The Golden Ratio: The Story of PHI pdf

马里奥·利维奥（Mario Livio）出生于 1945 年 6 月 19 日，他是一名以色列裔美国天体物理学家，也是普及科学和数学作品的作者。 24 年（1991-2015 年），他在太空望远镜科学研究所担任天体物理学家，该研究所负责运营哈勃太空望远镜。 他发表了 400 多篇关于宇宙学、超新星爆炸、黑洞、太阳系外行星和宇宙中生命出现等主题的科学文章。 [1] 他的关于无理数 phi 的书《黄金比例：世界上最惊人的数字 Phi 的故事》（2002 年）获得了皮亚诺奖和国际毕达哥拉斯数学通俗书籍奖。

The Golden Ratio: The Story of PHI pdf 马里奥·利维奥

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