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

1. 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.
The Great Pyramid
has Golden Geometry of the Golden Mean
What does it look like ? What are its Purposes
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.

2. 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.
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, ...

3. Lee Dickey's Geometry Corner
is interesting. It was discovered by Gabries Bosia. Find out more aboutconstructions for the golden mean geometry. I am interested
Geometry Corner
Three-Four-Five Triangle and the Golden Mean
The figure above, (click on it to see a larger version) shows how one may use the famous three-four-five triangle inscribed in a circle to construct the Golden Ratio. Of course this is not the most efficient construction in terms of the number of steps required, but it is interesting. It was discovered by Gabries Bosia. Find out more about constructions for the golden mean
I am interested in Geometry, including finite geometric structures, like finite projective planes and finite hyperbolic planes. Here are some very nice geometrical things.

4. The Golden Section - The Number And Its Geometry
Simple definitions; exact value and first 2000 decimal places; finding the golden section; continued Category Science Math Recreations Specific Numbers phi...... 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.
The Golden section ratio: Phi
Contents of this Page
The line means there is a Things to do investigation at the end of the section. What is the Golden Ratio (or Phi)? A simple definition of Phi
A bit of history...
Links on Euclid and his "Elements" ... More
What is the golden section (or Phi)?
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.
A simple definition of Phi
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: Phi = Phi + 1 In fact, there are

5. The Golden MeanThe Golden Mean The Golden Mean Is A Ratio That Is Present In The
Author and mathematics expert provides some historic details about Phi and the golden Ratio. Includes graphical examples and recommended resources. The golden mean. The golden mean (or golden Section), represented by the Greek letter phi, is one of high degree of precision. geometry. If you have a rectangle whose sides

6. Flower Of Life - The Golden Mean Spiral And The Merkaba - Article By Ronald L. H
THE NATURAL WORLD The golden mean The golden mean, or golden Ratio as it is known, is a transcendental (or irrational) number jut like other numbers such as Pi.
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

7. The Archdome - Golden Mean Design
geometry and the Archdome. The Archdome is built using sacred geometric proportion, better known as the golden mean
T he A rchdome™ • The Golden Mean
“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.

8. Abstract Art By Astrid Fitzgerald Based On The Golden Mean Proportions.
Abstract art by Astrid Fitzgerald based on sacred geometry and the golden mean Proportions
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 100 works of art. Site includes artist's statement, biography, reviews, current exhibitions, books, interviews, articles, links to philosophical geometry and contact information. PAINTINGS CONSTRUCTIONS WORKS ON PAPER PRINTS ... CONTACT / LINKS Please bookmark this site and return frequently for up-dates.
All works shown on 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.

9. Fibonacci Numbers, The Golden Section And The Golden String
Fibonacci numbers and the golden section in nature, art, geometry, architecture, music, geometry Category Science Math Specific Numbers Fibonacci Numbers...... The golden Section the Number and Its geometry The golden section is alsocalled the golden ratio, the golden mean and the divine proportion.
Fibonacci Numbers and the Golden Section
This is the Home page for Ron Knott's Surrey University web site on the Fibonacci numbers, the Golden section and the Golden string. The Fibonacci numbers are add the last two to get the next The golden section numbers are The golden string is
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 Numbers the Golden Section and the Golden String
together with their many applications What's New?
10 February 2003
Fibonacci Numbers and Golden sections in Nature
Fibonacci Numbers and Nature
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.

10. Sacred Geometry
Sacred Geometry
Everything in the universe follows the same blueprint or patterns of created by geometric designs that repeat over and over in an endless dance of sound, light and color. They are a matrix of grid energy created from a central source - which creates the reality in which we experience. At the physical level of conscious souls attach through electromagnetic energy grids which create the the illusion of space and time and allow us to experience duality, emotions, linear time. As all things are linked back to one creational source - through a web of sorts - myriad of grid energies - all of creational follows the same creational design - the Flower of Life of our Creation - The Tree of Life Sacred geometry is based on specific patterns - platonic solids. (See references below). If you examine the history of humanity you will see come to realize that everything is part of specific patterning. Stories of the creation of humanity all follow the same patterns. We move in cycles - the wheel of karma - the illusion of linear time - all crated by the same patterns of geometry. These patterns were once understood and taught by the ancient mystery school teachings - Initiations - then became lost in 'time' - to be rediscovered as we evolve as a soul group into higher consciousness awareness at this time. SACRED GEOMETRY AND THE GREAT PYRAMID
Linking The Great Pyramid to the Human Form
Charles Henry The Great Pyramid, The Golden Ratio and The Royal Cubit

11. Goddess Nut And Creation
It is creation based on sacred geometry. In the center of the image - womb - creation- is the golden mean Spiral that has been part of my research this week
Goddess Nut - Nuit The Phi Ratio - Spirals of Energy - Time
Nut - Nuit - Creational Goddess Metaphoric Creational Stories based on Sacred Geometry Saturday morning I woke up with this image in my mind- Creational 'blue' energies of me in a past/ parallel regression
Note - arm wearing a wrist watch over my mouth
Time - I am Time Traveling!
Something was tugging at my soul. The large 'cloud-like' image that seems to surround and protect me - focused in my mind as I lay there wondering what it was all about. Suddenly it was clear! The image represented an Egyptian goddess - but I couldn't remember her name. I saw her as a creational force - surrounding and protecting everything with her body. I ran to the computer and looked in my archived images of Egyptian goddesses images. There she was . . . Her name is Nut! Curious about her . . . I began to research knowing I would find many synchronicities . . . As I have recetly returned from a journey to Egypt - I realize that the sacred areas of Egypt - especially the Giza platueau are set up based on creational myths. When you visit these areas they initiate you to their truer meaning - the geometry of creation - so that you may move more easily into higher frequency. You are litterly in the creational energies of our reality.

12. 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
from T he
Phi Nest™ Home
Phi for Neo'phi'tes

Fibonacci Series

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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.) Phin 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+1) , or Note: The construction of phi with concentric circles was developed by Sam Kutler and submitted by Steve Lautizar.

13. C. Gilchrist: Sacred Geometry: Mandalas: "The Golden Mean Rectangle And The Phi
societies. Those initiates were most intimately aware of Sacred Geometryand its archetypes, including the golden mean reality. Many
Charles Gilchrist Mandalas
Gallery 11
The Golden Mean Rectangle and The Phi Ratio
The Golden Mean Rectangle and The Phi Ratio
An Interview With The Artist - Number 11
By Leslie Page
L.P. "Tape running, here we are again, Charles, continuing our ongoing conversation on Sacred Geometry and all the unbelievable connections it has to our everyday lives. I'm amazed, Charles, I truly am. This is our eleventh tape and I promised you our subject would be your choice this time. What are we going to talk about today?"
C.G. "Thank you, Leslie. Generally, when I take on a really bright student, like yourself, I begin by letting them ask the questions that first come to their minds. It seems to work pretty well. And so far we have been doing just that, but this is, as you just mentioned, our eleventh conversation and it feels pretty special to me."
L.P. "Really? In what way?"
C.G. "It's the number, Leslie. At least that's part of it."
L.P. "Of course..... numerology. One of our first conversations was about esoteric numerology, remember?" C.G. "Yes, very vividly. You have a natural affinity with mathematics, Leslie, in all its forms, which gives you an edge in this study. Eleven is a very special number; the first master number."

14. LycosZone Directory > Homework > Math > Geometry And Trigonometry > Golden Mean
What kind of golden mean Websites are you looking for? known as the golden ratioor golden section.This or you can Check out other geometry and Trigonometry and Trigonometry/Golden Mean
Search For: Lycos Zone Home Family Zone Teachers Zone What kind of Golden Mean Websites are you looking for? The Pentagram and the Golden Ratio "The 'ratio' has become known as the golden ratio or golden section.This ratio can be found in many places: in art, architecture, and mathematics"
Grade Level: 9-12
Check out other "Geometry and Trigonometry" Web Pages!
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15. The Golden Mean
Explains the theory behind the golden mean and how it can be constructed out of the Fibonacci series.Category Science Math Recreations Specific Numbers phi...... is Sacred geometry Philosophy and Practice by Robert Lawlor, published by Crossroad;Library of Congress number 8167703. This entire 'golden mean' site is
The Golden Mean
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.
The decimal representation of phi is 1.6180339887499... . You can find it in a number of places:

Number Series
If you start with the numbers and 1, and make a list in which each new number is the sum of the previous two, you get a list like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... to infinity>
This is called a 'Fibonacci series'.
If you then take the ratio of any two sequential numbers in this series, you'll find that it falls into an increasingly narrow range: 1/0 = Whoa! That one doesn't count.
and so on, with each addition coming ever closer to multiplying by some as-yet-undetermined number.

16. Flower Of Life - The Golden Mean Spiral And The Merkaba - Article By Ronald L. H
Sacred geometry is the study of geometric forms and their metaphorical geometric configurations)around the body will activate the golden mean Spiral that aids
(page 2)
A Little Philosophy on Sacred Geometry
Anybody can draw a form in geometry and it is just geometry; but when you relate Great Spirit or consciousness and the opening of the heart to geometry, you're creating Sacred Geometry . Therefore, Sacred Geometry is about how to open the heart and evolve the consciousness through geometric models. These models mirror your own consciousness. First cause sacred geometry is made out of light/consciousness. When you see how geometries fluidly transition into each other, you will see how they keep transcending and moving into a higher evolving pattern. When you understand that, you can then relate sacred geometry to the heart. And the spiral is the most important key. Sacred geometry is the study of geometric forms and their metaphorical relationships to human evolution as well as a study in fluid evolutionary transitions of mind, emotions, spirit, and consciousness reflected in the succeeding transition from one sacred geometric form (consciousness state) into another True sacred geometric forms never fixate or stagnate on one single form. Instead they are actually in constant fluid transcendence and change (evolve or devolve) from one geometric form to another at their own speed or frequency.

17. Chapter 15, Golden Mean 8
Divine Section. . 136. Yet the immediate use of the golden mean in geometry,during Plato's time. was even more remarkable. The Section
Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell)
The second half of the 5th century B.C. was the Golden Age of Greece. This was the period of her most beautiful art and architecture, and some of her wisest thinkers besides. Both owed much to the popular new study of geometry. By the start of the next century, geometry itself was entering its own classic age with a series of great developments, including the Golden Mean. The times were glorious in many ways. The Persian invaders had been driven out of Hellas forever, and Pericles was rebuilding Athens into the most beautiful city in the world. At his invitation, Greek mathematicians from elsewhere flocked into the new capital. From Ionia came Anaxa- goras, nicknamed "the mind." From southern Italy and Sicily came learned Pythagoreans and the noted Zeno of Elea. And their influence was felt over all Athens. High on the hill of the Acropolis rose new marble temples and bronze and painted statues. Crowds thronged the vast new open-air theater nearby, to hear immortal tragedies and comedies by the greatest Greek playwrights. These splendid public works were completed under the direction of the sculptor Phidias and several architects, all of whom knew and used the principles of geometry and optics. "Success in art," they insisted, "is achieved by meticulous accuracy in a multitude of mathematical proportions." And their buildings had a dazzling perfection never seen before-the beauty of calculated geometric harmony.

Mid_Atlantic Geomancy Sacred geometry Page A very nice simple account of some of TheMathematics of the golden mean A mathematical account of the golden Section
Greek Science and The Golden Section
Ancient Science and Mathematics
Selections from Julia E. Diggins, String, Straightedge, and Shadow Viking Press, New York , 1965. (Illustrations by Corydon Bell) Chapters 8, 9: Thales
Chapters 11, 12: Pythagoras and his Theorem

Chapter 13: Platonic Solids

Chapter 14: The Irrationals
... History of Mathematics Home Page
The Golden Section
The Golden Mean
An extensive site on the Golden Section in architecture and art. Lots of diagrams and links. A good place to start. The Golden Section in Art and Architecture
Jill Britton’s excellent slide show introduction to the Golden Mean. Fibonacci Numbers and The Golden Section
One of the best and most extensive sites I’ve found. Ron Knott's Surrey University Site The Golden Proportion
Examples of the proportion in nature, art, and architecture.
Sacred Geometry Home Page

A more general account of the relationship of geometric form to beauty. The page is very well done and gives a good idea of the Neoplatonic view of form and beauty. Mid_Atlantic Geomancy Sacred Geometry Page
A very nice simple account of some of the most persistent mathematical forms in Art and Nature. Nice Images!!

19. Excerpts From The Golden Mean Book And Calipher Set
Like geometry itself, the golden mean Calipers begin with the vesicapiscissacred symbol of the creative act. The vesica piscis
Click on the hot links at the bottom of the page to see other products manufactured by Now and Zen
The Golden Mean Book and Caliper Set by Now and Zen
Tools to Increase Spiritual Perception
Overview The Golden Mean is a way of looking at the world. It is a special relationship between a part and a whole that acts as a formula for harmony and beauty. Working with the Golden Mean is an ancient form of spiritual practice. Awareness of the Golden Mean's significance has been instrumental in the acceleration of culture throughout history and is now contributing to the emergence of a spiritual renaissance art movement. The Golden Mean Book and Caliper Set provide the knowledge and experience of this special relationship that will allow you to possess its power. This book describes the profound spiritual significance of the Golden Mean as well as the myriad ways it appears in the natural universe and in human culture. The Calipers promote an intuitive awareness of the Golden Mean relationshipthey serve as both a practical tool for adding harmony to your creations, as well as a symbol of visual philosophy. Contents 1. Introduction to the Golden Mean

that the golden mean, which is mathmaticaly idealized recursion, produces self awarenessamong any resonating wave system is that only this geometry produces
small wonder they call perfect onset predictability in the stock market, the HOLY GRAIL of market analysis. Golden Mean PHI recursion is the only resonance path out of chaos, it's onset shows onset of EMOTIONAL COHERENCE, and then you look at the picture of its geometry: (spin path of 3D Golden Mean spiral down a 60 degree light cone into fractal 3D dodeca/icos)
it IS the grail.. don't give up until you drink from the silver cup of sweet braid golden fleece piezoelectric geometry of song in the blood (sang graal) cup within cup, never overflows .. data infinitely compressible with no memory loss.. SPRING 96 from dan winter back to: Dan Winter, Home Page: Contents Directory
When Chrisopher Carolan found in"Spiral Calender", time's spiral at square root of Golden Mean

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