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Golden Ratio: more books (52)

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Mario Livio, 2003-09-23
The Golden Ratio and Fibonacci Numbers by R. A. Dunlap, 1998-03
The Return of Sacred Architecture: The Golden Ratio and the End of Modernism by Herbert Bangs M.Arch., 2006-11-14
The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty by Mario Livio, 2003-08-04
The Diet Code: Revolutionary Weight Loss Secrets from Da Vinci and the Golden Ratio by Stephen Lanzalotta, 2006-04-03
The Golden Mean or Ratio [(1+sqrt(5))/2] to 20,000 places by null, 2009-10-04
Non-Standard Positional Numeral Systems: Unary Numeral System, Golden Ratio Base, Fibonacci Coding, Quater-Imaginary Base, Negative Base
Golden Ratio the Story of Phi the Worlds by Mario Livio, 2002
Golden Ratio: Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search, Golden Spiral
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number [GOLDEN RATIO] [Paperback]
The Golden Ratio by Mario Livio, 2002
The Glorious Golden Ratio by Alfred S. Posamentier, Ingmar Lehmann, 2011-06
The Golden Ratio by Keith Flynn, 2007-02-15
Constants: Mathematical Constants, Physical Constants, Dimensionless Quantity, Avogadro Constant, Pi, Golden Ratio, Gas Constant

lists with details

Golden Ratio - Wikipedia, The Free Encyclopedia
In mathematics, and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio
http://en.wikipedia.org/wiki/Golden_ratio

Extractions: From Wikipedia, the free encyclopedia Jump to: navigation search For the Ace of Base album, see The Golden Ratio (album) The golden section is a line segment divided according to the golden ratio: The total length a + b is to the longer segment a as a is to the shorter segment b In mathematics and the arts , two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant , approximately 1.6180339887. Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea ) and golden mean Other terms encountered include extreme and mean ratio medial section divine proportion divine section (Latin: sectio divina golden proportion golden cut golden number , and mean of Phidias The golden ratio is often denoted by the Greek letter phi , usually lower case ( The figure on the right illustrates the geometric relationship that defines this constant. Expressed algebraically: This equation has one positive solution in the algebraic irrational number At least since the Renaissance , many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle , in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.
Golden Ratio
Sep 2, 2010 Although not naming it the Golden Ratio, around 300 BCE Euclid of The Golden Section, or Golden Ratio, divides a line at a point such
http://freemasonry.bcy.ca/symbolism/golden_ratio/index.html

Extractions: SYMBOLISM ARCHITECTURE INDEX OF PAPERS Download a 1.1MB PDF essay on the Golden Rato by clicking here View a 520k PowerPoint presentation on the Golden Rato by clicking here The golden section Although not naming it the Golden Ratio, around 300 BCE Euclid of Alexandria defined the proportion: "A straight line is said to have been cut into extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser." The precise value of the Golden Ratio is an irrational number, phi (1.61803399...), and, like the irrational number pi (3.14159265...) or e (2.71828183...), was considered by the Pythagoreans to be so horrific that its knowledge should be kept secret. The Golden Section, or Golden Ratio, divides a line at a point such that the smaller part relates to the greater as the greater relates to the whole: the ratio of the lengths of the two sides is equal to the ratio of the longer side to the sum of the two sides. a/b = b/a+b
Golden Ratio - CreationWiki, The Encyclopedia Of Creation Science
Sep 26, 2010 The golden ratio, otherwise known as the Divine Proportion or Phi, is a mathematical ratio with special properties and aesthetic
http://creationwiki.org/Golden_ratio

Extractions: SERVER UPGRADE COMPLETE! Please consider supporting this site Jump to: navigation search The golden ratio , otherwise known as the Divine Proportion or Phi , is a mathematical ratio with special properties and aesthetic significance. An enormous number of things in the universe are engineered around the ratio, ranging from the human body to the ark of the covenant to snail shells to the orbits of the planets. Some argue that the prevalence of the Golden Ratio is positive evidence of a common design plan uniting a wide variety of phenomena which share only their creator in common. Phi is derived by dividing a line segment into two parts in such a way that the ratio of the smaller segment to the larger segment is the same as the ratio of the large segment to the whole. The number is irrational, meaning it never ends or repeats in a decimal system. To the first ten decimals, it is 1.6180339887 ... A golden rectangle is one in which the ratio of length to height is 1:phi.
The Math Forum - Math Library - Golden Ratio/Fibonacci
The Math Forum s Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites
http://mathforum.org/library/topics/golden_ratio/

Extractions: Information about the Fibonacci series, including a brief biography of Fibonacci, the numerical properties of the series, and the ways it is manifested in nature. Fibonacci numbers are closely related to the golden ratio (also known as the golden mean, golden number, golden section) and golden string. Includes: geometric applications of the golden ratio; Fibonacci puzzles; the Fibonacci rabbit binary sequence; the golden section in art, architecture, and music; using Fibonacci bases to represent integers; Fibonacci Forgeries (or "Fibonacci Fibs"); Lucas Numbers; a list of Fibonacci and Phi Formulae; references; and ways to use Fibonacci numbers to calculate the golden ratio. more>> The Fibonacci Series - Matt Anderson, Jeffrey Frazier, and Kris Popendorf; ThinkQuest 1999
Golden Ratio
Although Euclid does not use the term, we shall call this the golden ratio. The definition appears in Book VI but there is a construction given in Book II,
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Golden_ratio.html
Golden Ratio - InfoVis:Wiki
DEFINITION. The golden ratio is an irrational mathematical constant with the approximated value of 1.6180339887. It is the relation between two quantities, where the ratio of the sum
http://www.infovis-wiki.net/index.php?title=Golden_Ratio
Golden Ratio - Encyclopedia Article - Citizendium
This is a draft article, under development and not meant to be cited; you can help to improve it. These unapproved articles are subject to a disclaimer.
http://en.citizendium.org/wiki/Golden_ratio

Extractions: The old townhall in Leipzig . The tower is positioned between the right (a) and left (b) sections so that equals the golden ratio. The golden ratio is a mathematical proportion that is important in the arts and interesting to mathematicians. In architecture and painting, some works have been proportioned to approximate the golden ratio ever since antiquity. The ratio itself is also known as the mean and extreme ratio , the golden section , the golden mean , and the divine proportion . The earliest existing description is found in the Elements of Euclid (Book 5, definition 3):
Category:Golden Ratio - Wikimedia Commons
The golden ratio (Latin sectio aurea) \frac 1 \varphi = \varphi 1;\; \varphi = English The golden ratio is an irrational number
http://en.wikipedia.org/wiki/Commons:Category:Golden_ratio

Extractions: From Wikimedia Commons, the free media repository Jump to: navigation search The golden ratio Latin sectio aurea): Deutsch: Der Goldene Schnitt ist eine irrationale Zahl English: The golden ratio is an irrational number Italiano: Sezione aurea è un numero irrazionale This category has the following 4 subcategories, out of 4 total. This category contains only the following page. The following 169 files are in this category, out of 169 total. Zolotoe setshenie.jpg
Golden Ratio - Simple English Wikipedia, The Free Encyclopedia
The golden ratio is an irrational number. If a person tries to write it, it will never stop and never be the same again and again, but it will start this
http://simple.wikipedia.org/wiki/Golden_ratio

Extractions: From Wikipedia, the free encyclopedia Jump to: navigation search If a person has one number a and another smaller number b , he can make the ratio of the two numbers by dividing them. Their ratio is a b . He can make another ratio by adding the two numbers together a b and dividing this by the larger number a . The new ratio is ( a b a . If these two ratios are equal to the same number, then that number is called the golden ratio . The Greek letter phi ) is usually used as the name for the golden ratio. For example, if b = 1 and a b , then . The second ratio ( a b a is then . Because these two ratios are equal, this is true: One way to write this number is is the number which, when multiplied by itself, makes 5: The golden ratio is an irrational number . If a person tries to write it, it will never stop and never be the same again and again, but it will start this way: 1.6180339887... An important thing about this number is that a person can subtract 1 from it or divide 1 by it. Either way, he will find the same number: The large rectangle BA is a golden rectangle; that is, the proportion b:a is 1:
Golden_ratio
www.awarmsoftfear.com/ CachedGolden Ratio Spiral the Breath of BrahmaThe Golden Ratio/Mean/Spiral is the mathematical expression of the life breath of a living universe.
http://www.awarmsoftfear.com/
All Items On Etsy, A Global Handmade And Vintage Marketplace.
Shop for unique golden_ratio from our artisan community. Buy and sell handmade or vintage items, art and supplies. Share stories through millions of items
http://www.etsy.com/search_results.php?includes[0]=tags&search_query=golden_
File:Golden Ratio.svg - Wikimedia Commons
=Golden Ratio, ab = 1.61 = (1+sqrAug 21, 2009 golden_ratio.svg (SVG file, nominally 397 � 70 pixels, file size 1 KB) ({{ Information
http://commons.wikimedia.org/wiki/File:Golden_Ratio.svg

Extractions: Reusing this file See below. This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. www.creativecommons.org/licenses/by-sa/3.0 CC-BY-SA-3.0 Creative Commons Attribution-Share Alike 3.0 true true Click on a date/time to view the file as it appeared at that time.
Mathematical Constants — Sage Reference Manual V4.5.3
sage a = pi + e + golden_ratio + log2 + euler_gamma + catalan + khinchin + twinprime + . sage gr = golden_ratio sage RR(gr) 1.61803398874989 sage R
http://www.sagemath.org/doc/reference/sage/symbolic/constants.html

Extractions: The following standard mathematical constants are defined in Sage, along with support for coercing them into GAP, GP/PARI, KASH, Maxima, Mathematica, Maple, Octave, and Singular: sage: pi pi sage: e # base of the natural logarithm e sage: NaN # Not a number NaN sage: sage: # natural logarithm of the real number 2 sage: sage: catalan # the Catalan constant catalan sage: khinchin khinchin sage: twinprime twinprime sage: mertens mertens sage: brun brun Support for coercion into the various systems means that if, e.g., you want to create sage: maxima pi %pi sage: singular pi pi sage: gap pi pi sage: gp pi 3.141592653589793238462643383 # 32-bit 3.1415926535897932384626433832795028842 # 64-bit sage: pari pi sage: kash pi # optional sage: mathematica pi # optional Pi sage: maple pi # optional Pi sage: octave pi # optional Arithmetic operations with constants also yield constants, which can be coerced into other systems or evaluated. sage: a pi e a pi + 4/5*e sage: maxima a %pi+4*%e/5 sage: RealField a # 15 *bits* of precision sage: gp a 5.316218116357029426750873360 # 32-bit
Golden Ratio - Definition
The golden ratio is a number, approximately 1.618, that possesses many interesting properties. It was studied by ancient mathematicians due to its frequent
http://www.wordiq.com/definition/Golden_ratio

Extractions: The golden ratio is a number , approximately 1.618, that possesses many interesting properties. It was studied by ancient mathematicians due to its frequent appearance in geometry . Shapes defined by the golden ratio have long been considered aesthetically pleasing in western cultures, reflecting nature's balance between symmetry and asymmetry. The ratio is still used frequently in art and design. The golden ratio is also known as the golden mean golden section golden number or divine proportion It is usually denoted by the Greek letter (phi) with (tau) being less common. Contents showTocToggle("show","hide") 1 Origin of name 11.3 Other The name "golden ratio" first seemed to have been used in the form sectio aurea , "golden section", by Leonardo da Vinci sculptor Phidias , who was long believed to have used the golden ratio in his designs. Two quantities are said to be in the golden ratio , if "the whole is to the larger as the larger is to the smaller", i.e. if
Golden Ratio: Facts, Discussion Forum, And Encyclopedia Article
Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from
http://www.absoluteastronomy.com/topics/Golden_ratio

Extractions: Home Discussion Topics Dictionary ... Login Golden ratio Overview In mathematics Mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.... s, two quantities are in the golden ratio if the ratio Ratio In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient... of the sum of the quantities to the larger quantity is equal to (=) the ratio Ratio In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient...
THE GOLDEN RATIO
The first clear definition of what has later become known as the Golden Ratio was given around 300 B.C by the founder of geometry as a formalized deductive
http://jwilson.coe.uga.edu/EMAT6680/Parveen/golden_ratio.htm

Extractions: T HE G OLDEN R ATIO by Nikhat Parveen, UGA Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of G old; the second we may name a P recious jewel. Kepler (1571- 1630) In everyday life, we use the word �proportion� either for the comparative relation between parts of things with respect to size or quantity or when we want to describe a harmonious relationship between different parts. In mathematics, the term �proportion� is used to describe an equality of the type: nine is to three as six is to two. The Golden Ratio provides us with an intriguing mingling, it is claimed to have pleasingly harmonious qualities. The first clear definition of what has later become known as the Golden Ratio was given around 300 B.C by the founder of geometry as a formalized deductive system , Euclid of Alexandria. In Euclid�s words: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. If the ratio of the length AC to that of CB is the same as the ratio of AB to AC, then the line has been cut in extreme and mean ratio, or in a Golden Ratio.
Golden Ratio: K-12 Lesson Plans, Class Activities & Background Information
Golden ratio, K12 lesson plans, class activities, science fair projects and background information.
http://www.juliantrubin.com/encyclopedia/mathematics/golden_ratio.html

Extractions: The golden section is a line segment sectioned into two according to the golden ratio . The total length a+b is to the longer segment a as a is to the shorter segment b In mathematics and the arts , two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is approximately 1.6180339887. At least since the Renaissance , many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle , in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.
Golden Ratio
The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b.
http://schools-wikipedia.org/wp/g/Golden_ratio.htm

Extractions: The golden section is a line segment sectioned into two according to the golden ratio . The total length a+b is to the longer segment a as a is to the shorter segment b In mathematics and the arts , two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is approximately 1.6180339887 (from the quadratic formula At least since the Renaissance , many artists and aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio can be expressed as a mathematical constant, usually denoted by the Greek letter phi). The figure of a golden section illustrates the geometric relationship that defines this constant. Expressed algebraically: This equation has as its unique positive solution the algebraic irrational number Other names frequently used for or closely related to the golden ratio are golden section (Latin: sectio aurea golden mean golden number , and the Greek letter phi ). Other terms encountered include
Golden Ratio - RationalWiki
Mar 18, 2010 The golden ratio (also referred to as the golden number or golden section) or has been known for millennia. It is defined as the ratio
http://rationalwiki.org/wiki/Golden_ratio

Extractions: Check out the "see also" or "references" sections, or Wikipedia's article for more detail. The golden ratio (also referred to as the golden number or golden section) or has been known for millennia. It is defined as "the ratio between two numbers such that the lesser is to the greater as the greater is to the sum" The golden section: The golden ratio applied to the division of a line A:B = B:(A+B) B:A = φ = 1.61803398874989484820458683436563811772030917980576 (approx) Its exact value is It has generally been thought to be pleasing and harmonious to human perception and is the basis of much classical architecture. The usage of the Greek letter phi to represent the golden ratio was suggested by mathematician Mark Barr from the first letter of Phidias (ancient Greek, Φειδίας), the sculptor who was alleged to have used it in creating statues for the Parthenon. The golden number (or an approximation) appears often in nature and is the convergent point of the ratio of successive terms of the Fibonacci sequence A rectangle with the ratio of adjacent sides equal to the golden ratio. It is supposedly particularly pleasant, visually.
Golden Ratio Evolver.net
Jun 24, 2010 A golden thread of synchronicities. A golden section of time. On June 3rd, John, Danielle, Rachel, and I embarked on a series of threads in
http://www.evolver.net/group/collective_unconscious_project/discussion/golden_ra

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