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phi
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Music, story and poetry of the Golden Ratio.
http://members.aol.com/loosetooth/phi.html
Information on the Golden Section, Divine Proportion, Fibonacci series and phi.
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The Phinest source to the golden section, golden mean, divine proportion, Fibonacci series and phi. Explore its application to art, design, life, beauty, mathematics, geometry, stock markets, theology, cosmology and more. Dedicated to providing you with the phinest™ information on The Golden Section, Ratio or Mean The Divine Proportion The Fibonacci Series 0, 1, 1, 2, 3, 5, 8, 13 and the golden number, Phi 1.6180339887 NEW PhiMatrix™ Graphic Design Software...Simple definitions; exact value and first 2000 decimal places; finding the golden section; continued fractions. Simple tricks for your calculator, puzzles and games.
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The Golden Section the Number and Its Geometry The icon means there is a Things to do investigation at the end of the section. The icon means there is an interactive calculator in this section. What is the Golden Ratio (or Phi A simple definition of Phi A...Extension of the number.
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The Golden Ratio Last updated March 27, 1996 1.61803398874989484820458683436563811772030917980576286213544862270526046281890 244970720720418939113748475408807538689175212663386222353693179318006076672635 443338908659593958290563832266131992829026788067520876689250171169620703222104 321626954862629631361443814975870122034080588795445474924618569536486444924104 432077134494704956584678850987433944221254487706647809158846074998871240076521 705751797883416625624940758906970400028121042762177111777805315317141011704666 599146697987317613560067087480710131795236894275219484353056783002287856997829 778347845878228911097625003026961561700250464338243776486102838312683303724292 675263116533924731671112115881863851331620384005222165791286675294654906811317 159934323597349498509040947621322298101726107059611645629909816290555208524790 352406020172799747175342777592778625619432082750513121815628551222480939471234 145170223735805772786160086883829523045926478780178899219902707769038953219681 986151437803149974110692608867429622675756052317277752035361393621076738937645 560606059216589466759551900400555908950229530942312482355212212415444006470340 565734797663972394949946584578873039623090375033993856210242369025138680414577 995698122445747178034173126453220416397232134044449487302315417676893752103068 737880344170093954409627955898678723209512426893557309704509595684401755519881 921802064052905518934947592600734852282101088194644544222318891319294689622002 301443770269923007803085261180754519288770502109684249362713592518760777884665 836150238913493333122310533923213624319263728910670503399282265263556209029798 642472759772565508615487543574826471814145127000602389016207773224499435308899 909501680328112194320481964387675863314798571911397815397807476150772211750826 945863932045652098969855567814106968372884058746103378105444390943683583581381 131168993855576975484149144534150912954070050194775486163075422641729394680367 319805861833918328599130396072014455950449779212076124785645916160837059498786 006970189409886400764436170933417270919143365013715766011480381430626238051432 117348151005590134561011800790506381421527093085880928757034505078081454588199 063361298279814117453392731208092897279222132980642946878242748740174505540677 875708323731097591511776297844328474790817651809778726841611763250386121129143 683437670235037111633072586988325871033632223810980901211019899176841491751233 134015273384383723450093478604979294599158220125810459823092552872124137043614 910205471855496118087642657651106054588147560443178479858453973128630162544876 114852021706440411166076695059775783257039511087823082710647893902111569103927 683845386333321565829659773103436032322545743637204124406408882673758433953679 593123221343732099574988946995656473600729599983912881031974263125179714143201...Essay and brief introduction by Edwin M. Dickey.
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Golden Ratio Teachers of algebra have spent adequate amounts of time teaching two major representations of mathematics: verbal and algebraic, but have spent too little time on two other critical representations: graphical and numerical. Furthermore, the infusion of computer and calculator technology...Examines the uses/occurances of phi in biology, art, and ancient times.
http://library.thinkquest.org/C005449
How to generate the number, GSP script for dividing segments, rectangle and other shapes, the rabbit problem and references.
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Golden Ratio Most people are familiar with the number Pi, since it is one of the most ubiquitous irrational numbers known to man. But, there is another irrational number that has the same propensity for popping up and is not as well...Provides a definition of Phi, and explains some mathematical background as well as a listing of 1000 digits of the number.
http://astronomy.swin.edu.au/pbourke/analysis/phi/
Explains the theory behind the golden mean and how it can be constructed out of the Fibonacci series.
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The Golden Mean Section represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, that seem to arise out of the basic structure of our cosmos. Unlike those abstract numbers, however, phi appears clearly and regularly...A list of questions gathered pertaining to Fibonacci and Golden Ratio.
http://mathforum.org/dr.math/tocs/golden.high.html
The column at yahoo.com answers the question "What is the "Golden Ratio" and what significance does it have?".
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What is the Golden Ratio Ratio and what significance does it have? KevinSt. Louis, Missouri Dear Kevin: We suspected that the Golden Ratio was somehow connected to the Golden Rule but by searching Yahoo! using the phrase, we learned that it's actually a numerical constant,...An interview with George Cardas, describing his use of the Golden Ratio in high-end audio equipment cables.
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Inter.View to George Cardas Golden sections and sequences in an unstable problem by Lucio Cadeddu Golden Ratio is an easy concept of elementary geometry which has had, and still has, great relevance both in human designs and in Nature. Recently it has had wide...A few words about Golden Number.
http://www.freewebz.com/goldenno
A presentation of the relationship between the Golden Ratio and the Fibonacci Numbers from the proceedings of the Friesian School.
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Ratio is an irrational number with several curious properties. It can be defined as that number which is equal to its own reciprocal plus one 1 1. Multiplying both sides of this same equation by the Golden Ratio we derive...Defines the "Golden Rectangle" based on phi and shows some formulars and drawings of the results.
http://mathworld.wolfram.com/GoldenRectangle.html
Short page describing the Golden Section. Includes a description of various constructions and history.
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These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the...At the Favorite Mathematical Constants page.
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Mathematical Constants My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally My book Mathematical Constants is now available for online purchase from Cambridge University Press (in the United Kingdom and in...Explores a connection between Golden Section on the one hand and Fibonacci and Lucas numbers on the other...
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The relation between Fibonacci numbers and Golden Section Section is the number often encountered when taking the ratios of distances in simple geometric figures. The Fibonacci numbers appear in arrangements of leaves because the Fibonacci numbers form the best whole number approximations to the Golden Section. There is...A paper relating the early discovery of the Golden Mean by the ancient Greeks and their methods of constructing it.
http://www.middlebury.edu/~harris/Humanities/TheGoldenMean.html
Project with art references and object construction lessons.
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Steve, Jeanette, and Marc's Final Project Welcome to the home page for OUR FINAL PROJECT THE GOLDEN RATIO Presented to you by: Steve Blacker, Jeanette Polanski, and Marc Schwach The purpose of this web page is to provide an introduction to the Golden Ratio and Fibonacci...An introduction to Phi, the golden rectangle, and Fibonacci numbers.
http://www.seephi.org/
This is an informative site on an interesting aspect of Geometry: The Golden Ratio.
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Welcome To the Golden Ratio ...A Project Gutenberg eBook with one million digits.
http://www.gutenberg.net/etext/744
A Project Gutenberg Etext.
http://www.gutenberg.net/etext/633
A web page with phi to 10,000 places.
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10000 decimal Golden Ratio This is the first publication of the Golden Ratio to 10,000 digits. If you know of an earlier one, please let me know. How was this done? Here's how. There's more We're now listed as a Useless Page (search for...The base angle of the largest trinalges of most representations of Sri Yantra are about 52 degrees, close to the base angle of the Great Pyrmaid of Cheops, which is 51deg50'. With such a base angle, the ratio of the hypotenuse to half the base is phi, the Golden Ratio.
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The base angle of the largest trinalges of most representations of Sri Yantra are about 52 degrees, close to the base angle of the Great Pyrmaid of Cheops, which is 51deg50 With such a base angle, the ratio of the...Explanation, presence in biology, art, and ancient art.
http://www.geocities.com/jyce3