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Summary: Golden Journey
Review: In "The Golden Ratio", Mario Livio takes us into the world of beauty. The mathematical properties of the number phi are revealed through enlightening examples taken from everyday life, from music and art,and from biology and economy. This is a joyful journey in time, beginning at the very dawn of history and moving on until modernity, that explores the many features through which the Golden Ratio unites our universe.
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Summary: Interesting book, interesting number
Review: In mathematics, there are a few irrational numbers that stand out from the infinitely crowded field. First in the bunch would probably be the square root of two, which was kind of the "first" irrational number. Then there is the everpresent pi, and then the less well-known but completely important "e". If there was a fourth place prize, however, it would probably go to the golden number, phi, or roughly 1.618.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.
Rating:
Summary: Interesting book, interesting number
Review: In mathematics, there are a few irrational numbers that stand out from the infinitely crowded field. First in the bunch would probably be the square root of two, which was kind of the "first" irrational number. Then there is the everpresent pi, and then the less well-known but completely important "e". If there was a fourth place prize, however, it would probably go to the golden number, phi, or roughly 1.618. 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.
Rating: 
Summary: There Are More Vital Math Teachings To Be Mastered
Review: Let's focus on adopting the METRIC SYSTEM (all most Americans seem to know about this VITAL part of Math is the approximate size of a 2 liter bottle). When every cashier at fast food restaurants have been trained to make proper change WITHOUT depending on electronic cash registers, then perhaps the quest for "phi" would be a sensible idea.
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Summary: Dear M. Livio, Esq., I need two rabbits for correct Phi
Review: Let's us assume, that you have bought two newborn rabbits. I hope you have taken male and female. While all is correct. You will must feed them; do hardly look after them, and so on. In third month you will have two pair rabbits, for the fourth month you will have 3 pairs, for the fifth month - 5 pair, on sixth - 8 pairs, and so on. See thevortextheory.com.
It is possible to speak about mysticism of a sequence Fhi very much and long. I am sure, that the economists will see in it a rise in prices on the goods. Physics will notice laws, which are shown in power transitions arising at transformations of elementary particles. The chemists will find adequate parities in a structure of chemical connections. I think that each of us will recollect a line of numbers from the life will find the numbers available in a sequence Phi. It is necessary only attentively to read this useful book. I do not speak already that you can tell then to the relatives, friends and colleagues on work. I am sure, that you will make on them indelible impression of educated and competently of man. vavivlad-rvc@mtu-net.ru
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Summary: A good read for those of us who like numbers
Review: Livio does a wonderful job of bringing to the table much of what as been discussed regarding the Golden Ratio/phi. The history of the number is presented in a very straight-forward manner, and informative to those of us who were confused as to what form the number was first recognized. Much of the book is spent discussing the various ways phi has played into nature and human society/culture. Actually, many of the the stories we are told relating to the application of phi are quate falase according to Livio, but the applications which nature presents are quite sound. After reading this book, you will probably agree also. So strap your reasoning caps on, grab some scrap paper and a pencil to work some of the appendix examples, and enjoy this delightful read (for both math and non-math buffs alike).
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Summary: Interesting, clever, well written
Review: Livio's book is a true Renaissance feat. Mathematics, science, art and aesthetics - all are related to the enigmatic phi.
Very enjoyable and stimulating!
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Summary: A great guide to an amazing number
Review: Livio's book is really an interesting look at a number similar to pi in that's an irrational number which displays itself in various places in nature, from the arrangement of petals on a flower to the logarithmic spirals of galaxies. Livio explains the original formulation of this number by Euclid and proceeds to address the various times in history in which it may have been employed by architects, artists and musicians. I think this is a really good book if you're interested in reading about the most "irrational of all irrational numbers".
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Summary: Pursuing the Mysteries of the Ubiquitous Number Phi
Review: Mario Livio, a cosmologist and art aficionado at the Hubble Space Telescope Center and the author of the previous book "The Accelerating Universe," wrote a lot about the irrational (never-ending, never-repeating) number phi, or the Golden Ratio, whose value is 1.6180339877... The story starts from these questions: Who discovered the Golden Ratio? Was phi used in the design of a Babylonian stela and Egyptian pyramids? The author pursues the answers to these questions, writing a series of his thoughts like a detective story. Then he describes the role of the Greek mathematicians Plato and Euclid, and the Italian mathematician Leonardo Fibonacci in the history of phi, together with the geometrical and arithmetical wonders connected to this number. One example of the wonders is the relation between the Fibonacci sequence and phi. The Fibonacci sequence 1, 1, 2, 3, 5, 8, ... is defined as a series of numbers in which each term is the sum of the two preceding terms. The ratio of successive numbers of this sequence approaches phi as we go farther and farther down the sequence. Next come the topics of phi found in nature and used in arts. The logarithmic spiral, which goes hand in hand with the Golden Radio, appears in the sunflower, the flight of a falcon, galaxies, etc. The author's study of many historical attempts to disclose the Golden Ratio in various works of art, pieces of music and poetry comes to the conclusion that ... (I have to refrain from writing the ending of the "detective story"). In the final chapter Livio considers the question: What is the reason that mathematics and numerical constants like phi play such a central role in topics ranging from fundamental theories of the universe to the stock market? Noting that the discussion about this question can fill the entire volume, the author gives a brief (but very understandable) description of the modified Platonic view and the natural selection interpretation. He also presents his personal opinion, which adopts complementarity of the above two views. This chapter whets readers' appetite for a possible next book on this topic to be written by Livio. I strongly recommend "The Golden Ratio" to scientists, artists and laypersons that are interested in the wonders of numbers and mathematics and in their relations to arts and nature.
Rating:
Summary: Pursuing the Mysteries of the Ubiquitous Number Phi
Review: Mario Livio, a cosmologist and art aficionado at the Hubble Space Telescope Center and the author of the previous book "The Accelerating Universe," wrote a lot about the irrational (never-ending, never-repeating) number phi, or the Golden Ratio, whose value is 1.6180339877... The story starts from these questions: Who discovered the Golden Ratio? Was phi used in the design of a Babylonian stela and Egyptian pyramids? The author pursues the answers to these questions, writing a series of his thoughts like a detective story. Then he describes the role of the Greek mathematicians Plato and Euclid, and the Italian mathematician Leonardo Fibonacci in the history of phi, together with the geometrical and arithmetical wonders connected to this number. One example of the wonders is the relation between the Fibonacci sequence and phi. The Fibonacci sequence 1, 1, 2, 3, 5, 8, ... is defined as a series of numbers in which each term is the sum of the two preceding terms. The ratio of successive numbers of this sequence approaches phi as we go farther and farther down the sequence. Next come the topics of phi found in nature and used in arts. The logarithmic spiral, which goes hand in hand with the Golden Radio, appears in the sunflower, the flight of a falcon, galaxies, etc. The author's study of many historical attempts to disclose the Golden Ratio in various works of art, pieces of music and poetry comes to the conclusion that ... (I have to refrain from writing the ending of the "detective story"). In the final chapter Livio considers the question: What is the reason that mathematics and numerical constants like phi play such a central role in topics ranging from fundamental theories of the universe to the stock market? Noting that the discussion about this question can fill the entire volume, the author gives a brief (but very understandable) description of the modified Platonic view and the natural selection interpretation. He also presents his personal opinion, which adopts complementarity of the above two views. This chapter whets readers' appetite for a possible next book on this topic to be written by Livio. I strongly recommend "The Golden Ratio" to scientists, artists and laypersons that are interested in the wonders of numbers and mathematics and in their relations to arts and nature.
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