41. Golden Ratio - RationalWiki Retrieved from http//rationalwiki.com/wiki/golden_ratio . Categories Logic Mathematics. Views. Article; Talk; Edit; fossil record. Personal tools http://rationalwiki.com/wiki/Golden_ratio

Golden ratio From RationalWiki Jump to: navigation search This article is a very brief description of the subject. It is not intended to give a full scientific explanation Please see the "see also" or "references" sections for further explanation. The golden ratio golden number golden section (when applied to the division of a line) 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 opposite sides equal to the golden ratio. It is supposedly particularly pleasant, visually.

42. Golden Ratio - Conservapedia edit References. http//www.beautyanalysis.com/index2_mba.htm. Retrieved from http//www.conservapedia.com/golden_ratio . Category Mathematics http://www.conservapedia.com/Golden_Ratio

Golden Ratio From Conservapedia Jump to: navigation search The golden ratio is a number, commonly known as phi ( ), defined as . The value of phi is Phi is an irrational number . In decimal form it is often written The golden ratio was first defined by Euclid of Alexandria around 300BC. His definition reads: 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. Contents The golden ratio in nature and art Fibonacci Numbers and the Golden Ratio The golden ratio in art References ... edit The golden ratio in nature and art The golden ratio appears in innumerable places in nature and art. The periods of the planets are all related by the golden ratio. The proportions of the bodies of many animals, including humans, dolphins, and ants are all based on the golden ratio. The Parthenon Egyptian Pyramids The Last Supper Ark of the Covenant ... Noah's ark , and even the common credit card are all based on the golden ratio. A dodecahedron, a solid in which each side is a pentagon, is related to the Golden Ratio in that both the surface area and the volume of a dodecahedron of unit edge length are functions of the Golden Ratio. Plato described the dodecahedron as the solid which the gods used for embroidering the constellation on the whole heaven.

43. Finds The Best Fit Of Binary System To A Set Of Given Observables define golden_ratio 0.381966011 // = (3 sqrt(5)) / 2 // define CONTOUR_OUTPUT_SUFFIX .contour // remark this line to prevent contour files (and an http://cfa-www.harvard.edu/~jdevor/MECI/source/utils/meci_singleIter.c

/************************************************************************ * Finds the best fit of binary system to a set of given observables * (see astro-ph/0510067 as well as the accompanied ReadMe file for further details) * * Written by Jonathan Devor (jdevor@cfa.harvard.edu) * Harvard-Smithsonian Center for Astrophysics * 60 Garden St., Cambridge, MA 02138 USA * compile: gcc meci_singleIter.c debil_lib.c -o meci_singleIter -lm -Wall -O4 * * run: meci q1.dblc LimbDarkTable.txt SunIsochrone.txt q1.meci q1.meci_err 5 5 5 * * plot: * * idl * IDL> .run listMECI.txt.idl * IDL> exit * * convertPS2jpg.s * convertPS2bmp.s * gzip *.ps *.contour *************************************************************************/ #include #include #include // for MAXFLOAT #include < -MAX_CONTOUR_LABEL_LEN+2) return (4) ; strcpy (labels[i], "0.") ; for (j = exponent+1 ; j < subsetLen ; i++) for (j = ; j < NUM_CONTOUR_LEVELS ; i++) fprintf (foutIDL, ",%s", labels[i]) ; fprintf (foutIDL, "], c_annotation=['0'") ; for (i = ; i < 0.0) LCweighting = -LCweighting * size ; score *= LCweighting ; // information weighting for (n = ; n

44. E CVS: Forecasts Urandom a); + define golden_ratio 1.618033989 + + define DEBUG(f, . . to the popup */ + if ((double) ww / wh golden_ratio) { + wh = ww / golden_ratio; http://www.mail-archive.com/enlightenment-cvs@lists.sourceforge.net/msg35995.htm

enlightenment-cvs Thread Date E CVS: forecasts urandom Enlightenment CVS Mon, 26 Feb 2007 10:26:27 -0800 _ enlightenment-cvs mailing list enlightenment-cvs@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/enlightenment-cvs E CVS: forecasts urandom Enlightenment CVS E CVS: forecasts urandom Enlightenment CVS E CVS: forecasts urandom Enlightenment CVS E CVS: forecasts urandom Enlightenment CVS E CVS: forecasts urandom Enlightenment CVS E CVS: forecasts urandom Enlightenment CVS E CVS: forecasts urandom Enlightenment CVS Reply via email to

45. -*-hoc 17Aug-2005 golden_ratio = (1.0 + sqrt(5.0))/2.0 lo = hi = n = 1 http://www.math.utah.edu/~beebe/software/java/fibonacci/Fibonacci4.hoc

46. Golden Ratio LinkedWords™ - Contextually Find And Manage Web Informati Added April 6, 2006, 233 am Found in page http//www.linkedwords. com/business/accounting/accounting-terms/asset-accounting/golden_ratio.php - Main http://www.linkedwords.com/business/accounting/accounting-terms/asset-accounting

March 31, 2008 golden ratio Web Users Web Publishers About Help Path: Home business accounting accounting-terms ... asset-accounting golden ratio Page Tools Clustered InsideWeb Language Contextual Path (URL): http://www.linkedwords.com/business/accounting/accounting-terms/asset-accounting/golden_ratio.php Keyword LookUp: all keyword pages categories linked keyword pages only Choose Category Arts Brands Business Computers Games Health Home Local News / Media Recreation Reference Science Shopping Society Sports More Search Options: Search within this category only Search the web... Main Categories Arts Brands Business Computers ... Sports Page Tools: (RSS, Email, Print, etc..) Generate RSS Email to Friend / Colleague Printer Friendly Format Add to Favorites ... Make Home Page Change Language Default French German Spanish ... Help Us Translate Archives: Home July August September ... February golden ratio This page contains listings contextually, grammatically and meaningfully related to the keyword/phrase '... golden ratio ...'. If you have text in any page containing the keyword/phrase '...golden ratio...'

47. Playing With Fibonacci In Visualization Layout Algorithms public static const golden_ratioNumber = (1 + Math.sqrt(5)) / 2; PI / (golden_ratio * golden_ratio);. Related articles you should check out http://danielmclaren.net/2008/01/playing-with-fibonacci-in-visualization-layout-

@import "/modules/geshifilter/geshifilter.css"; @import "/modules/node/node.css"; @import "/modules/system/defaults.css"; @import "/modules/system/system.css"; @import "/modules/user/user.css"; @import "/modules/devel/devel.css"; @import "/modules/relatedcontent/relatedcontent.css"; @import "/modules/comment/comment.css"; @import "/themes/danielmclaren/style.css"; danielmclaren.net Home Blogs Playing with Fibonacci in Visualization Layout Algorithms Jan 14 2008 - 1:32am Comments (0) Flash GraphVis Ideas ... Math The Fibonacci numbers are part of a sequence where each number is the sum of the two previous numbers. The first two numbers are ones so the sequence starts out like this: I won't get into the details but the Fibonacci sequence , the Golden Ratio , and the Golden Angle are all related and interesting and occur in various places in nature. When I heard about this I stashed a couple constants in my MathUtils class and played around with ways to use them for visualizations. That tomfoolery resulted in the following little app: This Flash movie is the result of playing with layout algorithms using the Golden Angle. The combobox lets you control the numbers that get highlighted, revealing some of the spirals that appear in the pattern.

48. Carl's Whine Rack: The Golden Ratio And The Fibonacci Series (Perl Program) my $golden_ratio = 0.5 * (1.0 + sqrt(5)); my $deviation = abs($golden_ratio$ratio) / $golden_ratio; printf % 3d %e\n , $iteration_number, $deviation; http://mbrisby.blogspot.com/2006/04/golden-ratio-and-fibonacci-series-perl.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=21734857"); var BL_backlinkURL = "http://www.blogger.com/dyn-js/backlink_count.js";var BL_blogId = "21734857"; Carl's Whine Rack Using GNU/Linux through creative laziness (and other topics as they strike my fancy) 14 April 2006 the Golden Ratio and the Fibonacci series (Perl program) I've been re-reading Dan Brown's The Da Vinci Code lately, and I was intrigued by the Golden Ratio and how it relates to the Fibonacci series. The Fibonacci series is such that each term is the sum of the previous two terms: The ratio of consecutive terms in the Fibonacci series converges on the Golden Ratio, which has a value of approximately 1.618. It also shows up in a geometric analysis of the pentacle. These properties are discussed in mathematical detail on the following Web pages: the Golden Ratio pentacle geometry I wanted to see this from a computational point of view, so I wrote a quick Perl program to compute the Fibonacci numbers and ratios out to around 100 terms. The program prints out deviations from the Golden Ratio, and the output shows a near-zero deviation after less than 40 terms. #!/usr/bin/perl -w

49. Core/vnl: Core/vnl/algo/vnl_bracket_minimum.cxx Source File include vcl_iostream.h 00016 00017 static const double golden_ratio = 1.618033988749894848; // = 0.5*(vcl_sqrt(5)1); 00018 static const double EPS http://www.lems.brown.edu/vision/vxl_doc/html/core/vnl/html/vnl__bracket__minimu

Main Page Classes Files Related Pages ... File Members core/vnl/algo/vnl_bracket_minimum.cxx Go to the documentation of this file. // This is core/vnl/algo/vnl_bracket_minimum.cxx #ifdef VCL_NEEDS_PRAGMA_INTERFACE #pragma implementation #endif #include " vnl_bracket_minimum.h vnl/algo/vnl_fit_parabola.h static const double static const double EPS = 1e-7; // Loose tolerance static const double EPSqr = 1e-14; inline void swap double double double x=a; 00023 a=b; 00024 b=x; class v f public f v double double v [0]=x; return f f v // Final function values at a,b,c stored in fa,fb,fc void double double double double double double // Set up object to evaluate function // Note that fn takes a vector input - f converts a scalar to a vector f(fn); if (b==a) b=a+1.0; 00047 fa = f(a); 00048 fb = f(b); if swap (a,b); swap (fa,fb); // Initial guess at c 00057 c = b+ GOLDEN_RATIO*(b-a); 00058 fc = f(c); while // Keep stepping until we go uphill again // Use parabolic interpolation to estimate position of centre double p,q; (a,b,c,fa,fb,fc,p,q); // Ensure q not within EPSqr of zero if else if // Estimate of centre of parabolic fit - ie minimum // For true quadratic function, minima is at b+p/q

50. Qabalistic Links Part 2 [Archive] - Pagan Forums MysticWicks http//wwwgap.dcs.st-and.ac.uk/~history/HistTopics/golden_ratio.html (http//www-gap. dcs.st-and.ac.uk/~history/HistTopics/golden_ratio.html) http://mysticwicks.com/archive/index.php/t-91999.html

Loans Xbox Mod Chip Buy Anything On eBay NFL Talk Football Forums ... PDA View Full Version : Qabalistic Links Part 2 Bethra April 19th, 2005, 02:58 PM Pentagrams, Pyramids and the Quabala. I have all ready displaide this image in the previous links thread but I would like to now take this a step further and show you a few more of the links. The Great Pyramids of Egypt were all aligned to the Dog Star, Sirius. It is infact not one star but a cluster of 5 stars arrainged in a circle. If you draw a line between each star you can make a pentagram. As I have already said Venus has an eight year cycle which when plotted draws a perfect pentagram in the sky. This image of the pentagram can be found in many forms in many different cultures. Bethra April 19th, 2005, 03:15 PM As I have perviously said the original Olypmic games were dedicated to Venus and were held every eight years in line with her eight year orbitary cycle. The original emblem of the Olympic games was a Pentical. The whole of the games were a cellibration held in the name of the Goddess Venus. At the introduction of Christianity the Olympic offichials decided to change the original emblem as it had far too many Pagan implications. They opted instead for the shape we now know today. The five rings interlocking. The five rings still symbolise the five points of the pentagram. Bethra April 19th, 2005, 03:28 PM

51. Golden Ratio - InfoVis:Wiki Wikipedia, Golden Ratio, 2005 Wikipedia.org, Golden Ratio, 19.10.2005, http//en.wikipedia.org/wiki/golden_ratio. Absoluteastronomy Absoluteastronomy http://www.infovis-wiki.net/index.php?title=Golden_Ratio

52. Math (LingPipe API) static double, golden_ratio The value of the golden ratio. static double, LN_2 golden_ratio. public static final double golden_ratio http://alias-i.com/lingpipe/docs/api/com/aliasi/util/Math.html

Overview Package Class Tree Deprecated Index Help ... METHOD DETAIL: FIELD METHOD com.aliasi.util Class Math java.lang.Object com.aliasi.util.Math public class Math extends Object A math utility class with static methods. Since: Version: Author: Bob Carpenter Field Summary static long[] An array of the Fibonacci sequence. static double The value of the golden ratio. static double The natural logarithm of 2. static double The log base 2 of the constant e , which is the base of the natural logarithm. Method Summary static void assertFiniteNonNegative String label, double x) Throws an illegal argument exception if the specified double value is not a finite non-negative number. static int byteAsUnsigned (byte b) Returns the integer value of reading the specified byte as an unsigned value. static double digamma (double x) Returns the value of the digamma function for the specified value. static boolean isPrime (int num) Returns true if the specified number is prime.

53. Title The Golden Ratio. . . http://www.geocities.com/lipa_lot/golden_ratio.htm dir=rtl

54. Photos From Golden Spiral fly 2 / /a /p p Intrigued by the Golden ratio theory a href= http//en. wikipedia.org/wiki/golden_ratio en.wikipedia.org/wiki/golden_ratio /a . http://api.flickr.com/services/feeds/photoset.gne?set=72157602141958578&nsid=100

55. Timepedia Chronoscope Introduction And Tutorial XYDataset; public class HelloChart implements EntryPoint { public void onModuleLoad() { double golden_ratio = 1.618; int chartWidth = 600, http://timepedia.org/chronoscope/docs/gwt/intro/

Chronoscope Blog Demo Gallery ... Group GWT Introduction Hello Chart a simple line chart Hello Chart Assuming you have Google Web Toolkit installed already. If not, http://code.google.com/webtoolkit/gettingstarted.html applicationCreator -out HelloChart com.example.client.HelloChart Edit src/com/example/HelloChart.gwt.xml and add a line to inherit Chronoscope. You'll also need to add chronoscope and gwtexporter to your CLASSPATH. For example, make a lib/ directory and put chronoscope.jar and gwtexporter.jar in it. Then add them to the -cp argument in HelloChart-compile and HelloChart-shell. HelloChart-compile HelloChart-shell Inherit org.timepedia.chronoscope.Chronoscope HelloChart.gwt.xml We'll use a json file for the dataset, it should be in the format: dataset.js Datasets with the same axis: identifier will share the same range axis, which is useful if they're units like "hours", "km", "kbps", "$", etc. Modify the index.html applicationCreator made and add the script tag to import dataset.js HelloChart.java Home About Blog Contact Us

56. Vimts=8sw=3sts=8noexpandtabcino= 5n-3f0^-2{2 */ Include Eh (*h)) *h = 0; /* Apply the golden ratio to the popup */ if ((double) *w / *h golden_ratio) { *h = *w / golden_ratio; } else if ((double) *w / *h http://web.enlightenment.org/viewvc/e_modules/calendar/e_mod_main.c?revision=1.1

57. Discover From Your Favorite Topic Or Web Page: En.wikipedia.org/wiki/Golden_rati Enter a topic or web address, discover more related. All Bookmarks Log In Register Submit Your Site Discover From. Google, Enter your search terms http://www.megite.com/url/:en.wikipedia.org/wiki/Golden_ratio

Enter a topic or web address, discover the surprises. All Bookmarks Log In Register Submit Your Site From Enter your search terms Submit search form Web www.megite.com About Us Megite Discover is a crowdsourcing service for web browsing provided by , a leading social news aggregator. Discovered Topics design art photography math ... COLOURlovers :: Color Trends + Palettes http://www.colourlovers.com/ color inspiration design tools B o o k m a r k D i s c ... Smashing Magazine http://www.smashingmagazine.com/ design magazine css blog B o o k m a r k D i s c ... deviantART: where ART meets application! http://www.deviantart.com/ wallpaper photo design photography B o o k m a r k D i s c ... Magic Ink: Information Software and the Graphical Interface http://worrydream.com/MagicInk/ usability design interface toread B o o k m a r k D i s c ... Authentic Jobs ~ Full-time and freelance job opportunities for designers and developers http://www.authenticjobs.com/ jobs employment design business B o o k m a r k D i s c ... Open Source Web Design - Download free web design templates. http://www.oswd.org/ css design templates webdesign B o o k m a r k D i s c ... Hausschrift-Liste Unternehmen-zu-Schrift - Typografie.info TypoWiki

58. IPhone Size Comparison Photos [Archive] - Mac Forums is the ratio of its longer side to the iPhone s shorter side in accordance with the golden ratio (http//en.wikipedia.org/wiki/golden_ratio)? p http://forums.macrumors.com/archive/index.php/t-322938.html

Mac Forums iPhone and iPod Touch Forums iPhone News Discussion PDA View Full Version : iPhone Size Comparison Photos katie ta achoo 06-30-2007, 06:35 PM I took some iPhone size comparison pictures today for y'all. Let's start in the kitchen.... http://images.macrumors.com/article/2007/06/30/IMG_6679_300.jpg The iPhone as compared to a slice of delicious cake. (http://flickr.com/photos/sabortijuana/656991619/) Read More (http://www.macrumors.com/iphone/2007/06/30/size-comparison-photos/) Lyle 06-30-2007, 06:39 PM Just so we're clear: How many layers in the cake? arn 06-30-2007, 06:40 PM how about iphone next to perfectly round and otherwise unmarked sphere. arn katie ta achoo 06-30-2007, 06:41 PM Just so we're clear: How many layers in the cake? Two pretty thick ones. It was about 3 inches high. The top layer was chocolate and the bottom layer was vanilla. There's one slice left.. I think I'll go finish it. :) Rojo 06-30-2007, 06:43 PM I like your wallpaper. Is that one of the standard ones already on the phone? siurpeeman 06-30-2007, 06:58 PM

59. Math::Basic API Reference golden_ratio constant Num MathBasicφ constant Num MathBasicphi constant Num MathBasicgolden_ratio. The golden ratio, roughly equal to http://moritz.faui2k3.org/pugs/docs/Perl6/API/Math/Basic.pod.html

Index This file was automatically generated from http://svn.pugscode.org/pugs/docs/Perl6/API/Math/Basic.pod on Wed Jun 6 22:16:47 2007 GMT, revision 16639. Math::Basic API reference Title Typical Usage Tags Constants ... Exported functions Title Math::Basic API reference Typical Usage use Math::Basic Tags The following export tags are available: :UNI :compat :constants Constants To export the constants provided by Math::Basic use the :constants tag when importing: use Math::Basic :constants; e constant Num Math::Basic::e The constant e , roughly equal to . This constant should not be confused with e The golden ratio, roughly equal to i constant Complex Math::Basic::i The constant i , which is defined as the square root of one constant Complex Math::Basic::one The constant value pi The constant pi , roughly equal to zero constant Complex Math::Basic::zero The constant value Exported functions The following functions are exported by default: abs our Num multi Math::Basic::abs ( Num $x ) our Int multi Math::Basic::abs ( Int $x ) our Complex multi Math::Basic::abs ( Complex $x ) The absolute value or modulus of $x , as denoted in mathematics by The absolute value of a complex number is a generalization of this basic operation.

60. Dmath: Math Routines For Python's Arbitrary-precision Decimal Type - Brian's Blo We now have acos , asin , atan , atan2 , ceil , cos , cosh , degrees , e , exp , floor , golden_ratio , hypot , log , log10 , pi , pow , radians , sign http://blog.case.edu/bmb12/2006/09/dmath_math_routines_for_pythons_arbitraryprec

brian's blog Past Entries blog.brianbeck.com, RTA Schedule 2.0 September Projects Hacking in Project Club Content types in Pagoda, Part 1: The Model ... Pagoda CMS Notes Recent Comments September 25, 2006 dmath: Math routines for Python's arbitrary-precision Decimal type posted by brian at 03:27 PM Yesterday Chris and I spent all day writing math functions for Python's Decimal type . The result is our new dmath library, available on Google Code and the Cheese Shop under the MIT/X11 license. Sparked by the routine for atan in my last post , I decided it wouldn't be too hard to go ahead and do the rest of the functions already offered by math and cmath . We now have acos asin atan ceil cos cosh degrees e exp floor hypot log pi pow radians sign sin sinh sqrt tan , and tanh Check it out: We're calling this release 0.9 because it just needs some testing and maybe some speed improvements, otherwise it's ready to use. There is currently some work being done in Python sandbox/trunk to convert the decimal module to C, and maybe they'll include fast versions of all these routines. But hey, you can use these right now! Arbitrary precision is one of the coolest things in programming. We spent a lot of time in

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