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The Golden Ratio: The Story of PHI, the World's Most Astonishing Number Paperback – September 23, 2003
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Top Customer Reviews
Phi received its original definition from Euclid as an "extreme and mean ratio" when a straight line is cut so that the ratio of the entire line to the longer division of the segment is the same as the ratio of the longer division of the segment to the shorter. And yet, much like the better known geometrical example of pi, phi turns out to have many more applications beyond its simplest geometrical definition. Though measurable, phi is an irrational number with relationships to the Fibonacci sequence, fractals, the physical structure of things from plant growth and spiral shell development to the appearance of large-scale objects like galaxies, and more. And beyond this, phi has been used as a basis applications in numerology and aesthetics.
Livio does a very good job of covering all this ground and more. He is especially good at giving us a historical overview of the development of our understanding of this important number as well as explaining the mathematics in a way that is complete but easy to understand.Read more ›
In this book, Livio gives a brief history of mathematics and phi's place in it. Intimately related to the Fibonacci numbers, a sequence of numbers in which any given number is the sum of the previous two (after the first couple); these numbers (1,1,2,3,5,8,13...) have shown up in some unlikely places such as sunflowers and nautilus shells. Livio shows us the significance of phi in both the mathematical and physical world.
Livio also makes a good case that phi may be the most overrated of all numbers. Although it has a wonderfully golden name, it actually doesn't live up to its reputation; Livio shows that phi's presence in art and architecture is more fictional than real and that there is nothing about phi that automatically confers aesthetic beauty. A good portion of the book is dedicated to debunking these golden myths.
Overall, this is a good book. Livio's writing is appealing to both mathematician and non-mathematician alike. He does have a tendency to meander from his topic, which can be distracting (even if entertaining), although he eventually does get back on track. For those who like reading about math and the significance of certain numbers (I have also read books on pi, e, i, 0 and infinity), this is a worthwhile read.
These sorts of number tricks abound in Livio's book, and the mathematics is not daunting. It is also a history of phi, which turns out to be a representative slice of the history of mathematics. Euclid knew the number, but Leonardo Fibonacci in the twelfth century developed the series with its ratio. It shows up in breeding rabbits; spirals in pine cones, sunflowers, galaxies, and hurricanes; tilings and fractals; and many more surprising places.Read more ›
Most Recent Customer Reviews
I love this book - beautifully told, clear language and fascinating historical details.Published 4 months ago by j. keefe
Very interesting book! I am a math student and I loved this book. It was a great read and very informative.Published 5 months ago by Ann Vann
Interesting overview of phi and its properties. The book gets a little dry about halfway through, reading more like a textbook. Still a good read.Published 5 months ago by Jason Wadleigh
Excellent book, most interesting and beautifully written. Hightly recommended.Published 5 months ago by Amazon Customer
A totally fascinating book about the essential order built into the universe.Published 6 months ago by Gerald McKibben
When the author is writing on the golden ratio, the book is interesting. When he is writing on matters directly related to the golden ratio, like its underlying mathematics, or... Read morePublished 7 months ago by Adam Orford