1. Golden Ratio - Wikipedia, The Free Encyclopedia From Wikipedia, the free encyclopedia. Jump to navigation, search. Not to be confused with Golden mean (philosophy), the felicitous middle between two http://en.wikipedia.org/wiki/Golden_ratio

Golden ratio From Wikipedia, the free encyclopedia Jump to: navigation search Not to be confused with Golden mean (philosophy) , the felicitous middle between two extremes, Golden numbers , an indicator of years in astronomy and calendar studies, or the Golden Rule 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. 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

2. 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/

Browse and Search the Library Home Math Topics Arithmetic/Early Number Sense/About Numbers : Golden Ratio/Fibonacci Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Fibonacci Numbers and the Golden Section - Ron Knott 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 more>> Aesthetics, dynamic symmetry, equations, the Divine Proportion, the Fibonacci sequence, the Golden rectangle, logarithmic spirals, formulas, links to other MathSoft pages mentioning the Golden Mean, and print references. Also available as MathML more>> Golden Ratio, Fibonacci Sequence - Math Forum, Ask Dr. Math FAQ

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4. PennTags /dkelly/golden_ratio PennTags / dkelly / golden_ratio. rss 2.0 subscribe to this page tagged fibonacci golden_ratio teaching by dkelly on 14JAN-07 http://tags.library.upenn.edu/dkelly/golden_ratio

post about PennTags dkelly subscribe to this page search related to golden_ratio + fibonacci + teaching golden_ratio from all users projects by dkelly Music and Science manuscript Archaeology of Cinema Adorno and Benjamin (aesthetics) ... make a new project view all projects owners tags copy ... BeL la BartoL k: an analysis of his music; with an introd. by Alan Bush. Call#: Van Pelt Library MT92.B37 L5 belongs to [none] project tagged fibonacci teaching by dkelly ...on 14-JAN-07 copy Symmetry as a Compositional Determinant: VII Bartok belongs to [none] project tagged fibonacci teaching by dkelly ...on 14-JAN-07 University of Pennsylvania library@pobox.upenn.edu

5. Flickr: Photos From Golden_Ratio Flickr is almost certainly the best online photo management and sharing application in the world. Show off your favorite photos to the world, securely and http://www.flickr.com/photos/tonydevencenzi/

YAHOO.util.Event.addListener(window, 'load', F._window_onload); YAHOO.util.Event.addListener(window, 'resize', F._window_onresize); YAHOO.util.Event.addListener(window, 'blur', F._window_onblur); YAHOO.util.Event.addListener(window, 'focus', F._window_onfocus); YAHOO.util.Event.addListener(window, 'unload', F._window_onunload); You aren't signed in Sign In Help Home The Tour ... Golden_Ratio's Photos Golden_Ratio's photos Collections Sets Tags Map ... View as slideshow var photostream_owner_nsid = "30147409@N00"; pretty lat/long Wine Tasting Some rights reserved. Uploaded on Dec 14, 2007 0 comments Konex Cultural Center Some rights reserved. Uploaded on Dec 14, 2007 0 comments La BombaChita Some rights reserved. Uploaded on Dec 14, 2007 0 comments At La BOMBA Some rights reserved. Uploaded on Dec 14, 2007 0 comments mmmmmmmm Some rights reserved. Uploaded on Dec 14, 2007 0 comments Street Art photos Buenos Aires photos Santa Catarina photos Sao Paulo photos Ilha Grande photos Rio photos Flamengo Game at Maracana Staduim photos Halloween 07 photos Whisky Fest photos Pirate Party photos More Sets (1,044 photos)

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7. Golden Ratio 18712008 Grand Lodge of British Columbia and Yukon A.F. A.M. Updated 2006/05/04 freemasonry.bcy.ca/symbolism/golden_ratio/index.html http://freemasonry.bcy.ca/symbolism/golden_ratio/index.html

SYMBOLISM ARCHITECTURE INDEX OF PAPERS 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 = a+b/a+2b = a+2b/2a+3b Fra Luca Paciola (1445-1517) published Divina Proportione The theological and philosophical implications in the name Divine Proportion It was first termed the Golden Section by German mathematician, Martin Ohm in a footnote in the 1835 second edition of

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9. Golden_ratio www.awarmsoftfear.com/ 2k - Cached - Similar pages 1365 (golden_ratio._algebraic_() should synthesize the value Robert Bradshaw points out that golden_ratio._algebraic_ might as well synthesize the value, instead of using a special-purpose function in qqbar.py (and http://www.awarmsoftfear.com/

10. Golden Ratio Spiral The Breath Of Brahma The Golden Ratio/Mean/Spiral is the mathematical expression of the life breath of a living universe. http://www.weare1.us/Golden_Ratio.html

HOME Read Chapter 8 from: Esoteric Anatomy: The Body as Consciousness by Bruce Burger, MA We invite you to contemplate an ancient vision of the universe as a living, breathing, conscious Being . . . and the ubiquitous Golden Spiral as the mathematical expression of the life breath of a living universe. Chapter 8 The Golden Spiral a Key To Understanding Energy in Nature All creation is the interweaving of cycles. From Galactic manifestation to subatomic waves, the universe is a vast spectrum of cycles. The cycles of birth and death, summer and winter, day and night, in-breath and out-breath weave the fabric of life. The ancient rishis (Yogi's who purified their body/minds and directly experienced the fundamental forces of creation) experienced the underlying unity of all cycles as the breath of Brahma and the ubiquitous periodicity of the universe as the rhythm of the life breath of a single harmonious Living Being. All bodies in nature or organized around the proportional harmonics of the rhythms of the Earth's breath. Bruce Rawles explains: The Divine Proportion was closely studied by the Greek sculptor, Phidias, hence, it was given the name Phi. Also known as the Golden Mean, the Magic Ratio, the Fibonacci Series, etc., Phi can be found throughout the universe; from the spirals of galaxies to the spiral of a Nautilus seashell; from the harmony of music to the beauty in art. A botanist will find it in the growth patterns of flowers and plants, while the zoologist sees it in the breeding of rabbits. The entomologist views it in the genealogy of a bee, and the physicist observes it in the behavior of light and atoms. A Wall Street analyst finds it in the rising and falling patterns of a market, the mathematician in the examination of the pentagram. . . . The ancient Egyptians used it in the construction of the great pyramids and in the design of hieroglyphs found on tomb walls . . . . Plato in his Timaeus considered it the most binding of all mathematical relations and makes it the key to the physics of the cosmos.1

11. Golden_ratio [the Libarynth] Trace » golden_ratio. (defconstant GOLDENRATIO (/ (+ 1.0 (sqrt 5.0)) 2.0)) golden_ratio.txt · Last modified 2007/06/10 1550 (external edit) http://libarynth.org/golden_ratio

the libarynth Trace: defconstant GOLDEN-RATIO sqrt see also: The Golden Ratio

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13. Golden_ratio /Main Page/Websites. Golden Ratio. Golden Ratio in Nature Why is it the Golden Section the best arrangement? Cynthia Lanius Lessons The Golden Ratio. http://gatornet.chapin.edu/~library/golden_ratio.htm

Main Page Websites Golden Ratio Golden Ratio in Nature Main Page Websites Golden Ratio Golden Ratio in Nature ... Cynthia Lanius' Lessons: The Golden Ratio

14. Golden_ratio.ic File Format Unrecognized View as HTML http://ftp.wustl.edu/pub/aminet/misc/math/ICalcScripts.lha

15. Eden Prairie High School: Golden_ratio.html The other more well known application of the Golden Ratio was its use as a mathmatical formula to determine visually pleasing proportions in architecture http://www.edenpr.k12.mn.us/ephs/arcadiaweb/Ratio/RatioGolden_Ratio.html

The other more well known application of the Golden Ratio was its use as a mathmatical formula to determine visually pleasing proportions in architecture and furniture construction. The ancient Greeks thought that this was the best possible ratio, and they built many buildings according to the Golden Ratio. The most famous of these is the Parthenon. For more information about the Golden Ratio, reference its relation to the construction of the Parthenon The Golden Ratio and Arcadia by Tom Stoppard When you think about plays and British literature, the last thing that may come to mind is mathematics. However, Tom Stoppard in his astonishing play, Arcadia , does this unthinkable act. With an interesting stretch of events, Stoppard weaves a mystery through two centuries, and ties it all together with the help of various different mathmatical concepts. Fermat's last thereom the Fibonacci sequence and the ever useful Golden Ratio. It is definitely worth checking out, but be prepared for some bawdy humor. Page by Alexis Render Back to the Arcadia homepage.

16. Golden_Ratio Golden Ratio Presentation Reflection. During my senior seminar in mathematics, I, along with a partner in the class, completed a presentation on the Golden http://www.mste.uiuc.edu/courses/mat764fa04/folders/lammw/Technology_Portfolio/T

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beta Welcome to RSS2GO - Your personal information assistant! pageTrackerAnalyser._trackPageview('/topic/page/1'); FeedItems golden ratio in the amen break The Amen Break and the Golden Ratio by mathematics educator and author, Michael S. Schneider. Schneider, having already researched and written about the golden ratio extensively, noticed it right away when hearing the the amen break for the first time (amen break previously on the blue). While some composers have been known to intentionally incorporate fibonacci numbers and the golden ratio read Found on: MetaFilter author michael composers educator ... in the amen break The Amen Break and the Golden Ratio by mathematics educator and author, Michael S. Schneider. Schneider, having already researched and written about the golden ratio extensively, noticed it right away when hearing the the amen break for the first time (amen break previously on the blue). While some composers have been known to intentionally incorporate fibonacci numbers and the golden ratio read Found on: MetaFilter author michael composers educator ... Radiohead Conspiracy Theories: Totally Nuts, or Just a Little Nuts?

18. HG Changeset Patch User Mike Hansen Mhansen@gmail.com Date _repr_() + golden_ratio + return golden_ratio def _latex_(self) + def 1.6180339887498950 + sage QQbar(golden_ratio) + 1.6180339887498946 . http://modular.math.washington.edu/home/mabshoff/release-cycles-2.10.1/alpha0/17

# HG changeset patch # User Mike Hansen < 3 + pi < 3 + sage: type(pi + sage: bool(pi <= 3 + pi <= 3 + sage: type(pi + sage: bool(pi ' + sage: mathml(pi) + + """ return " ' + sage: mathml(I) + + """ return "

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