: And the Science Deniers

Historical

Simon & Schuster Audio and Blackstone Publishing

Galileu e os negadores da ciencia (Em Portugues do Brasil)

FisicalBook

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Books by Mario Livio