The golden ratio mario livio
Rating:
7,3/10
601
reviews

Livio's book is meant to appeal to a wide audience. Essentially, I went into this book expecting to be, I don't know, told about Phi. This happens repeatedly throughout the book. Livio and his wife Sofie, a microbiologist, have three children. Not sure if that would make a difference, though, because Livio's treatment of this topic is really solid. He calls attention to Fibonacci's pedagogical genius. Livio addresses the key question about phi immediately.

It was still really fun. Unfortunately all of the other books 3 of them, some rare and out of print are heavily mathematic in their texts. Nevertheless, I have to admit that I found the chapter on periodic tilings and the significance of Penrose tiles difficult to understand. Langlois digitized the faces of male and female students and mathematically averaged them, creating two-, four-, eight-, sixteen-, and thirty-two-face composites. Imagine a line divided into a longer segment a and a shorter segment b ; the dividing point is placed so that the longer segment a compared to the shorter segment b is proportional to the entire length a+b compared to the longer segment a. The resulting ratio is phi, an irrational number equaling approximately 1.

Particularly important in the history mathematics and in Livio's account is the Fibonnaci sequence where the ratio of successive numbers increasingly approximates Phi. The deeper theme of the book is the relationship between mathematics and the real worldâdoes mathematics reflect our universe or does our universe strive to conform to mathematics a Platonic view? At least the rash of books for general audiences in this vein published in the last two decades suggests this. I have now only really fault the reader if it is just annoyingly read, and this was not one of those narrators. If you have the patience to juggle and manipulate the numbers in various ways, you are bound to come up with some ratios that are equal to the Golden Ratio. Black holes warp space in their vicinity so much that in Einstein's classical General Relativity, nothing can escape from them, not even light. Mario Livio is head of the Science Division at the Hubble Space Telescope Institute, where he studies a broad range of subjects in astrophysics, particularly the rate of expansion of the universe. This was an all-around entertaining book.

So I was stuck trying to decipher the text via the sparce English. Whether you are curious to know more about the golden number, the golden ratio, the golden triangle, rectangle, rhombohedra, golden sequences, or golden trees I heartily recommend this book! Primary supporting sciences are: 1 Design disciplines, 2 Communication disciplines, and 3 Information disciplines. 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. 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. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who It is a great book. Do we have the permission of Anonymous to give this in print using the ellipsis: 1.

I gained a new appreciation for their achievement from reading this book. 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. 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. Get yer head out of your ass! Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. This equality yields Phi, an irrational number beginning with 1. Fechner went further and measured the dimensions of thousands of rectangular-shaped objects windows, picture frames in the museums, books in the library , and claimed in his book Vorschule der Aesthetik to have found the average ratio to be close to the Golden Ratio.

It has even been found to be connected to the behavior of the stock market! Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. Now fold b so that it is perpendicular to a. Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. 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 truly amazing to see how often this number and ratio are found in nature. Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality.

The discovery, the relevance, the applications and help it provided Am I nerd for voluntarily reading this? But Livio is a debunker too. 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. But sometimes the drawn out history lesson left my interest to wander. Maybe that's what makes it beautiful. I appreciated the sensibility Livio showed in this work, specifically in his loyalty to the scientific method.

This book was given to me by my daughter and son-in-law. When extirpating the superstitious mind, we must be careful not to throw the baby out with the wash. 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. For Mario Livio, phi, the Golden Ratio, evokes this holy wonder, and he sets out to make us feel it too. The structure of the book is excellent -- each section moves smoothly and, often, chronologically into the next, while still bring divided by subject.

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. Un numero, un rapporto che ritroviamo o che molti studiosi hanno trovato in molte opere dell'uomo e opere della natura. 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. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1. Michael Godkewitsch of the University of Toronto, for example, pointed out that average group preferences often do not reflect the most preferred choice.

When Livio does manage to address phi directly, he does so by debu Having expected a book filled to the brim with Phi related information, I feel let down by the end result. I suppose credit where it's due a lot of this is actually debunking the bible codesque shit, but why is it even the focus of a serious book. 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. The widths of the spirals of pinecones and various flowers display the ratio as due patterns in the breeding of rabbits.