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

Euclid discovered it. Humanity's first recognition of "incommensurability" or the existence of irrational numbers - any number that cannot be expressed as a ratio of two integers. Until that event, Pythagorean foundation based upon the notion that no irrational numbers exist. After that, the Pythagoreans' unusual worship of "number" declined in its appeal to the...more

Euclid discovered it. Humanity's first recognition of "incommensurability" or the existence of irrational numbers - any number that cannot be expressed as a ratio of two integers. Until that event, Pythagorean foundation based upon the notion that no irrational numbers exist. After that, the Pythagoreans' unusual worship of "number" declined in its appeal to the masses. Separation of math/religion/philosophy. Livio's discussion of the number is brilliant - its history, its evidence in many physical and mathematical constructs and even its arguable ability to predict or define aesthetical beauty. I especially enjoyed his explanation of Phi's relationship to Fibonacci numbers and what appears to be an ever-increasing explanation of their combined relevance to "growth". The final chapter includes a discussion of the 'surprise' associated with newly discovered mathematics and their implications to the physical universe. Particularly intriguing to me ... is math a purely human construct - derived from our "earthly" understanding and observation of our own universe? Or is God a divine mathematician - math is the fabric of Creation. Livio wisely offers no opinions, but opens the door to philosophical and religious ideas at the center of the minds of Plato, Euclid, Pythagoras, Kepler, Galileo, Newton, Einstein, Feynman, Penrose and Wolfram. While their opinions on the question are well-described by Livio - they are certainly diverse...and largely speculative. I recommend this book to anyone interested in better understanding math's relationship to the physical universe and, specifically, the wonders of phi and Fibonacci. Dave   hide

The book is quite interesting, though at times, it feels like a tedious history lesson.

Very interesting book about an irrational number, how and where it is and has been used.

geometry and beauty - who knew they went hand in hand?

cool.

Great book. . . it is very interesting how frequently in nature this number appears. . the later chapters get too much into whether or not the golden ratio was intentionally incorporated into ancient artworks or not. . .I stopped reading about then

NICE!

The best balance of number theory, history, and relevance of any of the numerous books on this topic.

this is a thinking person's book. after watching pi, i found this book. this really makes you wonder if there really may be a man behind the curtain. the number is everywhere!!!