The Golden Ratio
The Story of Phi, the World's Most Astonishing Number
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The Golden Ratio
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Narrated by:
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Mel Foster
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By:
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Mario Livio
About this listen
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 2,000 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.
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The Equation That Couldn't Be Solved
- How Mathematical Genius Discovered the Language of Symmetry
- By: Mario Livio
- Narrated by: Tom Parks
- Length: 11 hrs and 45 mins
- Unabridged
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Overall4.5 out of 5 stars 67
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Performance4.5 out of 5 stars 58
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Story4.5 out of 5 stars 58
For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two prodigies ultimately proved that the quintic cannot be solved by a simple formula. The first popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.
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5 out of 5 stars
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Historical Perspective Appreciated
- By Michael Hanrahan on 01-22-20
By: Mario Livio
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A Brief History of Infinity: The Quest to Think the Unthinkable
- Brief Histories
- By: Brian Clegg
- Narrated by: Gordon Griffin
- Length: 9 hrs and 3 mins
- Unabridged
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Overall4.5 out of 5 stars 41
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Performance4.5 out of 5 stars 35
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Story4.5 out of 5 stars 35
Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy.We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a
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3 out of 5 stars
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Really not great in Audio, not great otherwise
- By Michael on 03-29-13
By: Brian Clegg
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A Most Elegant Equation
- Euler’s Formula and the Beauty of Mathematics
- By: David Stipp
- Narrated by: Sean Pratt
- Length: 5 hrs and 2 mins
- Unabridged
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Overall4 out of 5 stars 310
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Performance4.5 out of 5 stars 277
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Story4 out of 5 stars 274
Bertrand Russell wrote that mathematics can exalt "as surely as poetry". This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity, or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections.
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3 out of 5 stars
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Good treatment of the subject
- By Kindle Customer on 04-09-18
By: David Stipp
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To Explain the World
- The Discovery of Modern Science
- By: Steven Weinberg
- Narrated by: Tom Perkins
- Length: 10 hrs and 43 mins
- Unabridged
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Overall4 out of 5 stars 261
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Performance4.5 out of 5 stars 220
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Story4 out of 5 stars 218
In this rich, irreverent, and compelling history, Nobel Prize-winning physicist Steven Weinberg takes us across centuries, from ancient Miletus to medieval Baghdad and Oxford, from Plato's Academy and the Museum of Alexandria to the cathedral school of Chartres and the Royal Society of London. He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world--they did not understand what there is to understand or how to understand it.
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4 out of 5 stars
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How the world created a Newton
- By Gary on 03-02-15
By: Steven Weinberg
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Significant Figures
- The Lives and Work of Great Mathematicians
- By: Ian Stewart
- Narrated by: Roger Clark
- Length: 11 hrs and 39 mins
- Unabridged
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Overall4.5 out of 5 stars 255
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Performance4.5 out of 5 stars 212
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Story4.5 out of 5 stars 212
In Significant Figures, acclaimed mathematician Ian Stewart introduces the visionaries of mathematics throughout history. Delving into the lives of twenty-five great mathematicians, Stewart examines the roles they played in creating, inventing, and discovering the mathematics we use today. Through these short biographies, we get acquainted with the history of mathematics.
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3 out of 5 stars
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Beware
- By Anton Kurtz on 12-08-18
By: Ian Stewart
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The Invention of Science
- A New History of the Scientific Revolution
- By: David Wootton
- Narrated by: James Langton
- Length: 22 hrs and 5 mins
- Unabridged
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Overall4 out of 5 stars 135
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Performance4.5 out of 5 stars 120
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Story4.5 out of 5 stars 121
In this fascinating history spanning continents and centuries, historian David Wootton offers a lively defense of science, revealing why the Scientific Revolution was truly the greatest event in our history. The Invention of Science goes back 500 years in time to chronicle this crucial transformation, exploring the factors that led to its birth and the people who made it happen. Wootton argues that the Scientific Revolution was actually five separate yet concurrent events that developed independently.
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2 out of 5 stars
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A Good Read Spoiled
- By David A. Donnelly on 12-23-16
By: David Wootton
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Euclid's Window
- The Story of Geometry from Parallel Lines to Hyperspace
- By: Leonard Mlodinow
- Narrated by: Robert Blumenfeld
- Length: 8 hrs and 13 mins
- Unabridged
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Overall4 out of 5 stars 594
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Performance4.5 out of 5 stars 420
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Story4.5 out of 5 stars 422
Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology.
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5 out of 5 stars
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Wow!
- By Eric on 08-13-10
By: Leonard Mlodinow
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The Story of Western Science
- From the Writings of Aristotle to the Big Bang Theory
- By: Susan Wise Bauer
- Narrated by: Julian Elfer
- Length: 8 hrs and 3 mins
- Unabridged
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Overall4.5 out of 5 stars 293
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Performance4.5 out of 5 stars 250
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Story4.5 out of 5 stars 255
Far too often, public discussion of science is carried out by journalists, voters, and politicians who have received their science secondhand. The Story of Western Science shows us the joy and importance of reading groundbreaking science writing for ourselves and guides us back to the masterpieces that have changed the way we think about our world, our cosmos, and ourselves.
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4 out of 5 stars
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Good text, tedious book structure
- By Diane K. on 10-07-15
By: Susan Wise Bauer
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When Einstein Walked with Gödel
- Excursions to the Edge of Thought
- By: Jim Holt
- Narrated by: David Stifel
- Length: 15 hrs and 19 mins
- Unabridged
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Overall4.5 out of 5 stars 636
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Performance4.5 out of 5 stars 539
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Story4.5 out of 5 stars 541
Does time exist? What is infinity? Why do mirrors reverse left and right but not up and down? In this scintillating collection, Holt explores the human mind, the cosmos, and the thinkers who’ve tried to encompass the latter with the former. With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot.
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5 out of 5 stars
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A good overview of scientific theory
- By MJ Walters on 09-11-18
By: Jim Holt
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The King of Infinite Space
- Euclid and His Elements
- By: David Berlinski
- Narrated by: Arthur Morey
- Length: 3 hrs and 54 mins
- Unabridged
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Overall4.5 out of 5 stars 45
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Performance4.5 out of 5 stars 39
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Story4.5 out of 5 stars 40
Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over 2,000 years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics. In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements.
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5 out of 5 stars
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Funniest Highest and Fullest math overview
- By Francisco Garcia on 12-12-22
By: David Berlinski
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The Structure of Scientific Revolutions
- By: Thomas S. Kuhn
- Narrated by: Dennis Holland
- Length: 10 hrs and 14 mins
- Unabridged
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Overall4 out of 5 stars 1,155
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Performance4 out of 5 stars 833
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Story4 out of 5 stars 815
A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were - and still are. The Structure of Scientific Revolutions is that kind of book.
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3 out of 5 stars
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The problem is not with the book
- By Marcus on 08-09-09
By: Thomas S. Kuhn
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The House of Wisdom
- How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance
- By: Jim Al-Khalili
- Narrated by: Simon Vance
- Length: 10 hrs and 26 mins
- Unabridged
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Overall4.5 out of 5 stars 351
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Performance4.5 out of 5 stars 313
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Story4.5 out of 5 stars 314
The Arabic legacy of science and philosophy has long been hidden from the West. British-Iraqi physicist Jim Al-Khalili unveils that legacy to fascinating effect by returning to its roots in the hubs of Arab innovation that would advance science and jump-start the European Renaissance.
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4 out of 5 stars
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Very interesting book, well-narrated for sure
- By Roderic Rinehart on 11-07-20
By: Jim Al-Khalili
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The Upright Thinkers
- The Human Journey From Living in Trees to Understanding the Cosmos
- By: Leonard Mlodinow
- Narrated by: Leonard Mlodinow
- Length: 12 hrs and 29 mins
- Unabridged
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Overall4.5 out of 5 stars 202
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Performance4.5 out of 5 stars 178
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Story4.5 out of 5 stars 179
In this fascinating and illuminating work, Leonard Mlodinow guides us through the critical eras and events in the development of science, all of which, he demonstrates, were propelled forward by humankind's collective struggle to know. From the birth of reasoning and culture to the formation of the studies of physics, chemistry, biology, and modern-day quantum physics, we come to see that much of our progress can be attributed to simple questions - why? how? - bravely asked.
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5 out of 5 stars
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10/10 Got What I Wanted.
- By Austin on 09-22-15
By: Leonard Mlodinow
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The Logical Leap
- Induction in Physics
- By: David Harriman
- Narrated by: Erik Singer
- Length: 10 hrs and 8 mins
- Unabridged
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Overall4 out of 5 stars 164
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Performance4.5 out of 5 stars 82
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Story4.5 out of 5 stars 82
Beginning with a detailed discussion of the role of mathematics and experimentation in validating generalizations in physics-looking closely at the reasoning of scientists such as Galileo, Kepler, Newton, Lavoisier, and Maxwell-Harriman skillfully argues that the inductive method used in philosophy is in principle indistinguishable from the method used in physics.
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5 out of 5 stars
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Quite refreshing
- By Eric on 10-12-10
By: David Harriman
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Einstein and the Quantum
- The Quest of the Valiant Swabian
- By: A. Douglas Stone
- Narrated by: Gabriel Vaughan
- Length: 11 hrs and 9 mins
- Unabridged
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Overall4.5 out of 5 stars 71
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Performance4.5 out of 5 stars 61
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Story4.5 out of 5 stars 61
Einstein and the Quantum reveals for the first time the full significance of Albert Einstein's contributions to quantum theory. Einstein famously rejected quantum mechanics, observing that God does not play dice. But, in fact, he thought more about the nature of atoms, molecules, and the emission and absorption of light - the core of what we now know as quantum theory - than he did about relativity.
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5 out of 5 stars
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educational and fun
- By Amjad on 12-04-13
By: A. Douglas Stone
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Leonardo's Brain
- Understanding da Vinci's Creative Genius
- By: Leonard Shlain
- Narrated by: Grover Gardner
- Length: 8 hrs and 4 mins
- Unabridged
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Overall4 out of 5 stars 832
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Performance4.5 out of 5 stars 738
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Story4 out of 5 stars 738
Bestselling author Leonard Shlain explores the life, art, and mind of Leonardo da Vinci, seeking to explain his singularity by looking at his achievements in art, science, psychology, and military strategy (yes), and then employing state of the art left-right brain scientific research to explain his universal genius. Shlain shows that no other person in human history has excelled in so many different areas as Da Vinci and he peels back the layers to explore the how and the why.
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3 out of 5 stars
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As distracted as Da Vinci
- By D. McCracken on 05-12-15
By: Leonard Shlain
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The Scientist in the Early Roman Empire
- By: Richard Carrier
- Narrated by: Richard Carrier
- Length: 18 hrs and 29 mins
- Unabridged
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Overall4.5 out of 5 stars 49
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Performance4.5 out of 5 stars 45
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Story4.5 out of 5 stars 43
In this extensive sequel to Science Education in the Early Roman Empire, Dr. Richard Carrier explores the social history of scientists in the Roman era. Was science in decline or experiencing a revival under the Romans? What was an ancient scientist thought to be and do? Who were they, and who funded their research? And how did pagans differ from their Christian peers in their views toward science and scientists?
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5 out of 5 stars
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This Book is a Bombshell
- By James on 06-15-18
By: Richard Carrier