21. How Does PHI/Golden Mean Based Recursion Create Dimple Inside Out-Ness? inside. This is the 'New Sacred geometry of Compassion'. How Does PHI/GoldenMean Based Recursion Create Dimpling. Inside OutNess? http://www.zayra.de/soulcom/dimple/

How the Heart Opens: Sacred Geometry and the New Science of Compassion - The Heart's Labyrinthine Electrification: 1.Dimple, 2. 'Turn Inside Out" from Dan Winter 12/3/2000 The essential thing we have learned about PHI / Golden Ratio harmonics from years of harmonic analysis of EKG during bliss , is that indeed the completion of the 'turning inside out' process IS the New Science of Compassion. What is marvelous for those interested in labyrinth studies is that work is precisely the topo map to HOW to turn inside enacted outside you, so that you can DO it (compassion) inside you. The animation of turning inside out on the 7 color moebius map of the origin of matter, co-defines the 7 spin (symmetries) of the tetra ( as seen in the heart muscle geometry ) AND when projected onto 'flatland' (2D) codefines the LABYRINTH ( animation below). When this turning inside out ness of both the HEART electrification AND the labyrinth is mapped going to it's limit or boundary or final 3D fractal symmetry, we literally get the animation of the holy grail The essential point for teaches of the ultimate map to successful turning inside out ness (labyrinth), is to translate the topological skill learned kinesthetically from the labyrinth - into what you do INSIDE your heart when you CHOOSE to feel someone outside AS IF they were inside. This is the 'New Sacred Geometry of Compassion'.

22. *Golden Mean* MD as was done in fig.1. Line MD crosses line EF at point G. Point G cuts EF at thegolden mean of EF. With these illustrations, using simple geometry of line http://www.asis.com/asis/golden.html

The Golden Mean - We find in the ASIS logo, two methods of constructing the golden proportion using Euclidean tools. The logo represents a system or series of systems that ever resolve themselves in harmony and usefulness. The golden proportion was selected to be an integral part of the logo representing Access Solutions Information Services. The construction is a network of scribed arcs and straight lines that resolve themselves in useful relationship. We are able to arrive, through technological, conceptual, human based rationality at a relationship that nature exudes. Nature can't help herself, it's just how the flower grows. But man can stray and create abominations. So many of us live far removed from natural structure and as we venture into cyber space we are even further removed from order that can keep us sane. Our logo pays homage to nature's wisdom and serves as a reminder that with a little care, we can structure our world in a way that gives us beauty and peaceful resolve. Information requires perspective or context. The relevance of information is based on its usefulness.

23. Golden Mean - Wikipedia The golden mean has interesting properties when used as the base of a number systemsee golden mean base. geometry has two great treasures one is the http://www.wikipedia.org/wiki/Golden_mean

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Other languages: Deutsch Svenska Golden mean From Wikipedia, the free encyclopedia. The Golden mean , also called Golden ratio Golden section Golden number or Divine proportion , usually denoted by the Greek letter phi , is the number the unique positive real number with 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 Equivalently, they are in the golden ratio if the ratio of the larger one to the smaller one equals the ratio of the smaller one to their difference: After simple algebraic manipulations (multiply the first with a b and the second with ( a b b ), both of these equations are seen to be equivalent to

24. Golden Mean is interesting. It was discovered by Gabriel Bosia. Find out more aboutconstructions for the golden mean. geometry. I am interested http://www.math.uwaterloo.ca/~ljdickey/geometry_corner/golden_mean/

The Golden Mean The Golden Mean (or golden ratio ) is a famous number that has been know from ancient times. For example some ancient buildings were built with this ratio used for its proportions. Here is an algebraic conditions that defines the golden ratio. It is positive and subtracting 1 from it gives a number that equals its reciprocal. So, it satisfies the equation x-1 = 1/x. It is not hard to show that the golden mean is one half of the sum of one and the square root of 5. Since the square root of 5 is about 2.236, and one plus the square root of 5 is 3.236, the golden ratio is approximately 1.618. The geometric construction that I have seen most often golden ratio uses a square A, B, C, D. Find the midpoint of the side AB and call it M. Make the circle with center M that passes through C (and D). Let E be the point where this circle meets the ray AB. Then the ratio AE / AB equals the ratio AB / BE. It is easy from this that that AE/AB is the golden ratio. Click here to see a picture (coming soon). A recent and surprising construction is one given by George Odom . George constructs an equilateral triangle ABC with vertices on a circle. Let M be the midpoint of AB and N be the midpoint of AC. Then the ray MN meets the circle at a point P. The ratio MP/MN is the golden ratio. Click here to see a picture (coming soon). Another pleasant surprise construction is given by Gabriel Bosia . Gabriel starts with the famous pythagorean triangle with sides 3, 4, and 5. Construct the circle of diameter 5 with center at the midpoint of the hypotenuse.

25. E-z Geometry Project Topics geometry Desert Architecture. Go to Top. golden mean The goldenmean; Mathsoft - golden mean; Access Indiana - golden mean. Go to Top. http://www.e-zgeometry.com/links/plinks.htm

e-zgeometry Project Topics A to F G to M N to R S to Z Binary #'s Cartography Centers of Triangles Constructions ... Topology Binary Numbers: Binary Color Device Number Bases Conversion Modular Arithmetic Modular Arithmetic ... Go to Top Cartography: Value of Maps History of Cartography Making Maps Easy to Read Map Projections by National Geographic ... Go to Top Centers of Triangles: Go to Top Constructions: Kutztown - Constructions Go to Top Cyrptography: Introduction to Cyrptography (Course) Seminar in Cyptography Magic Decoder Game Breadking the Code (PBS Series) ... Cyptography Problem Mahony High - Cryptography Go to Top Fermat's Last Theorem: Visualizing Fermat's Last Theorem Fermat's Last Theorem FLT Dr. Math - FLT ... Fermat's Last Theorem - AMS Mahony High - Fermat Page Go to Top Fibonacci Numbers: Course on Fibonacci Numbers (Holy Cross) Fibonacci Numbers and the Golden Section - Surrey Fibonacci Numbers Fibonacci Numbers in Nature - Surrey ... Fr. Chris's Fibonacci Page Mahony High - Fibonacci Page Go to Top Figurative Numbers: Triangular Numbers Triangular Numbers Lesson Triangular Numbers - Fayette Square Numbers - Fayette ... Go to Top Four Color Theorem: The Four Color Theorem (Quite Technical) Four Color Theorem - Mega Math Four Color Theorem - Georgia Tech The Most Colorful Math of All - Mega Math ... The Four Color Problem - Email Mahony High - 4 Color Page History of the 4 Color Theorem Go to Top Fractals: Cool Math - Fractal Gallery Earl's Fractal Art Gallery Fract-Ed Fractal FAQ ... Dr. Math - Fractals

26. Under Siege: The Golden Mean In Architecture By Michael Ostwald For The Nexus Ne relationship between geometric forms and other forms say geometry and architecture bya number of recent authors investigating the golden mean in architecture http://www.nexusjournal.com/Ostwald.html

Abstract. Michael Ostwald briefly describes the Golden Mean and its history before examining the stance taken by a number of recent authors investigating the Golden Mean in architecture. He addresses the theories of Husserl, Derrida and Ingraham, who separately affirm that tacit assumptions about the relationship between geometric forms and other forms - say geometry and architecture - must be constantly questioned if they are to retain any validity. Under Siege: The Golden Mean in Architecture Michael J. Ostwald Department of Architecture Faculty of Architecture, Building and Design, University of Newcastle University Drive, Callaghan, NSW 2308 AUSTRALIA Introduction E dmund Husserl's Origin of Geometry was originally written as an appendix to his The Crisis of European Sciences and Transcendental Phenomenology . Significantly, in the Origin of Geometry Husserl examines geometry from a historical perspective not a mathematical one. For Husserl the elevation of geometric forms to transcendental status (as, for example, the basis of universal beauty) presupposes the connection between such forms and some "ideal" or "original" form. An example of this is found in Vitruvius, who maintains that th

27. Golden Proportions In A Great House: Palladio's Villa Emo By Rachel Fletcher For cocurator of the exhibit Harmony by Design The golden mean and author of traveledto Chicago, Washington, and New York, she teaches geometry and proportion http://www.nexusjournal.com/N2000-Fletcher.html

Abstract. Rachel Fletcher examines Palladio's Villa Emo, reviewing the sources for harmonic proportions in architecture from Vitruvius to Alberti, and discussing both the rational proportions found in the plan of the villa published in the Quattro Libri as well as the incommensurable Golden Mean. Golden Proportions in a Great House: Palladio's Villa Emo Rachel Fletcher 113 Division St. Great Barrington, MA 01230 USA A mong the great houses of the Renaissance is Palladio's Villa Emo at Fanzolo in Northern Italy, built in the 1550s to realize Lunardo Emo's dream of a family seat in the country. Palladio's methods of harmonizing buildings organically with their physical surroundings borrow from rural traditions and local farm customs. The massive south-facing entry ramp in front, for example, serves as a threshing floor, where grain may be spread in the sun to dry. Palladio adopted a number of classical rules of building recorded in the ten books of De architectura by the Latin theorist Vitruvius, well known for applying mathematical proportion to a building's measures and equally adept at achieving harmony in more pragmatic and natural ways.

28. Mathsoft: Functional Iteration: The Golden Mean References 12, 1999) 376. MS El Naschie, The golden mean in quantum geometry, knot theory andrelated topics, Chaos Solitons Fractals 10 (1999) 13031307; MR 2000c11213. http://www.mathsoft.com/mathresources/constants/iteration/article/0,,1971,00.htm

search site map about us  + news  + ... product registration The Golden Mean References H. E. Huntley, The Divine Proportion: A Study in Mathematical Beauty , Dover, 1970. M. Ghyka, The Geometry of Art and Life , Dover, 1977. J. Kappraff, Connections: The Geometric Bridge Between Art and Science , McGraw-Hill, 1991. B. Grunbaum, Branko and G. C. Shephard, G.C., Tilings and Patterns , W.H. Freeman, 1987; MR 88k:52018 C. F. Linn, The Golden Mean: Mathematics and the Fine Arts , Doubleday, 1974. D. Benjamin and the editors of Time-Life books, Mathematics , rev. ed., Time-Life Books, 1970. M. Boles, The Golden Relationship: Art, Math, Nature , 2nd ed., Pythagorean Press, 1987. K. Wiedman, The Golden Mean , part of Rashomon's Home Page K. H. Rosen, Discrete Mathematics and its Applications , 2nd ed., McGraw-Hill, 1991. S. Vajda, Fibonacci and Lucas numbers, and the Golden Section: Theory and Applications , Halsted Press, 1989; MR 90h:11014 C. S. Ogilvy, Excursions in Geometry , Dover, 1969. E. Maor, e: The Story of a Number , Princeton Univ. Press, 1994; MR 95a:01002 J. D. Lawrence

29. For Bob And All Teachers And Students Of Sacred Geometry a right to say that one and a half turns of the golden mean or the We are obviouslytalking about Sculptured Jewelry Artwork and not Sacred geometry or math http://www.sangraal.com/Discussion/00000028.htm

San Graal School of Sacred Geometry News Research and Discussion Page Home Contents Search Post ... Previous Up For Bob and All Teachers and Students of Sacred Geometry From: Ray Flowers Date: 14 Jul 2001 Time: Remote Name: Comments Hi Bob, I am assuming that the Bob posting information about Mr. Tenen is of course Bob Dratch, who is apparently part of the Meru Foundation's Advisors and has at times, spoken in Mr. Tenen's behalf. I am asking this of you because you have made it your business to contribute, and it seems that you want to share. If you are not Bob Dratch, please accept my apologies, and I then direct this post to all the math and Sacred Geometry teachers who might contribute their great wisdom to our conversation and to all students of Sacred Geometry who might ask questions and share what they have learned. It is my anticipation that cool heads with good information can teach us more than we know. There are several follow-up facts that have questions for which I can find no answers. I receive many post from readers that do not understand. It is certainly not my quest to belittle anyone, but there are questions, which, if answered, could create an understanding for everyone. The questions below reflect many of the comments that I have received from folks who truly want to understand but seem afraid to ask because of fear of lawsuit. The purpose of this post is intended to ask pertinent questions for the readers of the San Graal website, and not to condemn the situation in any way.

30. Corrective Notice By Daniel E. Winter keywords San Graal School of Sacred geometry Bookstore, Dan Winter, Daniel Winter,Crystal Hill, Phi Harmonics, Sacred geometry, golden mean Spiral, Heartbeat http://www.danwinter.com/corrnote.html

This Corrective Notice by Daniel E. Winter is posted in accordance with the Findings of Fact, Conclusions of Law, and Order of the Hon. Charles J. Siragusa, Federal District Judge for the Western District of New York in Rochester, NY, dated September 11, 1998, in re Tenen v. Winter. On February 27, 2001, USDJ Charles J. Siragusa issued a new order consistent with Mr. Raymond Flowers' assertion that he was not Mr. Winter's website manager, as was stipulated by Mr. Winter in the original Findings of Fact, Conclusions of Law, and Order in re Tenen v. Winter dated September 11, 1998. Consequently Mr. Flowers' identification as "my [Mr. Winter's] website manager" has been removed from this Corrective Notice. USDJ Siragusa otherwise reaffirmed his original September 11, 1998 Findings of Fact, Conclusions of Law, and Order in its entirety , and Mr. Flowers' name continues to appear elsewhere in this original Order. The new February 27, 2001 Order applying exclusively to Mr. Flowers will be posted on this website shortly. Until that time, text of this order is available on request to danwinter-corrective@lycos.com

31. Sacred Geometry Like the golden mean Spiral, this geometric progression has no beginning and no Thisgeometry artistically symbolizes this relationship, and as such, may be a http://www.spiritlight.com/sacred_geometry_forms.htm

Sacred Geometry Forms Properties Associated with the Form Torus The first shape to emerge out of the genesis pattern. It governs many aspects of life including the human heart with its seven muscles that form a Torus. The torus is literally around all life forms, all atoms, and all cosmic bodies such as planets, stars and galaxies. It is the primary shape in existence. Vesica Piscis The crucible of the creating process. An opening to the womb from which all geometric forms are born. A symbol of the fusion of opposites and a passageway through the world’s apparent polarities. The geometric image through which light was born. Also the geometry for the human eye. Flower of Life The geometric power symbol, which activates energy coding in the mind, helping one to access their “light body.” It is the primal language of the universe—pure shape and proportion. This interlocking circle design has the ability to unlock memories that are deep within our being because it is a primary energy/language pattern that has a resonance with all things within us and around us. Shown here with a harmonic overlay.

32. The 'Golden Mean' In Number Theory are given by suitable pinary (pinary, p prime) powers of the golden mean. crystalswith padic internal symmetries, von Neumann's Continuous geometry, the role http://www.maths.ex.ac.uk/~mwatkins/zeta/goldenmean.htm

The ' Golden Mean ' in number theory Planat, et. al. have subjected certain arithmetic functions to a type of analysis appropriate to signal processing and discovered a type of power law in the frequency spectrum possibly involving the Golden mean C. Castro, "Fractal strings as the basis of Cantorian-Fractal spacetime and the fine structure constant" [abstract:] "Beginning with the most general fractal strings/sprays construction recently expounded in the book by Lapidus and Frankenhuysen, it is shown how the complexified extension of El Naschie's Cantorian-Fractal spacetime model belongs to a very special class of families of fractal strings/sprays whose scaling ratios are given by suitable p inary ( p inary, p prime) powers of the Golden Mean. We then proceed to show why the logarithmic periodicity laws in Nature are direct physical consequences of the complex dimensions associated with these fractal strings/sprays. We proceed with a discussion on quasi-crystals with p -adic internal symmetries, von Neumann's Continuous Geometry, the role of wild topology in fractal strings/sprays, the Banach-Tarski paradox, tesselations of the hyperbolic plane, quark confinement and the Mersenne-prime hierarchy of bit-string physics in determining the fundamental physical constants in Nature." Castro's observation possibly linking the 'Golden String' to a function central to the behaviour of certain eigenvalues in random matrix theory (which in turn appears to be deeply linked to the behaviour of the nontrivial zeros of the Riemann zeta function).

33. A History Of The Golden Mean / Section / Ratio, Divine Proportion And Phi geometry has two great treasures one is the theorem of the division of a line intoextreme and mean ratio letter of Phidias (1), who used the golden ratio in http://evolutionoftruth.com/goldensection/history.htm

The Phi Nest now has its own domain with new content at http://goldennumber.net Please update your bookmarks. The Phi-Nest™ on the Golden Number Home Phi for Neo'phi'tes Fibonacci Series Divine Proportion/ ... Links History While the proportion known as the Golden Mean has always existed in mathematics and in the physical universe, it is unknown exactly when it was first discovered and applied by mankind. It is reasonable to assume that it has perhaps been discovered and rediscovered throughout history, which explains why it goes under several names. Uses in architecture date to the ancient Egyptians and Greeks Euclid (365BC - 300BC), in "Elements," referred to dividing a line at the 0.6180399... point as dividing a line in the extreme and mean ratio. This later gave rise to the use of the term mean in the golden mean. The Egytians used both pi and phi in the design of the Great Pyramids . The Greeks, who called it the Golden Section, based the entire design of the Parthenon on this proportion. It was also used by Phidias, a famous Greek Sculptor. (1)

34. Golden Mean Caliper/book The golden meanthe heart of sacred geometry-is a special relationship betweena part and a whole that acts as a formula for harmony and beauty. http://www.ylana.com/goldenm.htm

Golden Mean Book and Caliper Set (book and 14" caliper) by Stephen McIntosh Sorry, out of print and out of stock on this SUPERB tool and guide! Tools to Increase Spiritual Perception The Golden Mean-the heart of sacred geometry-is a special relationship between a part and a whole that acts as a formula for harmony and beauty. Creatively using the Golden Mean is an ancient form of spiritual practice. This 64-page book describes the profound significance of the Golden Mean as well as the myriad ways it appears in the natural universe and in human culture. With over 90 diagrams and illustrations, it combines enjoyable reading with concise, in-depth insights. The Calipers are a practical tool for adding harmony to your creations, as well as a symbol of visual philosophy-they give you a fun way to discover and apply the Golden Mean relationship. As a tool of the emerging "Spiritual Renaissance art movement," the Golden Mean Set is not only for artists, it is useful for anyone interested in the behaviors of spirit. "A recent confirmation of the vitality of the Golden Mean as an organizing principle of this emerging art movement can be found in a group of crop circle patterns that appeared in southwest England during the summer of 1996. Many of these huge and complex formations that mysteriously appeared in farmer's fields made prominent use of sacred geometry and fractal mathematics in their designs."

35. Geometry Forum: Winter 95 Outposts - III The geometry Forum Newsletter. Anderson and I need to know examples of where the Fibonaccisequence is found in nature and how that relates to the golden mean. http://mathforum.org/Outposts/W95p3text.html

Forum Outposts The Geometry Forum Newsletter Winter 1995, page 3 Ask Dr. Math!, continued Look at the sequence 1/(-1/2), 1/(-1/3), 1/(-1/4), and notice again that the denominators -1/2, -1/3, -1/4, ..., are going to zero. Again, we would want the limit of this sequence to be 1/0, but looking at the sequence, it simplifies to -2, -3, -4, ..., and it goes to negative infinity. So which would we assign to 1/0? Negative infinity or positive infinity? Instead of just assigning one of these willy nilly, we say that infinity isn't a number, and that 1/0 is indeterminate. I hope this helps. Ken "Dr." Math Dear Dr. Math: My name is Erica Anderson and I need to know examples of where the Fibonacci sequence is found in nature and how that relates to the Golden Mean. This is for Pre Calculus class. Thanks for your help. Hey Erica, I love this problem. The Fibonacci sequence happens all the time in nature, so much it is amazing. I am having trouble not just sitting here and listing all the occurrences that I can think of, but I will try to resist sending you a seven-page e-mail message. A few examples: Think about a pine cone. Have you ever noticed that the petals spiral up in two directions? Well, the number of petals it takes to get once around is almost always a Fibonacci number.

36. Alternating Series, Geometry, Theory Of Everything (TOE) By Osher Doctorow logics, LogicBased Probability-Statistics, and p1 or pn proximity-geometry-topologyas are very closely related to the golden Ratio or golden mean (not the http://mathforum.org/epigone/geometry-research/pamwhahher

Alternating Series, Geometry, Theory of Everything (TOE) by Osher Doctorow reply to this message post a message on a new topic Back to geometry-research Subject: Alternating Series, Geometry, Theory of Everything (TOE) Author: osher@ix.netcom.com Date: Wed, 19 Jun 2002 16:29:51 -0700 From: Osher Doctorow osher@ix.netcom.com, Wed. June 19, 2002 3:41PM In my various contributions here and in real-analysis@ams.org and http://www.superstringtheory.com/forum, The Math Forum

37. The Golden Mean & The Great Pyramid - Www.ezboard.com Enter your email address A service provided by SmartGroups.com, InvisibleCollege I Sacred geometry The golden mean The Great Pyramid, http://pub135.ezboard.com/finvisiblecollegefrm16.showMessage?topicID=7.topic

38. Sacred Geometry Searched for golden mean/Bodes Law, 0, 9/28/02 92747 am, dwcooper11. golden Blossoms,Pi Flowers, 0, 9/26/02 71431 pm, dwcooper11. Sacred geometry..Fractal links http://pub135.ezboard.com/finvisiblecollegefrm16

Trans-Dimensional/Time Travel Enter your email address: A service provided by SmartGroups.com Invisible College I > Sacred Geometry Invite Friends! Login Register Your Free Account (Required) Search Help ... Need help logging in? The Invisible College is now four boards, each with it’s own unique characteristics and flavor. Invisible College II /Trans-Dimensional/Time Travel Invisible College III / The Institute for Chaos Studies Forum Invisible College IV / ~RENCA~ incuBLOGula-UPDATED DAILY I believe the future is only the past again, entered through another gate. Sir Arthur Wing Pinero Please Post in the proper heading and thread. All inappropiate , posts will be deleted...at once if not sooner ! No one enjoys chaos more than me...if it's done in an orderly fashion. Thanks DWCooper 1 visitor in the last 15 minutes: Members - 1 Guest - Anonymous Topic Replies Last Comment Started By Snow Crystal Photo Selection 3/13/03 9:55:28 am 12/8/02 10:33:18 am Entropy 11/7/02 10:22:55 am Pale Rider Searched for Golden Mean/Bodes Law 9/28/02 9:27:47 am Golden Blossoms, Pi Flowers

39. Geometry - A To Z Home's Cool Homeschooling Math geometry Math for Morons Like Us Everything from parallel lines to volumes ofprisms and a couple of word problems are covered. The golden mean The golden http://www.gomilpitas.com/homeschooling/explore/geometry.htm

YOU ARE HERE: HOME EXPLORATIONS 4 KIDS MATH Earn your certificate from the comfort of your own computer. A to Z Home's Cool Homeschooling Explorations 4 Kids I am Ann Zeise , your guide to the best and most interesting and useful sites and articles about home education on the web. Search This Site The Web Home New Kids Links One Exploration A Day Contact Ann Zeise ... Free Newsletter Site Index: A B C D ... Z Advanced Math Math 4 Teens Calculators History of Math High School Math Algebra Geometry Trigonometry Calculus Math 4 Kids Art Math Connection Calendars Clocks Logic Games ... Word Problems Math Curriculum Math Books Math Software Math Stuff Explorations 4 Kids Computer Literacy Fine Arts General Interest Language Arts ... Social Studies A to Z Home's Cool Home Just Beginning Concerns Regional Information ... Holiday Directory Geometry The Adventures of Super Triangle What's stronger than a square? More powerful than a rectangle? Able to hold up huge bridges and big skyscrapers? It's - the amazing, super-powerful triangle!

40. The Golden Rectangle And The Golden Ratio I have since found the construction in geometry, by Harold R. Jacobs. I was just watchingthe awardwinning, short documentary, Fibonacci and the golden mean. http://www.jimloy.com/geometry/golden.htm

Return to my Mathematics pages Go to my home page The Golden Rectangle and the Golden Ratio click here for the alternative Golden Rectangle and Golden Ratio page This diagram shows a golden rectangle (roughly). I have divided the rectangle into a square and a smaller rectangle. In a golden rectangle, the smaller rectangle is the same shape as the larger rectangle, in other words, their sides are proportional. In further words, the two rectangles are similar. This can be used as the definition of a golden rectangle. The proportions give us: a/b = (a+b)/a This fraction, (a+b)/a, is called the golden ratio (or golden section or golden mean). Above I have defined the golden rectangle, and then said what the golden ratio is, in terms of the rectangle. Alternatively, I could have defined the golden ratio, using the above equation. And then a golden rectangle becomes any rectangle that exhibits this ratio. From our equation, we see that the ratio a/b=1/2+sqr(5)/2 -1/2+sqr(5)/2 or 0.61803398875 . . .) is called the golden ratio. Also, other mathematical quantities are called phi. The golden ratio is also called tau. Some people call the bigger one (1.61803398875 . . .) Phi (an uppercase phi) and the smaller one (0.61803398875 . . .) phi.

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