The Golden Ratio: The Story of Phi, the World's Most Astonishing NumberThroughout 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 phifixated 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. 
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Very well researched!  Goodreads
The scholarship in this book is extremely poor.  Goodreads
Livio makes math and the golden ratio easy to read.  Goodreads
A thorough overview of a fascination slice of nature  Goodreads
A good insight into why maths can be neat.  Goodreads
Review: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
User Review  Lee Belbin  GoodreadsA very readable book about some remarkable properties of numbers, with a focus on the 'golden ratio': The irrational number  the ratio that just looks good and has been used knowingly and unknowingly in many applications. A good insight into why maths can be neat. Nice history and personalities. Read full review
Review: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
User Review  Paul Brooks  Goodreadswonderfully readable and easy to grasp. a great book for any library. Read full review
Contents
THE PITCH AND THE PENTAGRAM  12 
THE DIVINE PROPORTION  124 
APPENDICES  255 
Copyright  
2 other sections not shown
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Abu'lWafa aesthetic ancient angles appears arithmetic artists astronomer Babylonians base beauty Benford's law calculate century B.C. claims composed concept construction cube described diagonal digits dimensions discovered Divine Proportion dodecahedron Egyptian equal equation Euclid example exist expressed fact false vacuum famous Fibonacci numbers Fibonacci sequence Figure fractal fractions galaxies geometry Golden Ratio Golden Rectangle Golden Section Greek human icosahedron interest irrational numbers Kepler known length Leonardo logarithmic spiral Luca Pacioli Madonna mathe mathematician mathematics means measure Modulor nature obtain Pacioli painter paintings pairs Parthenon pattern Penrose Penrose tilings pentagon pentagram percent petals phyllotaxis physicist Piero planets Platonic solids Platonic view poem precisely prime problem properties published Pyramid Pythagoras Pythagorean quasicrystals question represent Reprinted with permission shape side simple sphere square stars symbol symmetry theorem theory tiling tion triangle universe whole numbers words wrote