Rating: 
Summary: Not what I expected
Review: This book is for mathematicians, not artists. Coming from both the science and art world myself I was disapointed a bit. Too much time is spent trying to debunk the use of the golden ratio in art stricly based on an analysis done in a manner suitable only if you are planning to launch a rocket but totally beside the point in the world of visual arts. In that field, the author misses the point entirely. Works of art are perceived with the eyes, often at a glance for architecture, and only in the context of the building on the field, not with an inch garduated ruler on a piece of paper. The section on the Parthenon is particularily wrong in that aspect and not even accurate in the materials used (the text and the pictures do not correlate). When treating art and architecture in this book, the author spends too much time analyzing if the artist/architect was consciously using the golden ratio on paper and doing a poor job at that. I don't care if he was. What I care about is the end result. Many artists probably do not think about mathematics when creating but the fact remains that many buildings and works of art follow the proportions of the golden ratio. And here the mistake the author makes is analyzing building in the eyes of a scientist, not in the eyes of an architect/artist. One example is when he says the Parthenon does not really follow the golden ratio proportions because if you include the lower stairs and edges of the roof in the rectangle, it doesn't fit anymore. Well, I have news for you, architecture is all about the overall appearance of a building, the main lines, what the human standing up at a distance from the building will see. The best test is, blurr your eyes at a frontal picture of the Parthenon taken on the field, from a distance and you will see the golden rectangle fits like a glove. If you want to get an idea of the artistic flair of this author, read the section on Le Corbusier where he compares the Modulor man to the Michelin man ;)
Rating: 
Summary: Very interesting, well written
Review: This book is well written and does a good job of discussing the number phi. The author presents a lot of mathematical history and shows that he has done some in depth research concerning the use of this number throughout history. The book addresses many myths about where the number phi appears. One example is that some historians believe that phi was used in the construction of the pyramids, the author addresses these theories with a thorough examination of why he believes that this isn't so. Along the way he provides may citations and mathematical examples to support his ideas. This book covers the history of the golden ratio in a very thorough manner and is written so that people with both a mathematical background or a non-mathematical background can understand the concepts presented. I recommend this book to anyone interested in mathematics or mathematical history.
Rating: 
Summary: Two books in one; one pretty good, one tedious
Review: This book, as its name suggests, is about an interesting number, the golden ratio (which I prefer to call "tau," but the author usually refers to as "phi," though explaining the reason for both symbols). For those who do not know what this number is, it can be defined in many ways, but the simplest is as the number which, when it is squared, is increased by 1. The fact that all the other definitions gives the same number is the reason for its great interest among recreational mathematics fans.The biggest problem with this book is that it tries to do two different things. One of the "two books" that I see in this one is about the _mathematical_ properties of the golden ratio. And this part of the book covers a lot of ground, and as a result I like it very much, as one of the few recreational math books I've seen recently that is easy to read yet still teaches me something I didn't know before I read it. The other part, however, is simply a refutation of claims made by many people that this or that artist consciously employed the golden ratio in his work. And it's interesting at first, but becomes tedious as he marshals more and more evidence refuting these claims. If the book confined itself to a discussion of the mathematical properties of the golden section (which is intimately related to such things as the Fibonacci sequence, Penrose tilings, and quasi-crystals), it would have merited 5 stars from me. But the attempt to refute all the artistic claims causes it to bog down for me, and causes me to cut one star off. One thing that totally puzzles me is his terminological decision to use "phi" rather than "tau." Since "phi" comes from a tribute to Phidias (a famous Greek architect/sculptor) and one of the points of the book is that neither Phidias nor his contemporary Greeks actually used the number in their designs, his statement that he uses "phi" to conform with most recreational math books is strange. I would, as I have said, gone with "tau," which was the earlier-introduced symbol and has the merit of coming from the initial of the Greek word for "section" (in keeping with the term "golden section" for this number).
Rating:
Summary: beauty, mathematics, mysticism: all in a number
Review: This is a book of 253 pages and 10 appendices about a number called the golden ratio. I confess that I have not read it thoroughly. But I believe that I have seen enough to give it 5 stars and review it intelligently. It is a book for mathematicians and non-mathematicians alike. The first question I asked was how can an entire book be devoted to one number. Well Beckman wrote a book about the number pi and certainly that was interesting. There is a lot to say about the geometry of pi and many mathematical and statistical properties it has. Some including the Buffon needle problem are related by Livio in this book. He contrasts pi to the golden ratio (phi) which also has geometric and mystical properties. The quantity pi is a transcendental number meaning it is not the solution of any algebraic equation. On the other hand phi is algebraic as it is the solution to a quadratic equation. Other strange properties of phi are:
1. If you subtract 1 from it you get its reciprocal
2. Add 1 to it and you get its square To see the marvelous algebraic and geometric properties of phi you need only scan through the 10 appendices. Scan through the book and the pictures show you the many artistic properties related to phi. Although algebraic phi is an irrational number. By applying the quadratic formula to its solution (see Appendix 5 in the book) you will see that its solution involves the square root of 5. Pythagoras and his followers in ancient Greece were said to have discovered irrational numbers (a natural consequence when you study right triangles) and hid this knowledge from the populous. Phi is defined by Euclid as the "extreme and mean ratio". As Livio quotes Euclid " A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser". This leads to an equality of proportions that yields phi=1.6180339887 rounded to ten decimal places. If you have the time read the book thoroughly. Write a review that adds to what has been said if you like. Or skim through the pages and appreciate the artist properties of phi along with its algebraic and geometric properties. Read about fractals and myths. Enjoy this wonderful book!
Rating:
Summary: Excellent & Unbiased
Review: This is a great book on phi. I like how Livio stayed objective and consistant throughout, disproving most of the New Age-y fluff sometimes associated with this number.
Rating:
Summary: Story of Phi
Review: This is a most engaging book about the history and use of the Golden Ratio, Phi. I feel the history of phi and the rest of mathematics is treated in an outstanding way. I recommend this book to mathematicians, scientists, to those of the general public with a desire to learn; and, especially, to young people in middle school and beyond who are eager to explore. I wish I had read this book 50 years ago.
Rating: 
Summary: I'm not a mathematician, but I find this book shallow.
Review: This is one of the lightest pieces of fluff that I have read in a while. With holes in Livio's arguments and almost no serious analysis, this book is not for any reader who has more than a high school education. The text boils down to a combination of the occasionally justified opinions of the author and an assortment of trivia that might have been interesting had they not been summarized so cursorily. In a book about something described as, "Astonishing," Livio oversimplifies his explanations to the point that every conclusion seems utterly mundane. He has also tried to cram too many topics into a very short book, giving none of them their due. Unless this is to be read as a first introduction to the ideas of mathematics, the history of mathematics, the history of science, etc., I recommend that you try to find something better. Best wishes and happy reading...
Rating:
Summary: Good intro to a fasinating subject
Review: This latest in what seems a deluge of science-history books, we have a good book bringing together the history of phi. At times there is an info overload, especially if you are familiar with some of the material, but informative if you're new to it. In the last chapter, the author's philosophical discussion seems to conclude this, "I don't want to pick either option" even though he tries to come up with one from a merging of these two: Phi & math are inherent in the universe and are the same everywhere or math is simply a human construct describing what we see. Well, it is inherent in the universe (such as phi everywhere). We put words and figures to describe it, however other beings would use different figures to write 1+1=2, but the meaning would be the same. The author seems to want to accept this fact - and not accept it - at the same time. The last chapter, especially the last two pages, would have been more intelligent if he wasn't trying to make everyone happy. See also Miranda Lundy's "Sacred Geometry," David Slatner's "The Joy of Pi," Robin Heath's "Sun, Moon & Earth," Gary Meisner's extensive website, "Phi: The Golden Number," and Dean's website "Mathematical Signatures in Nature: A Sign of Design."
Rating:
Summary: More like the Golden Bore
Review: What a depressing book this turned out to be. I thought a book about the "golden section" would have been interesting but in the hands of Mario Livio it is pure pain. To give a few examples... The author discusses the theory that the golden ratio was used by the builders of the pyramids and refutes it easily. And then continues to refute it for page after page. Then he does the same thing with the Parthenon, destroying the theory using the exact same reasons he used for the pyramid, explaining them in the same level of detail. But he isn't done yet. We get to have the same discussion again when we look at Renaissance paintings. I didn't really care about the discussion when discussing the pyramids but by the time I heard the argument for the third time I was ready to find something else to read. As he discusses the history of the golden section he goes into side trips to discuss anyone who had even the slightest relationship with phi. Anyone who has never heard of Kepler may find this interesting even if it is irrelevant to phi but I just started skimming pages hoping for something a little meatier. There is a little spark here and there that kept me reading hoping for more but more never arrived. A writer with a greater interest in the mathematics of phi could have made this a fun and interesting book. Livio seems to think the math is boring so he avoids it like the plague and creates a book that completely misses the point and ends up being a total bore.
Rating:
Summary: Fascinating, but too much filler.
Review: When ML is discussing Phi and all the places it shows up in nature and equations, the book is extremely fascinating. However, there's way too much filler material. Biography of artists, history of numbers, etc. that isn't really needed for the reader to enjoy the story of Phi.
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