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Title: The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
ISBN: 0767908163
Author:
Mario Livio
Publicate Date: 2003-09-23
Publish: 2003-09-23
List Price: $14.95
Average Customer Rating: 4.0
Format: Paperback
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Amazon Lowest New Price: $6.46
Amazon Lowest Used Price: $2.93
Amazon Merchant Price: $10.17
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| Customer Review: |
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1: Crackpotiana
subtitled: The Story of PHI, the World's Most Astonishing Number
that's alot of hype for the irrational number 1.6180339887... . the author barrages the reader with hyperbole. 'mysterious', 'astonishing', 'amazing', 'wonderful', 'beautiful', 'fascinating', 'curious', 'crucial', 'unimagined', 'divine', etc. etc. not just astonishing, but "the World's Most Astonishing Number".
horse feathers. the people who are 'fascinated' by this are the same who freak out when they see 11:11 on a digital clock; the same who have 'lucky' numbers; the same who fear Friday the 13th.
in fact there are more 'crucial' AND more 'astonishing' numbers. how about 0 or 1 or 2 or 10 or infinity? i guarantee you that if we changed our everyday number base from 10 to , say, 13 that the wheels would fall off of this old bus. now THAT is 'crucial'. and 'divine'? please! what could be more 'divine' than 1? maybe 2 :-) . 'astonishing'? 1 is 'astonishing'. it factors into EVERYTHING! it's everywhere and in everything. 0 doesn't factor into anything. these are more 'astonishing' than phi.
Dali knew how to capitalize off of frenzied hype, so he threw together the "Sacrament of The Last Supper" and when phi's superstitious cultists found out that it featured the 'divine' proportion they took care of turning that ugly, mediocre effort into a 'divine' icon.
the author is supposedly a PhD? whatever.
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2: A bit tiresome. The title seems misleading to me.
I bought this book with a thirst to know about this number phi. I did learn about the number phi. However a large part of the book was devoted to instances where various people thought the number phi was present but the author spent considerable time developing the opinion or fact that phi was not influencing this or that particular instance. I got REALLY tired of that.
For me, the first chapter and a half or so and the last two chapters were the meat of the matter for my interest. The book was worth it for the last chapter.
I think that the author would have been better to write a book titled "Why Is Mathematics So Effective?" That seemed to be the central question that really drove the author.
I don't regret reading it. I just feel it wasn't really the book I signed up for.
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3: 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!
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4: 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
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5: 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!
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