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Katolog > Science > Math > Recreations > Specific Numbers > phi


Phi is the Greek letter representing the golden ratio, also called the golden mean or the golden proportion. Break a line segment into two such that the ratio of the whole to the longest segment is the same as the ratio of the two segments, that ratio is the golden ratio. Phi = 1.618034...
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Links:

American Phi
http://members.aol.com/loosetooth/phi.html

American Phi

Music, story and poetry of the Golden Ratio.
members.aol.com/loosetooth/phi.html
The 'Phi-Nest'
http://goldennumber.net/

The 'Phi-Nest'

Information on the Golden Section, Divine Proportion, Fibonacci series and phi.
goldennumber.net
The Golden Section - the Number and Its Geometry
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html

The Golden Section - the Number and Its Geometry

Simple definitions; exact value and first 2000 decimal places; finding the golden section; continued fractions. Simple tricks for your calculator, puzzles and games.
www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html
The Golden Ratio
http://www.cs.arizona.edu/icon/oddsends/phi.htm

The Golden Ratio

Extension of the number.
www.cs.arizona.edu/icon/oddsends/phi.htm
The Golden Ratio: A Golden Opportunity to Investigate Multiple Representations of a Problem
http://www.ite.sc.edu/dickey/golden/golden.html

The Golden Ratio: A Golden Opportunity to Investigate Multiple Representations of a Problem

Essay and brief introduction by Edwin M. Dickey.
www.ite.sc.edu/dickey/golden/golden.html
The Golden Ratio
http://library.thinkquest.org/C005449

The Golden Ratio

Examines the uses/occurances of phi in biology, art, and ancient times.
library.thinkquest.org/C005449
Phi: That Golden Number
http://jwilson.coe.uga.edu/emt669/Student.Folders/Frietag.Mark/Homepage/Goldenratio/goldenratio.html

Phi: That Golden Number

How to generate the number, GSP script for dividing segments, rectangle and other shapes, the rabbit problem and references.
jwilson.coe.uga.edu/../../../../Goldenratio/goldenratio.html
Phi, the golden ratio
http://astronomy.swin.edu.au/pbourke/analysis/phi/

Phi, the golden ratio

Provides a definition of Phi, and explains some mathematical background as well as a listing of 1000 digits of the number.
astronomy.swin.edu.au/pbourke/analysis/phi
The Golden Mean
http://www.vashti.net/mceinc/golden.htm

The Golden Mean

Explains the theory behind the golden mean and how it can be constructed out of the Fibonacci series.
www.vashti.net/mceinc/golden.htm
Ask Dr. Math
http://mathforum.org/dr.math/tocs/golden.high.html

Ask Dr. Math

A list of questions gathered pertaining to Fibonacci and Golden Ratio.
mathforum.org/dr.math/tocs/golden.high.html
Ask Yahoo
http://ask.yahoo.com/ask/19991201.html

Ask Yahoo

The column at yahoo.com answers the question "What is the "Golden Ratio" and what significance does it have?".
ask.yahoo.com/ask/19991201.html
A brief introduction to Golden Ratio
http://www.tnt-audio.com/intervis/cardase.html

A brief introduction to Golden Ratio

An interview with George Cardas, describing his use of the Golden Ratio in high-end audio equipment cables.
www.tnt-audio.com/intervis/cardase.html
Golden Number
http://www.freewebz.com/goldenno

Golden Number

A few words about Golden Number.
www.freewebz.com/goldenno
The Golden Ratio and The Fibonacci Numbers
http://www.friesian.com/golden.htm

The Golden Ratio and The Fibonacci Numbers

A presentation of the relationship between the Golden Ratio and the Fibonacci Numbers from the proceedings of the Friesian School.
www.friesian.com/golden.htm
Golden Rectangle
http://mathworld.wolfram.com/GoldenRectangle.html

Golden Rectangle

Defines the "Golden Rectangle" based on phi and shows some formulars and drawings of the results.
mathworld.wolfram.com/GoldenRectangle.html
The Golden Section
http://www.perseus.tufts.edu/GreekScience/Students/Tim/Golden.html

The Golden Section

Short page describing the Golden Section. Includes a description of various constructions and history.
www.perseus.tufts.edu/GreekScience/Students/Tim/Golden.html
The Golden Mean
http://pauillac.inria.fr/algo/bsolve/constant/gold/gold.html

The Golden Mean

At the Favorite Mathematical Constants page.
pauillac.inria.fr/algo/bsolve/constant/gold/gold.html
Golden`s Section Formulas
http://milan.milanovic.org/math/english/relations/relation.html

Golden`s Section Formulas

Explores a connection between Golden Section on the one hand and Fibonacci and Lucas numbers on the other...
milan.milanovic.org/math/english/relations/relation.html
The Greeks and the Golden Mean
http://www.middlebury.edu/~harris/Humanities/TheGoldenMean.html

The Greeks and the Golden Mean

A paper relating the early discovery of the Golden Mean by the ancient Greeks and their methods of constructing it.
www.middlebury.edu/~harris/Humanities/TheGoldenMean.html
The Golden Ratio
http://www.geom.uiuc.edu/~demo5337/s97b/

The Golden Ratio

Project with art references and object construction lessons.
www.geom.uiuc.edu/~demo5337/s97b
See Phi
http://www.seephi.org/

See Phi

An introduction to Phi, the golden rectangle, and Fibonacci numbers.
www.seephi.org
Colin and Greg's Golden Ratio Page
http://members.tripod.com/~ColinCool/mathindex.html

Colin and Greg's Golden Ratio Page

This is an informative site on an interesting aspect of Geometry: The Golden Ratio.
members.tripod.com/~ColinCool/mathindex.html
The Golden Mean by Jerry Bonnell and Robert Nemiroff
http://www.gutenberg.net/etext/744

The Golden Mean by Jerry Bonnell and Robert Nemiroff

A Project Gutenberg eBook with one million digits.
www.gutenberg.net/etext/744
20,000 Digits
http://www.gutenberg.net/etext/633

20,000 Digits

A Project Gutenberg Etext.
www.gutenberg.net/etext/633
10,000 Digits
http://www.ac.wwu.edu/~stephan/webstuff/ratio.digits.html

10,000 Digits

A web page with phi to 10,000 places.
www.ac.wwu.edu/~stephan/webstuff/ratio.digits.html

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