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Golden Mean Geometry: more detail

Pythagorean Philosophy: Pythagorean tuning, Sacred geometry, Pythagoreanism, Golden mean, The golden verses of Pythagoras, Androcydes
The Geometry of the Sun God: Apollo's Golden Mean: Vol 1 by Keith Squires, 2005-03-21
The Ten Books on Architecture - Original Unabridged Version by Vitruvius Pollio, 2010-07-17
The Ten Books on Architecture - Latest Edition 2010 by Vitruvius Pollio, 2010-07-10
The Ten Books on Architecture by Vitruvius Pollio, 2010-06-25

lists with details

"Unified Field" Physics? Based On Golden Mean Ratio By Alex Kaivarainen
"Unified Field" Physics? based on Golden Mean Ratio by Alex Kaivarainen. comments from Dan Winter.. see Alex K. new " It appears, that Golden Mean play a crucial role in matter (rest mass) and elementary charge origination. mean ( the CONE of torus based on golden mean geometry .. which balances the forces..) of rigid structures with geometry, following Golden mean (I termed them "Harmonizators
http://www.soulinvitation.com/goldenphysics

Extractions: "Unified Field" Physics? based on Golden Mean Ratio by Alex Kaivarainen comments from Dan Winter.. - see Alex K. new: "It appears, that Golden Mean play a crucial role in matter (rest mass) and elementary charge origination. Symmetry shift of Bivacuum fermions, presented by truncated cones at my Figs. corresponds to Golden mean conditions, indeed. At this conditions a fusion of elementary particles, as a triplets of sub-elementary particles starts, as far they becomes stabilized by resonance exchange interaction with Bivacuum.
Great Golden Pyramid
has Golden Geometry of the Golden Mean. What does it look like? .. . Adam Maturanahas a web page about the golden mean geometry of the Cydonia site on Mars.
http://www.innerx.net/personal/tsmith/Gpyr.html

Extractions: Ikonos satellite image PBS NOVA has an Online Exploration of the Giza Pyramids and Sphinx with commentary by Mark Lehner and Zahi Hawass, who advocate an age of about 4,600 years for the Giza pyramids. Mark Lehner says "... we know ... the date of the pyramids ... mostly by context. The pyramids are surrounded by cemeteries of other tombs. ... we find organic materials ... that can be radiocarbon dated ... But primarily we date the pyramids by their position in the development of Egyptian architecture and material culture over the broad sweep of 3,000 years. ..." I agree with the dates of the materials found in the area of the Giza pyramids, but I do NOT agree that those materials, tombs, etc., are the materials, tombs, etc., of the builders of the Giza Pyramids and Sphinx. In my opinion, the builders were either the Ice Age Civilization of 36,525 to 11,600 years ago, or, at the latest, a part of a global Early Human Civilization that broke up about 6,000 years ago, and that the Giza Sphinx and Pyramids were already built about 5,100 years ago when Menes reunited Lower Egypt, including Giza, with Southern Upper Egypt.
Geometry In The Natural World
Clear examples of geometry (and golden mean geometry) in Nature and matter All typesof crystals, natural and cultured. The hexagonal geometry of snowflakes.
http://www.infinitetechnologies.co.za/articles/geometry1.html

Extractions: GEOMETRY IN THE NATURAL WORLD The Golden Mean: The Golden Mean, or Golden Ratio as it is known, is an irrational number just like other important numbers such as Pi. This means that it cannot be completely represented by our currently used number system, except as a formula ( Sqr (5)-1)/2. Just like Pi (approx. 3.1416) - Phi, or the Golden Ratio, has an endless number of digits after its decimal point and with no repetition of the digits sequences. Therefore, like other "Transcendental" numbers, its value can only be approximated (using our number system). What is the Golden Ratio, and why is it important? The Golden Ratio is approximately Besides for possessing some remarkable and unique characteristics, the Golden Mean is found in ALL living creatures on Earth. Along with the Fibonacci Sequence (which is a whole-number system approximating the Golden Ratio, discovered by Leonardo Pisano Fibonacci), this ratio is found in plants and animal life wherever one looks. For example, this ratio can be found in fingers one's hand, amongst many other places, and it is prevalent in the skeletal structure of all creatures. The Fibonacci Sequence is as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...
The Golden Section - The Number And Its Geometry
A Note on the geometry of the Great Pyramid Elmer D Robinson point dividing a linein the extreme and mean ratio. This later gave rise to the name golden mean.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html

Extractions: 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. More We will call the Golden Ratio (or Golden number) after a greek letter, Phi ) here, although some writers and mathematicians use another Greek letter, tau ). Also, we shall use phi (note the lower case p) for a closely related value. There are just two numbers that remain the same when they are squared namely and . Other numbers get bigger and some get smaller when we square them: Squares that are bigger Squares that are smaller is 4 is 9 is 100 One definition of Phi (the golden section number) is that to square it you just add 1 or, in mathematics:
The Golden Mean
is Sacred geometry Philosophy and Practice by Robert Lawlor, published by Crossroad;Library of Congress number 8167703. Click here for more golden mean
http://www.vashti.net/mceinc/golden.htm

Extractions: The Golden Mean (or Golden 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 in the realm of things that grow and unfold in steps, and that includes living things.
Sacred Geometry
golden mean AND PHI. golden mean SPIRAL. golden RATIO. golden RATIO PHI FUSION ANOMALY - golden mean. SACRED geometry AND THE GREAT PYRAMID
http://www.crystalinks.com/sacred_geometry.html

Extractions: Geometry of the Great Pyramid The term "sacred geometry" is used by archaeologists, anthropologists, and geometricians to encompass the religious, philosohical, and spiritual beliefs that have sprung up around geometry in various cultures during the course of human history. It is a catch-all term covering Pythagorean geometry and neo-Platonic geometry, as well as the perceived relationships between organic curves and logarithmic curves. Armenian Architecture
Flower Of Life - The Golden Mean Spiral And The Merkaba - Article By Ronald L. H
Ronald L Holt. Director, FOLR LLC "To the golden Spiral In All of Us". April 21, 1999. Experiencing Sacred geometry without Intellectually Understanding It Although the golden mean Spiral is principally derived by utilizing mathematics on Sacred geometry. Section 2) General Philosophical Relationship between Fibonacci and golden mean
http://www.floweroflife.org/spiral01.htm

Extractions: Ronald L Holt Director, FOLR LLC " To the Golden Spiral In All of Us" April 21, 1999 Experiencing Sacred Geometry without Intellectually Understanding It Although the Golden Mean Spiral is principally derived by utilizing mathematics, it is equally mystifying and intriguing to note that this mathematical spiral has additional properties that can be experienced by humans on a profound level that does not require an intellectual understanding of the mathematical principles. I would like to explore the phenomenon that ties the mathematical spiral to the experiential spiral. In practical terms, they are one and the same. It will take a bit of explanation to demonstrate the probably ridiculous notion that the golden mean spiral can be experienced most simply as a profound feeling of love. Simply put, the Golden Mean Spiral is a doorway that weaves the ethereal and material dimensions together. In another context I would say that God left us one door of eternal mystery and exploration¾ the Golden Mean Spiral or the door of love . In this article we will explore how, in fact, the Golden Mean Spiral is an expression of the basic energy of creation that we call
Flower Of Life - The Golden Mean Spiral And The Merkaba - Article By Ronald L. H
golden mean Spiral and the Merkaba", the golden spiral is an inherent component within both angular and spherical geometry Through the golden spiral, all geometry transcends form
http://www.floweroflife.org/holomatrix01.htm

Extractions: Director, Flower of Life Research August, 2000 Foreward When Drunvalo and Dan Winter introduced me to sacred geometry, I passed through a doorway that held a vast new perspective of reality that caused me to grow internally. As I continued to study I found that I was left with many new tools with which I could work. Yet I felt "stuck" (in a good way) inside a geometric puzzle of reality that I intuitively felt was only a portion of what we are or are capable of becoming. I am writing this article with the intention of helping to inspire more people to embrace sacred geometry as a way to move even further beyond it. I hope you all continue to explore until you find your own unique path that leads you to the understanding of sacred geometry on a deeper level that will then allow you to see beyond sacred geometry in order to understand and claim more of your greater being. What is the effect of this study? It results in a greater humility, because it beckons the individual to step beyond our accepted history and definitions of reality and to embrace a greater understanding of who we really are. There will always exist so much more to our being than we can imagine. Creation (and all that exists within it) can be modeled by sacred geometry. Sacred geometry appears to be the blueprint underlying the many aspects of creation. Sacred geometry and the holographic nature of reality are models that enable us to fathom the possibility that we are the universe, but yet we are still more. Our true being defies all descriptions or boundaries. We are boundless beings made of pure principle itself.
The Archdome - Golden Mean Design
Sacred geometry and the Archdome. The Archdome is built using sacredgeometric proportion, better known as the golden mean proportion.
http://www.archdome.com/goldenmean.html

Extractions: Space is naturally curved; people were never meant to be boxed in." Jocelyn Eastland, Graduate Architect Observe the gentle curves of nature. They are based on a mathematical proportion called the Golden Mean. The Golden Mean goes on forever and ever. The whole universe is based on that mathematical proportion . . . your body, the fish, the trees, the galaxy, tornadoes and the flow of wind and water... Sacred Geometry and the Archdome The Archdome is built using sacred geometric proportion, better known as the Golden Mean proportion. In mathematical terms, the Golden Mean is a ratio of the irrational number .618.... : 1 or 1 : 1.618..... This means that if you constructed a rectangle (or a wall) to Golden Mean proportions, its sides would be in a ratio of 1 (foot, yard, inch whatever) to 1.618... times that. For example: If a wall was 10 feet in height, to be in Golden Mean proportion its length would have to be either 16.18 or 6.18 feet. Now 1.618033988875.... is an irrational number which goes on forever and ever and ever. So what happens when you build a wall using this endless Golden Mean ratio of proportion? Well the wall is (supposedly) a finite structure. However, when it is built using this proportion, a dynamic is created, and the dynamic is this: The wall, as the physical representation of the Golden Mean ratio, is a continuum that approaches the Infinite, but never reaches it: It approaches perfect balance, the Ideal, but can never capture it. The dynamic essence of any structure using this proportion, is endless motion towards perfection.
Abstract Art By Astrid Fitzgerald Based On The Golden Mean Proportions.
An exhibition based on sacred geometry and the golden mean Proportions. Includes paintings, constructions, works on paper and prints.
http://www.astridFitzgerald.com/

Extractions: ABSTRACT ART BY ASTRID FITZGERALD An Exhibition of Fine Art including Paintings, Constructions, Works on Paper and Prints based on the harmonious relationships of the Golden Mean Proportions View over 200 works of art. Site includes artist's statement, bio, reviews, exhibitions, books, interviews, articles, links to philosophical geometry and contact information. PAINTINGS CONSTRUCTIONS WORKS ON PAPER PRINTS ... RECENT WORK New! SCREENS ABOUT THE ARTIST ABOUT THE WORK BOOKS ... EXHIBITIONS New! CONTACT / LINKS BOOKS ON CREATIVITY AND CONSCIOUS LIVING BY ASTRID FITZGERALD ART FOR HEALING GRANT PROGRAM All works shown on www.astridFitzgerald.com are provided for non-commercial online viewing. Any recording to other media, redistribution, use in derivative works, or other appropriation without express permission is strictly prohibited.
The 'Phi-Nest': Source To The Golden Section, Golden Mean, Divine Proportion, Fi
The "PhiNest" information on the golden Section, Divine Proportion, Fibonacci series and phi. Five (5) and Phi. geometry. History. Life. Human Hand A source to some of Net's "phi-nest" information on the. golden Section / mean / Proportion / Ratio / Number,
http://www.goldennumber.net/

Extractions: for insights into the pervasive appearance of Phi in life and the universe. It's not often that you find a intriguing and thought-provoking mystery novel that's a creative and clever blend of mathematics, the creations of Leonardo Da Vinci, sacred geometry, history and religion. The Da Vinci Code by Dan Brown , is creating much awareness and inquiry into the Fibonacci series, the golden section and phi. Yes, these are quite real in mathematics and this site has been devoted to exploring them for years before this book was published.
Fibonacci Numbers, The Golden Section And The Golden String
Player. The golden section and geometry The golden section is also calledthe golden ratio, the golden mean and the divine proportion.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

Extractions: a sequence of 0s and 1s which is closely related to the Fibonacci numbers and the golden section. There is a large amount of information at this site (more than 200 pages if it was printed), so if all you want is a quick introduction then the first link takes you to an introductory page on the Fibonacci numbers and where they appear in Nature. The rest of this page is a brief introduction to all the web pages at this site on Fibonacci and the original problem about rabbits where the series first appears, the family trees of cows and bees, the golden ratio and the Fibonacci series, the Fibonacci Spiral and sea shell shapes, branching plants, flower petal and seeds, leaves and petal arrangements, on pineapples and in apples, pine cones and leaf arrangements. All involve the Fibonacci numbers - and here's how and why. The Golden section in Nature
The 'Phi-Nest': Source To The Golden Section, Golden Mean, Divine Proportion, Fi
The golden Section, Ratio or mean. that s a creative and clever blend of mathematics,the creations of Leonardo Da Vinci, sacred geometry, history and
http://goldennumber.net/

Extractions: for insights into the pervasive appearance of Phi in life and the universe. It's not often that you find a intriguing and thought-provoking mystery novel that's a creative and clever blend of mathematics, the creations of Leonardo Da Vinci, sacred geometry, history and religion. The Da Vinci Code by Dan Brown , is creating much awareness and inquiry into the Fibonacci series, the golden section and phi. Yes, these are quite real in mathematics and this site has been devoted to exploring them for years before this book was published.
Geometry Of Phi And The Golden Section
Learn more about phi and geometry on the Penrose Tiling and Quasi some of Net s phinest information on the golden Section / mean / Proportion / Ratio
http://goldennumber.net/geometry.htm

Extractions: daily diet. Phi and Geometry Phi is one of the two great treasures of geometry Phi or Φ, was described by Johannes Kepler as one of the "two great treasures of geometry." (The other is the Theorem of Pythagoras.) In a triangle it forms the dimensions of the great pyramids of Egypt. A ruler and compass can be used to form the "golden rectangle" used by the Greeks in the Parthenon (See also the Orthogons page.) Phi also defines the dimensions of a pentagon. Phi can be constructed from concentric circles whose sizes are in a ratio of 1 : 2 : 4. Draw a tangent from the small circle through the other two and the ratio of AC to AB is , as AB = 2 * 3 and AC = 15 , which by factoring out the 3 can be reduced to a ratio of 2 to (5 , or Note: The construction of phi with concentric circles was developed by Sam Kutler and submitted by Steve Lautizar.
Geometry Of Phi And The Golden Section
Phi appears in many aspects of geometry and has many unique, intriguing relationships and properties. Five (5) and Phi. geometry. History. Life. Human Hand A source to some of Net's "phinest" information on the. golden Section / mean / Proportion / Ratio / Number,
http://www.goldennumber.net/geometry.htm

Extractions: daily diet. Phi and Geometry Phi is one of the two great treasures of geometry Phi or Φ, was described by Johannes Kepler as one of the "two great treasures of geometry." (The other is the Theorem of Pythagoras.) In a triangle it forms the dimensions of the great pyramids of Egypt. A ruler and compass can be used to form the "golden rectangle" used by the Greeks in the Parthenon (See also the Orthogons page.) Phi also defines the dimensions of a pentagon. Phi can be constructed from concentric circles whose sizes are in a ratio of 1 : 2 : 4. Draw a tangent from the small circle through the other two and the ratio of AC to AB is , as AB = 2 * 3 and AC = 15 , which by factoring out the 3 can be reduced to a ratio of 2 to (5 , or Note: The construction of phi with concentric circles was developed by Sam Kutler and submitted by Steve Lautizar.
Goddess Nut And Creation
It is creation based on sacred geometry. The golden mean or golden ratio as the Greekscalled it (1.6180341.618304) is also called the Fibonacci spiral and is
http://www.crystalinks.com/nute.html

Extractions: Nut - Nuit - Creational Goddess Metaphoric Creational Stories based on Sacred Geometry This is an infra-red photo of me taken on July 4, 1987 in my home as I did a past life regression. There are many messages hidden within the photo. On epart of the ecotoplasmic form appears as Nut surrounding me. The energies developed as blue - the color frequency of the future - or higher frequency of experience t which we are returning. There is a hand over my mouth - with a wrist watch which represents Time Travel. I have recently returned from a journey to Egypt. There you discover the geometry of the land is linked to the mythology of its people. Nut - pronouned Noot - was the Egyptian goddess of the sky and of the heavens. She was the daughter of the air god, Shu and water goddesses, Tefnut. Nut was typically depicted as a woman with blue skin - her body covered with stars - standing on all fours - leaning over her husband, Geb - representing the sky arched over the Earth. During the day, Nut and Geb are separated, but each evening Nut comes down to meet Geb and this causes darkness. If storms came during the day, it was believed that Nut had some how slipped closer to the Earth.
The Golden Mean Resource Center
Cover Image, geometry of Design Studies in Proportion and Compositionby Kimberly Elam. TShirts and More from The golden mean Shop.
http://www.vashti.net/mceinc/store/

Extractions: Items purchased through the links on this page help support the Golden Mean site. Sacred Geometry: Philosophy and Practice by Robert Lawlor, published by Crossroad; Library of Congress number 81-67703. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio. A Beginner's Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science by Michael S. Schneider. The Curves of Life: Being an Account of Spiral Formations and Their Application to Growth in Nature, to Science, and to Art: With Special Reference by Theodore Andrea, Sir, Cook. The Divine Proportion: A Study in Mathematical Beauty by H. E. Huntley. The Geometry of Art and Life by Matila Costiescu Ghyka. by Robin Heath (Illustrator). Sacred Geometry by Miranda Lundy. Geometry of Design: Studies in Proportion and Composition by Kimberly Elam. A Mathematical History of the Golden Number [UNABRIDGED] by Roger Herz-Fischles, Roger Herz-Fischler. Fascinating Fibonaccis: Mystery and Magic in Numbers by Trudi H. Garland.
Golden Mean
The golden mean can be determined via geometry by taking a square with all sidesequal to 1, drawing an arc with the center of radius at the midpoint of one
http://www.halexandria.org/dward101.htm

Extractions: The Golden Mean can be construed as the basis of philosophy and Sacred Geometry , one of the Transcendental Numbers , and is typically derived from Fibonacci Numbers According to Robert Lawlor [1], Ancient geometry rests on no a priori axioms or assumptions. Unlike Euclidian and the more recent geometries, the starting point of ancient geometric thought is not a network of intellectual definitions or abstractions, but instead a meditation upon a metaphysical Unity, followed by an attempt to symbolize visually and to contemplate the pure, formal order which springs forth from this incomprehensible Oneness. It is the approach to the starting point of the geometric activity which radically separates what we may call the sacred from the mundane or secular geometries. Ancient geometry begins with One , while modern mathematics and geometry being with Zero Other authors have noted that Both the ancient Greeks and the ancient Egyptians used the Golden Mean when designing their buildings and monuments. Artists as diverse as Leonardo da Vinci and George Seurat used the ratio when constructing their paintings. These artists and architects discovered that by utilizing the ratio 1 : 1.618..., they could create a feeling of order in their works. Even today, artists are still using this proportion in their works, and scientists, like Roger Penrose are discovering new things about the Golden Mean and its place in science, mathematics, and nature.
Sacred Geometry
The golden mean (or F) is by its nature the essential ingredient in Sacred geometry,Numerology, and as it turns out, Connective Physics and science in general
http://www.halexandria.org/dward095.htm

Extractions: Tradition holds that over the entrance to Platos Academy was written the words: Agewmetrhtoz mhdeiz eisitw Only he who is familiar with geometry shall be admitted here (Apparently a knowledge of the Greek language was also important.) This website is not quite so stringent, and will happily admit any she who is interested in entering. (The guys will, of course, still need some geometry.) Alternatively, anyone who can carry a tune may enter in a bucket or by any other means. Music is, after all, based on geometry and mathematics. For anyone who doesnt think of themselves as being familiar with geometry, the words attributed to Platos school might be considering insulting, and thereby construed to have little or no validity. Any grapes from the discourteous must inevitably be sour. This circumstance is indeed unfortunate in that anyone who is not familiar with geometry, anyone who does not appreciate the premise that Philosophy is about understanding the meaning of a mathematical ratio (the Golden Mean ), and anyone who adheres exclusively to a literal interpretation of spiritual teachings...
Golden Ratio - Wikipedia, The Free Encyclopedia
and b which stand in the golden ratio is also (in older texts) expressed as thelength is cut in extreme and mean ratio . Mathematical uses. geometry has two
http://en.wikipedia.org/wiki/Golden_mean

Extractions: (Redirected from Golden mean The golden ratio proportio divina or sectio aurea ), also called the golden mean golden section golden number or divine proportion , usually denoted by the Greek letter phi , is the number Table of contents 1 Properties 2 Mathematical uses 3 Aesthetic uses 4 See also ... edit It is the unique positive real number with and the equally interesting property 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 equation with a b or the second equation with ( a b b ), both of these equations are seen to be equivalent to and hence The fact that a length is divided into two parts of lengths a and b which stand in the golden ratio is also (in older texts) expressed as "the length is cut in extreme and mean ratio". edit Geometry has two great treasures: one is the Theorem of Pythagoras ; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of

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