Download The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio
It is not secret when attaching the creating skills to reading. Checking out The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio will certainly make you obtain even more sources as well as sources. It is a manner in which could boost exactly how you neglect as well as understand the life. By reading this The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio, you could more than exactly what you obtain from other publication The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio This is a well-known book that is published from famous author. Seen kind the author, it can be trusted that this publication The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio will certainly offer numerous motivations, concerning the life and also encounter as well as every little thing inside.
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio
Download The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio
The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio. Welcome to the most effective internet site that offer hundreds type of book collections. Below, we will provide all books The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio that you require. Guides from famous authors and authors are given. So, you could appreciate currently to get one at a time kind of publication The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio that you will search. Well, related to the book that you want, is this The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio your option?
The way to obtain this book The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio is extremely simple. You might not go for some places and also spend the moment to only find the book The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio As a matter of fact, you may not always obtain guide as you want. But right here, just by search and locate The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio, you can get the lists of the books that you actually expect. In some cases, there are several publications that are showed. Those books obviously will certainly impress you as this The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio collection.
Are you interested in mostly books The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio If you are still perplexed on which one of guide The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio that must be purchased, it is your time to not this website to look for. Today, you will require this The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio as one of the most referred publication and also most required book as resources, in various other time, you can delight in for a few other publications. It will depend upon your prepared demands. But, we consistently suggest that books The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio can be a great infestation for your life.
Also we discuss guides The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio; you may not find the published books right here. Numerous compilations are provided in soft data. It will precisely give you much more perks. Why? The initial is that you may not need to lug the book almost everywhere by satisfying the bag with this The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio It is for guide is in soft data, so you can wait in gizmo. After that, you can open up the gadget almost everywhere and also review the book correctly. Those are some few advantages that can be got. So, take all advantages of getting this soft file publication The Golden Ratio: The Story Of Phi, The World's Most Astonishing Number, By Mario Livio in this site by downloading and install in web link given.
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.
- Sales Rank: #2419737 in Books
- Published on: 2014-12-02
- Formats: Audiobook, MP3 Audio, Unabridged
- Original language: English
- Number of items: 1
- Dimensions: 6.75" h x .50" w x 5.25" l,
- Running time: 10 Hours
- Binding: MP3 CD
From Publishers Weekly
Most readers will have at least dim memories from geometry class of the irrational number pi. Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account, the first on the subject written for the layperson. Phi is the golden ratio of antiquity (1.6180339887), a never-ending number so lauded for its harmonious qualities that in the 16th century it was dubbed the divine proportion. It is related to phenomena as diverse as the petal arrangements of roses, the breeding patterns of rabbits and the shape of our galaxy. Phi is also claimed to have been crucial in the design of the Great Pyramids, the composition of the Mona Lisa and the construction of Stradivarius violins. Livio (The Accelerating Universe) carefully investigates these and other claims and does not hesitate to debunk myths perpetuated by overzealous enthusiasts he calls "Golden Numberists." This is an engaging history of mathematics as well, addressing such perennial questions as the geometric basis of aesthetic pleasure and the nature of mathematical objects. Useful diagrams and handsome illustrations of works under discussion are amply provided. Livio is gifted with an accessible, entertaining style: one typical chapter bounds within five pages from an extended discourse on prime numbers to a clever Oscar Wilde quote about beauty to an amusing anecdote about Samuel Beckett and finally to an eminently clear explanation of G"del's incompleteness theorem. With a guide to the history of ideas as impassioned as Livio, even the math-phobic can experience the shock and pleasure of scientific discovery. This thoroughly enjoyable work vividly demonstrates to the general reader that, as Galileo put it, the universe is, indeed, written in the language of mathematics.
Copyright 2002 Reed Business Information, Inc.
From School Library Journal
Adult/High School-Take something as simple as a line segment and mark it at just the right place. Looking at it with a mathematician's eye, an interesting relationship appears: the ratio between the whole line and the larger of the pieces it was broken into is the same as the ratio of the larger piece and smaller piece. Better known as "the golden ratio" or phi, 1.618- is a number that has fascinated humans for several hundred years, and people have claimed evidence of phi in all manner of things. Livio takes readers on a treasure hunt for phi from ancient times through the present. On the way, he debunks a number of popular myths (e.g., the notion that Mondrian used it in his abstract paintings) and does a wonderful job explaining the Fibonacci sequence and its relationship to phi. Small, black-and-white photos and reproductions demonstrate items mentioned in the text. While it may seem that the author wanders in his expositions, his excursions into history and number games add fun and depth for those who wish to follow. To get the most out of The Golden Ratio, it is best to have an understanding of algebra and basic trigonometry, although the book is great for general readers who don't mind working a little to gain a lot of understanding.
Sheila Shoup, Fairfax County Public Library, VA
Copyright 2003 Reed Business Information, Inc.
From Scientific American
Most schoolchildren learn the importance of the number ϖ, or pi (3.14159...), early on in their mathematical training. The area of a circle? ϖ (r2). Circumference? 2ϖr. But for astrophysicist Livio, the number φ, or phi (1.61803...), holds more wonder. Known as the Golden Ratio, Golden Number and other names related to gold or divinity, phi can be used to describe the characteristics of seashells, sunflowers, paintings and pentagrams. Livio traces the history of phi's discovery in tandem with the development of arithmetic, algebra and higher mathematics, examining along the way whether its value was factored into the construction of the Egyptian pyramids or the Parthenon of Greece. Practical examples placed throughout the story, requiring nothing more than a handheld calculator or some scratch paper, help to illustrate phi's relevance to mathematics and the world at large.
Editors of Scientific American
Most helpful customer reviews
163 of 172 people found the following review helpful.
"The World's Most Astonishing Number"
By Timothy Haugh
Are some numbers more important than others? Certainly numbers like the primes, pi and "e" have properties that make them interesting to mathematicians and physical scientists alike. Then there are numbers like 7, 13 and 666 that have other connotations for theologians, numerologists and the like. And yet, some numbers have not gotten their due in recent years. Phi--a number variously referred to as the golden ratio, golden section, and divine proportion among others--is one. But Mario Livio has written a book in an attempt to remedy this situation.
Phi received its original definition from Euclid as an "extreme and mean ratio" when a straight line is cut so that the ratio of the entire line to the longer division of the segment is the same as the ratio of the longer division of the segment to the shorter. And yet, much like the better known geometrical example of pi, phi turns out to have many more applications beyond its simplest geometrical definition. Though measurable, phi is an irrational number with relationships to the Fibonacci sequence, fractals, the physical structure of things from plant growth and spiral shell development to the appearance of large-scale objects like galaxies, and more. And beyond this, phi has been used as a basis applications in numerology and aesthetics.
Livio does a very good job of covering all this ground and more. He is especially good at giving us a historical overview of the development of our understanding of this important number as well as explaining the mathematics in a way that is complete but easy to understand. He is also very good at presenting the various mystical ways phi has been interpreted over the centuries, giving each a rigorous challenge--rejecting many but open-minded to the possibilities that any good Platonist would be.
In fact, if there is a weakness in this book, it is that Livio spends a lot of time covering these more esoteric applications of phi. And yet, these applications are part of the history of the number and cannot be ignored whatever a reader might feel about the value of these applications. Phi may not quite live up to the hype as "the world's most astonishing number" but certainly any reader with an interest in mathematics will not want to miss this book.
122 of 129 people found the following review helpful.
Interesting book, interesting number
By mrliteral
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.
94 of 100 people found the following review helpful.
All About 1.618033988749894848204586834365638117720309179...
By Rob Hardy
Of all the irrational numbers, the best known is pi, which shows up all over the place. However, if you read _The Golden Ratio: The Story of Phi, The World's Most Astonishing Number_ (Broadway Books) by Mario Livio, you will gain an appreciation for the ubiquity of another irrational with all sorts of amazing properties. You can try this one on your calculator: Phi equals 1.6180339887... (As an irrational, its string of numbers goes infinitely beyond the decimal point, and you can be sure computers have calculated it to millions of places). Take the inverse of that number; that is, divide it into one. You will get 0.6180339887...; in other words, the inverse looks just like phi itself, but with a zero instead of one left of the decimal. Or try this: start with a 1, followed by a 1. The next number will be the two previous ones added together, which is 2; the next number, in turn, is again the two previous ones added together, which is 3. The series goes 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... This is the famous Fibonacci sequence, and is investigated widely within this book as it is intimately connected to phi. Take any number in the series and divide it by the number before it, and you will get a number close to phi; the higher the number in the series, the closer the result comes. (13 / 8 = 1.615 ; 55 / 34 = 1.6176....).
These sorts of number tricks abound in Livio's book, and the mathematics is not daunting. It is also a history of phi, which turns out to be a representative slice of the history of mathematics. Euclid knew the number, but Leonardo Fibonacci in the twelfth century developed the series with its ratio. It shows up in breeding rabbits; spirals in pine cones, sunflowers, galaxies, and hurricanes; tilings and fractals; and many more surprising places. Livio has enormous fun giving and explaining all these examples. Showing up as it does all over the place, perhaps phi is just being seen because that is what is being looked for. Livio, whose day job is being Head of the Science Division at the Hubble Space Telescope Science Institute, is refreshingly dismissive of attempts to try to see a Golden Ratio in everything, which people have tried to do for centuries. It isn't in the pyramids, nor in the Parthenon, nor in Leonardo's paintings.
Without forcing the issue, however, it is easy to see that the Golden Ratio, logarithmic spirals, and Fibonacci numbers are all over the place; there is even a _Fibonacci Quarterly_ mathematical journal. This leads to larger final issues, which Einstein expressed as the question, "How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?" Do mathematical concepts have a universal and timeless existence "out there" and are just waiting for us to discover them? Or is mathematics a human invention that resides only within the human brain? It can't be surprising that this classic conundrum is not definitively solved here. Livio's ideas about it, however, well expressed and tied to this remarkable numerical constant, are well worth thinking about.
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio PDF
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio EPub
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio Doc
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio iBooks
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio rtf
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio Mobipocket
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number, by Mario Livio Kindle
Tidak ada komentar:
Posting Komentar