The Golden Ratio: The Story of PHI, the World's Most Astonishing Number

Average customer rating:

"The Goden Ratio" by Mario Livio

Not the only imperfect book around

A strange, beautiful, and rare bird!

Some very interesting, many dead ends

The most sublime of numbers-well characterized

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
Mario Livio
Manufacturer: Broadway
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books
General Geometry | Geometry & Topology | Mathematics | Science | Subjects | Books
Research | Mathematics | Science | Subjects | Books
General Geometry | Geometry & Topology | Mathematics | Professional Science | Professional & Technical | Subjects | Books
Similar Items:

Zero: The Biography of a Dangerous Idea

e: The Story of a Number

An Imaginary Tale: The Story of "i" [the square root of minus one]

The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

The Divine Proportion

ASIN: 0767908163
Release Date: 2003-09-23

Book 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.

Customer Reviews:

"The Goden Ratio" by Mario Livio.......2007-10-09

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.

Not the only imperfect book around.......2007-07-13

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.

A strange, beautiful, and rare bird!.......2007-06-04

I had thought the Golden Ratio was simply the ideal aesthetic ratio between the length and the height of a painting or that of objects within a painting. According to Author Mario Livio, however, it has very little to do with the arts but a great deal to do with nature and the laws of physics, as well as some amazing abstract mathematical characteristics (discovered over the last several centuries). I believe the sub-title of the book is correct: it IS the world's most astonishing number. In other words, though it does not in the author's view have much to do with the Mona Lisa, the Parthenon, or the Pyramids, it does have some fascinating connections to nature, as well as numbers in the abstract, and their characteristics.

Well, what is the Golden Ratio anyway? Basically, phi or the Golden Ratio is such that if you break a line AB into 2 parts by adding point C to make AC and CB, such that AC is greater than CB and AC/AB = AB/AC. I t sounds pretty boring, but it gets a lot better, since it is also the convergence of something called the Fibonacci Sequence, a set of numbers beginning with 0 such that any 2 consecutive numbers added together equals the next number in the sequence (0,1,1,2, 3, 5, 8, 13, etc.). The Fibonacci Sequence can also be proved to be the same as the continued fraction of all 1's and also the convergence of the continuous nested square roots of 1's. (You can look on the net to see what these expressions look like, both somehow very satisfying aesthetically). I was amazed that these connections could have been made at all with phi, and that the Fibonacci Sequence is the most irrational of all possible numbers; that is, it converges the most slowly to its final irrational value. Call me weird, but that just blew me away!

I was most amazed that minds could think of these abstract things, and that the math connections to phi worked out so beautifully. Phi's abstract qualities are, in my opinion, every bit as impressive as its connections to nature itself (galaxies, sunflowers, hurricanes, and more). How did they think this stuff up, and why does it fit together so well? Some of the more bizarre are as follows:

The inverse of phi has the same numbers to the right of the decimal point as phi itself.

The square root of phi also has the same numbers to the decimal point as phi.

The sum of 10 consecutive Fibonacci numbers is = to the 7th number times 11.

The unit digit of a given Fibonacci number occurs exactly every 60 numbers.

All Fibonacci primes have prime subscripts (with the exception of 3).

The product of the first and third Fibonacci numbers in a set of 3 consecutive Fibonacci numbers is within 1 of the 2nd number squared.

Who would even think of looking into such things, and why does it work out so well?

There were also a couple of tangential points that were really neat to me. How about the First Digit Phenomenon (Benford's Law), that says if you have a random set of numbers, the probability of the first digit being a 1 is greater that it being a 2 is greater that it being a 3, and so on. How is that even possible in the real world? I'll have to think about that one a little more. And how about proof for the irrationality of the square root of 2? This elegant little proof was worth the price of the book, at least for me. It is a derivation of something called reductio ad absurdum: you prove something is true by starting with the opposite assumption and taking it to its logical conclusion to prove it can't be true.

Finally, I was struck by a broader question raised by the Mario Livio: how is it that math can so concisely define the laws of nature (gravity, motion, etc.)? I don't think that thought once crossed my mind throughout my high school and college careers in engineering! The book says that Kepler's Third Law, for example, states that the square of a planet's period divided by the cube of its semi-major axis is constant for all planets. How does that work out so well in such a brief, elegant formula, and how in the world did Kepler think of it? Are we talking Coincidence or Creator?

I was a little let down by this book as far as art is concerned; Livio simply doesn't believe it is a factor (except for a little 20th century art in the cubist genre perhaps). But I was surprisingly excited by some of the abstract characteristics of the Golden Ratio, and the minds that somehow put it all together. It was as exciting to me as seeing rare, beautiful, exotic creatures on a TV nature show.

The Golden Ratio is a strange, beautiful, and rare bird indeed!

Some very interesting, many dead ends.......2007-04-06

A lot of the early section about the history of mathematics, natural occurences, and the appearance of the phi is amazingly interesting.

Unfortunately, Livio then proceeds on a wild goose chase to mention many of the instances in which people have presumed (generally incorrectly) that various artists, writers, and other such public figures used phi in their work.

This book is certainly worth reading for the explanation of the origin of phi but I would recommend skimming the sections about artists, poetry, and musicians.

The most sublime of numbers-well characterized.......2007-03-18

Well titled, this book is an adventure. It is clear, concise, interesting and thought provoking.
I used it as inspiration for a course on the philosophy of architecture.

Book Description

The problems of medical care confront us daily: a bureaucracy that makes a trip to the doctor worse than a trip to the dentist, doctors who can't practice medicine the way they choose, more than 40 million people without health insurance. "Medical care is in crisis," we are repeatedly told, and so it is. Barely one in five Americans thinks the medical system works well. Enter David M. Cutler, a Harvard economist who served on President Clinton's health care task force and later advised presidential candidate Bill Bradley. One of the nation's leading experts on the subject, Cutler argues in Your Money or Your Life that health care has in fact improved exponentially over the last fifty years, and that the successes of our system suggest ways in which we might improve care, make the system easier to deal with, and extend coverage to all Americans. Cutler applies an economic analysis to show that our spending on medicine is well worth it--and that we could do even better by spending more. Further, millions of people with easily manageable diseases, from hypertension to depression to diabetes, receive either too much or too little care because of inefficiencies in the way we reimburse care, resulting in poor health and in some cases premature death. The key to improving the system, Cutler argues, is to change the way we organize health care. Everyone must be insured for the medical system to perform well, and payments should be based on the quality of services provided not just on the amount of cutting and poking performed. Lively and compelling, Your Money or Your Life offers a realistic yet rigorous economic approach to reforming health care--one that promises to break through the stalemate of failed reform.

Customer Reviews:

useful book on current healthcare economics.......2004-08-25

This book is probably an important addition to the literature on healthcare economics. It offers a good corrective to the politics out there. It reminds us that healthcare spending is not wasted spending, in the sense that it almost always adds value. It also points out that in many ways the costs of healthcare are FALLING.

The real question is how can we continue to improve the value of our healthcare dollar? Cutler concurs with many conservative healthcare analysts that the real problem is that the incentives in the American healthcare system are wrong. The incentives are aligned in favor of healthcare interventions rather than health. He proposes to address this incentive problem by having the government intervene in the market by providing the right incentives. In essence, the government would post-hoc realign the incentives by rewarding quality after-the-fact and beyond fees for services. In addition, he would subsidize insurance to create universal coverage.

This is an interesting idea. At the very least, it makes the important observations that the current system is rife with market failures due to the government-imposed structure of the market.

He does not seriously investigate other options. Both single-payer and conservative proposals are rejected with a single paragraph each. This probably misses some significant arguments from each. My sense is that he only sees one kind of market failure when there are at least two. The first problem has to do with incentives, which he sees.

The second problem has to do with information that is not efficiently used. Many of the conservative thinkers on this have argued that IT ought to provide significant cost-savings. In essence, 13% of our economy is still operating without the information processing that has revolutionalized the information economy.

Tort Reform Ignored.......2004-08-03

While I found Dr Cutler's analysis penetrating, I was disappointed that he did not discuss in any detail the large impact on medical costs of medical malpractice lawsuits. Not only do these lawsuits increase malpractice insurance premiums of physicians and health insurance premiums of patients, they lead to wasteful defensive medicine, as physicians do unnecessary tests and procedures in order to reduce the risk of malpractice suits. Tort reform is essential to control rising medical costs.

compelling approach to fix the broken American health system.......2004-01-29

Forty million Americans lack health care insurance and costs leap three and four times the inflation rate yet few Americans feel the system provides adequate care. Harvard economics professor and health-care expert Dr. David M. Cutler believes that the problem lies with the inability for most people to understand opportunity costs based on choices that may not lead to an improved life quality. The government and medical leadership exacerbate the problem with saving money as their solution, ignoring effectiveness. He makes a strong case on how much health care has dramatically improved over the past five decades as dramatized by longer productive life spans. Dr. Cutler believes that more money should be spent on further medical advances and that universal coverage for all needs should be implemented so that the present day uninsured can afford care rather than drain at a more costly rate the system. The key is to change from a system that economically encourages doctors to choose techniques that are not always the best for the patient factoring in cost and life quality to a system that reimburses doctors for quality service (not as hard as it first sounds).

Though at times the medical supply and demand is difficult to grasp, YOUR MONEY OR YOUR LIFE makes a powerful well written argument to reengineer a system in which political band aids fail everyone. The case for quality and the explanation of choices are well done and surprisingly easy to follow while offering a seemingly radical but compellingly logical approach to fixing the broken American health system.

Harriet Klausner

Average customer rating:
Your Money or Your Life: Strong Medicine for America's Health Care System
David M. Cutler
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback
ASIN: B000OKSAFI

Average customer rating:
Adventures of Captain Simon Suggs: Late of the Tallapoosa Volunteers; Together with Taking the Census and Other Alabama Sketches (Library Alabama Classics)
J. Hooper
Manufacturer: University Alabama Press
ProductGroup: Book
Binding: Paperback

Comic | General | Literature & Fiction | Subjects | Books
19th Century | British | World Literature | Literature & Fiction | Subjects | Books
19th Century | United States | World Literature | Literature & Fiction | Subjects | Books
United States | Short Stories | Literature & Fiction | Subjects | Books
British | Short Stories | Literature & Fiction | Subjects | Books
General | Humor | Entertainment | Subjects | Books
Similar Items:

Incidents in the Life of a Slave Girl (Dover Thrift Editions)

The Autobiography of Benjamin Franklin: Second Edition (Yale Nota Bene)

America: A Concise History, Volume 2: Since 1865

ASIN: 0817307060

Average customer rating:
Simon Suggs' adventures: Late of the Tallapoosa volunteers. Together with "Taking the census," and other Alabama sketches. With a portrait of Captain Simon Suggs
Johnson Jones Hooper
Manufacturer: T.B. Peterson & brothers
ProductGroup: Book
Binding: Unknown Binding
ASIN: B00087AM6M

Book Description

A one-of-a-kind guide to the great American singing groups from the Andrews Sisters to the New Kids on the Block

Here is the definitive history of pop and rock vocal groups: from the Ink Spots and the Modernaires of the 1940s, the Coasters and the Platters of the 1950s, the Chiffons and the Shangri-Las of the 1960s, to the Pointer Sisters, the Jackson 5, and En Vogue of the 1970s and beyond. Singing groups were crucial in shaping today's pop music, and this book entertainingly and authoritatively tells the story of more than 350 classic acts spanning five decades. Each entry is packed with facts about the group's career, key members, and musical impact. With extensive discographies and rare photos, this giant reference book is a browser's delight, filled with musical lore that will appeal to casual fans and to serious collectors and aficionados alike.

"Your book on singing groups has taken me back to a time, a people, and a music that I love. As far as I'm concerned, you've made the greatest contribution to music for the '90s and beyond." -Ben E. King, The Drifters

"I've never been so thoroughly entertained while being informed." -Frankie Valli, The Four Seasons

Customer Reviews:

A Wealth Of Information.......2000-04-25

A perfect source of information for those days when you want to remember music of the past. Great for settling disputes, answering trivia questions, or just getting the cobwebs out of the musical side of your brain. Highly recommended for all music lovers libraries.

Book Description

This collection looks from a variety of angles at the human body as it resists the determinations of gender, sexuality, socialization, and history. Ranging from classical hermaphrodites, Bruegel's blind faces and Weimar transgender surgery, via Gentlemen Prefer Blondes, state-socialist sport and Proust, to Barbie, Lari Pittman, American Psycho, IVF, and video dance, the 16 essays question the relationship between politics, culture, and desire.

Average customer rating:

Indeterminate Bodies
Naomi (Edt)/ Taylor, Lib (Edt)/ C Segal
Manufacturer: Palgrave Macmillan 01/1//2003
ProductGroup: Book
Binding: Paperback
ASIN: B000N5O4EU

Book Description

Tells how radio and television became an integral part of American life, of how a toy became an industry and a force in politics, business, education, religion, and international affairs.

Customer Reviews:

Excellent overview of the formative years of US broadcasting.......2004-09-05

This book is the second in a series of three books that comprehensively cover the American broadcasting and radio industry from the very beginning through 1970. This particular book covers the period between 1933 and 1953, when much of the current structure (networks, sponsorship, etc) of the business were solidified. The whole series is outstanding, especially volumes I & II, both of which I would highly recommend to anyone interested in understanding how the US radio/TV business evolved.

Amazon.com

Don't let the title mislead you: The Essential Guide to Digital Set-Top Boxes and Interactive TV isn't a primer for using WebTV's enhanced services. This book is for software, programming, and TV professionals looking to capitalize on this paradigm shift in the delivery of information and entertainment. With that in mind, Gerard O'Driscoll has done a masterly job of condensing a complex subject.

The book starts off by briefly explaining the roles of the various international standards groups and taking you through the building blocks of digital TV. O'Driscoll is clearly familiar with digital TV's underlying technology, offering detailed information about competing operating systems, development platforms, and broadband networks.

Less clear are the benefits and drawbacks to all of the factors involved. O'Driscoll occasionally touches upon these--such as when he notes Microsoft's difficulties in cracking the digital set-top business--but too often he fails to provide analysis of why a certain method works better than another, or why one technology has been more successful in gathering momentum. For example, he notes that electronic cash as a potential digital TV application must be safe from counterfeiting and other forms of fraud, but he doesn't mention what initiatives are underway to prevent them. It would also be helpful to have an idea of how viable such applications are in the near future.

Nonetheless, this is a useful, if seriously technical, guide to what the future of TV may hold. For software developers and television executives alike, The Essential Guide to Digital Set-Top Boxes and Interactive TV is just that--essential. --John Frederick Moore

Topics covered: Building blocks of a digital TV system, architecture of a set-top OS, middleware standards, set-top application development, choice of broadband intranet applications, and general principles of designing for a TV environment.

Customer Reviews:

The Essential Guide to Digital Set-Top Boxes and Interative TV.......2007-10-03

I received this book two days ago. Unfortunately, all figures and fotos are damaged (smudgy print). I would like to replace it.

Thanks,

Uvermar

Overhyped title, poor content.......2003-09-03

I bought this book about 2 years ago however I never finished it, lately I picked it up again looking for some reference information and then I knew why I never finished it in the first place.
Aside from what other readers have pointed out about bad organization, cut and paste manufacturers' white papers and wishlists, I found the inconsistency in presenting the information in this book to be the prevalent pattern. Within the same section the reader is presented with sub-sections with completely different layouts : one technology is explained with graphs, the other with bullets, another one with a short paragraph etc...
Some information is explained extensively without merit, example : a set-top web browser uses HTML for displaying internet content (duh) and then he goes for about 2+ pages on how HTML works with explanation about HTML tags and the Back and Forward buttons etc...
A major technology like MPEG-2 didn't get the coverage it deserved.
Finally this author took advantage of the fact that not many books cover this specific area about interactive TV and with a misleading title like the "essential" guide he's under delivering big time. I highly don't recommend this book.

A good introduction to a complicated subject.......2002-03-28

A lot of the information contained in THE ESSENTIAL GUIDE TO SET-TOP BOXES AND INTERACTIVE TV is specialized and arcane. Of course, this shouldn't be that great of a surprise, given the relatively small size of this particular field at the moment. The material covered in this book should give the newcomer to the field a lot of the valuable and fundamental information that they'll need to know. Unfortunately, some of the data is out of date, and there are several new things that have come about since the publication of this book. It's useful for someone who is just getting started, but I'd like to see a new edition written some time soon that takes the material mentioned here and goes farther with it.

There is quite a lot of information that's been packed into this book. In fact, at times it almost appears too compressed and some topics could have used much more elaboration. In particular, the chapter that deals primarily with the possible Internet applications only brushes the surface of what could be discussed. The topics that are touched on include: Digital TV (an overview), enhanced TV, set-top hardware architecture, set-top server architecture, set-top operating systems, set-top middleware, set-top platforms, set-top application development (Intranet, Internet and otherwise), electronic program guides, and set-top smart cards. As you can no doubt tell, this is a staggering amount of material to get through in only about three hundred pages. Obviously the level of detail is not going to be terribly high, but it is worth it to get an introduction to so many different topics.

For the programmers out there, think of this ESSENTIAL GUIDE as a breadth first search. It covers a wide range of areas, but it does so superficially. As something you read once to get a feel for the terminology and the particulars, this book is quite good. But it's not very effective as a resource or a reference, because the in-depth material one would need simply isn't present. A good introduction only.

A Disappointing Hodge-Podge of Information.......2001-03-16

I purchased this book about 6 months ago (I write this review in March 2001). I have, on several occassions since attempted to derive some value from it. Unfortunately, it is a hodge-podge of unordered facts. It was substantially out of date even at the time of my purchase. Several of the companies and products discussed no longer exist. There seems to have been little thought as to the overall organization of information. I agree with the other reviewer who stated it seemed like this was a cut-and paste from information provided from the various manufacturers.

While you can learn somewhat out-dated information about the set-top box industry if you work at it - and believe me you have to work to make sense out of this information - there is very little here that cannot be learned by spending a few hours surfing the net. Even if it wasn't substantially out of date, it would be extremely difficult to recommend this book to anyone other than someone who MUST have access to this specific information and they can't find it anywhere else.

Exciting subject area.......2001-02-07

I read O'Driscoll's guide to home networking and decided to also buy his second book on set-top boxes. Although some of the product specific information is a little dated since 1999, the remaining generic content will stay relevant for many years to come. Excellent source for engineers and technical marketeers who want to take advantage of the many opportunities that are beginning to emerge from digital and interactive television

Books:

Books Index

Books Home

Recommended Books