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

Reading this book was a stimulating experience. Exploring the mathematical principles and theories studied by various past cultures and how they employed them isn't a new idea but this author is uniquely good at it. Other authors in this genre, such as Amir Aczel can sometimes be guilty of spending too much time on sculpting the biography of a math genre and leaving its concepts severely under-explained. Livio however, created what I felt to be an adequate mix between math teaching an math biography. The result for me was to become greatly interested in a genre of study I formerly felt to be too clouded in obscurity for anyone but the balding, quirky, pocket-protector and horn-rimmed glasses wearing geeks of the world to make sense of.

I appreciated the sensibility Livio showed in this work, specifically in his loyalty to the scientific method. This genre tends to produce the occasional crank who with a theory that sounds beautiful but fails to stand up to unbiased and rigorous testing. It's admirable when a someone can instead treat their theory with reservations and honestly subject it to a barrage of tests, attempting to disprove it, before presenting it to the world. And while Livio does bring up scores of wild theories proposed throughout history on the relation of the golden ratio, pi, and the Fibonacci sequence to any piece of soul-stirring art, music, or architecture, he faithfully presents the holes and counter-points, reserving his enthusiasm for the truly provable and profound. This book is not meant to disprove the connection between irrational numbers and our sense of beauty, harmony and proportion, but rather to help sift through the weak theories and teach the principles surrounding those that have proven themselves and stood the test of time.

The book surveys various people and cultures who employed mathematics in their building, artistic, and musical endeavors in a chronological order, trying to determine how deep their knowledge was and how deliberate their use of higher mathematics. It sorts through the claims made by different authors and researches that individuals from the pyramid builders to the early philosophers to the renaissance painters to the modern artists/musicians perhaps knew of the irrational numbers and incorporated them into their works. Necessary to understanding each group or famous person to which the question of expert mathematical foreknowledge is posed, is a brief study of their biographical information and contributions to history. So this book functions as a nice primer to studying some of these people, especially Euclid, Plato, and Pacioli. As well as studying various people it also spends a couple chapters on the presence of irrational numbers (or our ability to recognize them) in nature. Needless to say, it goes into great detail on each topic. Surprisingly, the level of detail never becomes so intricate that the book loses rhythm & readability, and the author doesn't hide behind the voices of the many people and works he cites throughout this work.

I really enjoyed this book and I suppose the purpose of many works of a scientific or scholarly nature - such as this one - are to transfer an understanding or at least stimulate an interest in an idea, and to that end I am quite satisfied with it.