Golden Ratio

Zusatztext [An] entertaining review of the history of mathematics . . . A nice mental workout. Linda Schlossberg! San Francisco Chronicle Engagingly enthusiastic . . . It's hard not to feel inspired and even unsettled by the hidden order Livio reveals. New Scientist Numbers aficionados will delight in astrophysicist Livio's history of an irrational number whose fame is second only to that of pi. . . . Livio's encyclopedic selection of subjects! supported by dozens of illustrations! will snare anyone with a recreational interest in mathematics. Booklist Informationen zum Autor 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. He is the author of one previous book, The Accelerating Universe (2000). He is a frequent public lecturer at such venues as the Smithsonian Institution and the Hayden Planetarium. He lives in Baltimore, Maryland. Klappentext The first book for the layperson on a mathematical relationship that has obsessed mathematicians, philosophers, scientists, and artists since ancient Greece--an omnipresent number considered to be "divine."1 PRELUDE TO A NUMBER Numberless are the world's wonders. --Sophocles (495-405 b.c.) The famous British physicist Lord Kelvin (William Thomson; 1824-1907), after whom the degrees in the absolute temperature scale are named, once said in a lecture: "When you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind." Kelvin was referring, of course, to the knowledge required for the advancement of science. But numbers and mathematics have the curious propensity of contributing even to the understanding of things that are, or at least appear to be, extremely remote from science. In Edgar Allan Poe's The Mystery of Marie Roget, the famous detective Auguste Dupin says: "We make chance a matter of absolute calculation. We subject the unlooked for and unimagined, to the mathematical formulae of the schools." At an even simpler level, consider the following problem you may have encountered when preparing for a party: You have a chocolate bar composed of twelve pieces; how many snaps will be required to separate all the pieces? The answer is actually much simpler than you might have thought, and it does not require almost any calculation. Every time you make a snap, you have one more piece than you had before. Therefore, if you need to end up with twelve pieces, you will have to snap eleven times. (Check it for yourself.) More generally, irrespective of the number of pieces the chocolate bar is composed of, the number of snaps is always one less than the number of pieces you need. Even if you are not a chocolate lover yourself, you realize that this example demonstrates a simple mathematical rule that can be applied to many other circumstances. But in addition to mathematical properties, formulae, and rules (many of which we forget anyhow), there also exist a few special numbers that are so ubiquitous that they never cease to amaze us. The most famous of these is the number pi (?), which is the ratio of the circumference of any circle to its diameter. The value of pi, 3.14159 . . . , has fascinated many generations of mathematicians. Even though it was defined originally in geometry, pi appears very frequently and unexpectedly in the calculation of probabilities. A famous example is known as Buffon's Needle, after the French mathematician George-Louis Leclerc, Comte de Buffon (1707-1788), who posed and solved this probability problem in 1777. Leclerc asked: Suppose you have a large sheet of paper on the floor, ruled with parallel straight lines spaced by a fixed distance. A needle of length equal precisely to the spacing between the lines is thrown completely at random onto the paper. What is...

Autorentext
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. He is the author of one previous book, The Accelerating Universe (2000). He is a frequent public lecturer at such venues as the Smithsonian Institution and the Hayden Planetarium. He lives in Baltimore, Maryland.

Klappentext
The first book for the layperson on a mathematical relationship that has obsessed mathematicians, philosophers, scientists, and artists since ancient Greece--an omnipresent number considered to be "divine."

Zusammenfassung
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.

Leseprobe
1

PRELUDE TO A NUMBER

Numberless are the world's wonders.
--Sophocles (495-405 b.c.)

The famous British physicist Lord Kelvin (William Thomson; 1824-1907), after whom the degrees in the absolute temperature scale are named, once said in a lecture: "When you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind." Kelvin was referring, of course, to the knowledge required for the advancement of science. But numbers and mathematics have the curious propensity of contributing even to the understanding of things that are, or at least appear to be, extremely remote from science. In Edgar Allan Poe's The Mystery of Marie Roget, the famous detective Auguste Dupin says: "We make chance a matter of absolute calculation. We subject the unlooked for and unimagined, to the mathematical formulae of the schools." At an even simpler level, consider the following problem you may have encountered when preparing for a party: You have a chocolate bar composed of twelve pieces; how many snaps will be required to separate all the pieces? The answer is actually much simpler than you might have thought, and it does not require almost any calculation. Every time you make a snap, you have one more piece than you had before. Therefore, if you need to end up with twelve pieces, you will have to snap eleven times. (Check it for yourself.) More generally, irrespective of the number of pieces the chocolate bar is composed of, the number of sn…

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