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Title: The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
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Manufacturer: Broadway
List Price: $14.95
Our Price: $6.70
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| The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Broadway Excellent Job | | One of the best books I've read. It is an in depth study of the Golden Ratio...the history, purpose, relationship to other concepts. I am intrigued by math, art, and science and found this book very, amusing. You will need a basic understanding of high school math to fully appreciate some of it. Oh, by the way, the author shoots down most other author's claims that the golden ratio has been used in classic architecture and art. Superb job Mario Livio! | | The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Broadway Many errors in the book | | I happened to notice that he says Babylonians found the general solution for the quadratic. General solution of the quadratic was given by Bhaskara. The author has not read Fibbonaci's book. Fibonacci himself said in the preface that he learnt new math from India. Fibonacci numbers were found by Hemachandra. there were many other errors...I would not recommend to my students | | The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Broadway another mysterious and fascinating irrational number like pi and e | Several years ago I prepared a review for amazon on this book. Since that time there have been many others to contribute. There are those like me who found it fascinating and gave it five stars, others that gave it a 4 or a 3 because they quibbled with the author over some mathematical issues and finally agroup that really hated it and found it boring and gave it only 1 or 2 stars. Some of those in the third group claim to be mathematicians but thought the book had too detailed. I don't see how a true mathematician could not love this book. Here is what I wrote that I still believe.
The book is 253 pages and 10 appendices about a number called the golden ratio. I give it 5 stars. 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.
Livio also discusses the relationship between the ratio and our concept of beauty (i.e. the quality of the perfect face). It is also interesting that in his new book on the impossibility of solving the 5th degree polynomial by radicals Livio relates the Galois theory of groups to concepts of symmetry. There he also attributes our perception of besuty to symmetry.
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!
| | The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Broadway "The Goden Ratio" by Mario Livio | | Highly readable and fascinating book by the well-respected Mario Livio. See http://en.wikipedia.org/wiki/Mario_Livio The book does not require a math background to understand or appreciate. Traces the origins and applications of the golden ratio through time, nature and art. Explores (and generally refutes) myths and misconceptions about the golden ratio. Highly recommended. Fascinating reading. Dan Brown (author of "the DaVinci Code") reportedly loved the book. | | The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Broadway Not the only imperfect book around | I like Livio's cautionary tone throughout the book, ie he's not a starry-eyed Golden Numberist, who believes that the Ratio is the only measure of beauty and proportionality in the universe. That's probably his strongest point.
For one, I'm not so interested in the application of the Golden Ratio or Fibonacci sequence (also somewhat discussed in the book) to art in general. What's so great about Salvador Dali using the Ratio in "Sacrament of the Last Supper", or its apparent extensive use by Bela Bartok in his compositions? In fact, I found a tad irritating Livio's habit of filling page after page discussing the supposed use of the Ratio by some painter or musician, just to conclude that probably it was all just coincidental. Also annoying, at the beginning of the book, is his characterization as "famous" applied to almost every person cited. As if I didn't know that Einstein, Buffon, Pythagoras and Lord Kelvin are all famous!
On the other hand, I enjoyed the book rather terse treatment of the Ratio and the Sequence in pure plane geometry and Platonic solids, and even more interesting is the brief discussion of their serendipitous presence in nature --chambered nautilus and tree's leaf arrangements (phyllotaxis). Brief, sadly.
I also confess to having gotten a little bored and glassy-eyed, and pretty often had to lie down, half-asleep, on my bed while reading this book. Livio often goes off on a tangent, as I said before, following false leads, dead-ends, and even the occasional windmill. After all, I guess that's the price the reader has to pay when the author's trying to meet the publisher's magical, and very much de rigueur, rational proportion of about 250 pages per book.
In conclusion, and on a positive note, this book at the least (re)sparked my interest in the history of number theory, and other special numbers and figures (like 1, zero, pi, e, and i). So, I can't say I wasted my money when I bought it.
| | The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Broadway Product Description | Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!
The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
From the Hardcover edition. |
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