Author(s): Mario LivioDownload
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.
Some Reviews: 349 in Goodreads.com
I really enjoyed this. The scope of the book was great, through history with stops at art, architecture, music, galaxies, and snails. I really appreciated the skeptical debunking of a lot of the golden ratio claims made about the Pyramids, Parthenon, and even the Mona Lisa. With that nonsense out of the way what really blew my mind was the “surprise” aspect of how the golden ratio turns up in the solutions to other problems. And finally, the last chapter was probably my favorite… the philosophical questions about our perception of a mathematical univers. The most incredible part of the book- the part that will keep me awake, was Benford’s Law.
I’m still not sure how Benford’s Law can even be possible. Seriously. I’m going to lie away at night wondering “WHAT DOES THIS ALL MEAN?”
This is a full history of most math topics, with a focus on Phi, the Golden Ratio. The author starts with a trip through the development of numbers, from counting numbers, to integers, to rationals, to reals, all the way to complex numbers. He then goes into a study of the development of the golden ratio, from geometric contructions of pentagons and pentagrams. He also devotes plenty of team to the Fibonacci sequence and its close relation to Phi.
It’s a solid math book, but does have some amusing asides riddled throughout. With so many non sequiturs, the book sometimes seems like a book version of Pop-up videos.
A little odd that this book is promoted by a Dan Brown quote about pyramids, then it pretty soon after proceeds to prove that the pyramids were in fact NOT erected with the golden ratio in mind and further that “Numerology” is often a hoax, in an almost Umberto Ecoesque fashion, often the basis for Brown thrillers.
Also, I definitely expected to be more, “Astonished” with this novel, instead I found it to read more as a “Golden Ratio: Fact or Fiction”?
That said, once I got past the, “hmm is this book just marketed inauthentically?” I actually found it quite interesting and challenging for a mathematic mind! The mention of both Godel’s incompleteness theorem AND Hofstadter’s Godel Escher Bach were super bonuses.
Sweet read! Just don’t expect some magic theorem about how like phi lead Jefferson to write the Declaration of Independence. (Upon further investigation this reviewer does notice that a few words in the preamble, “We” and “these” are of length 2 and 5 respectively, both Fibonacci numbers, so what do I know).
I read this book out of curiosity and out of a desire to get a firmer grasp on the question of whether mathematics is a creation of man or something discovered by man. I lean in the direction that it is both. I believe it is the language of the universe. As with any language, it has grammar, internal structure, consistencies and inconsistencies (irrational numbers) which are necessary to create, encode, store, and transmit meaning.
Livio’s presentation is interesting and accessible enough for people normally befuddled by math to comprehend most of it. Theory of Knowledge teachers may find it helpful as background reading for any work they do with their students in Mathematics as Area of Knowledge. IB Math teachers may enjoy some of the examples as classroom activities they could share with their students.
The Story of Phi is an interesting one. I enjoyed the history lesson and seeing just how the Golden Ratio pops up in crazy, unexpected places. Also, how people have tried to force its presence in odd places such as poetry, the construction of a violin and the Egyptian Pyramids. My favourite bit had to be the chapter on all of the formulaic shortcuts that come from Fibonacci series, which is in direct relation to the Golden Ratio. It is interesting how predictable seemingly random numbers can be. Mario does go off on some tangents that seem to go on for too long (particularly about fellow cosmologist, Johannes Kepler), but overall it was a very informative, enlightening read.
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