61. Sacred Geometry Searched for golden mean/Bodes Law, 0, 9/28/02 927 am, dwcooper11. golden Blossoms,Pi Flowers, 0, 9/26/02 714 pm, dwcooper11. Sacred geometry..Fractal links and http://p068.ezboard.com/finvisiblecollegefrm16

Fill out your e-mail address to receive our - Association Correlating Non-Essential Research- Newsletter Powered by YourMailinglistProvider.com Invisible College I > Sacred Geometry Invite Friends! Login Register Your Free Account Search Help ... Need help logging in? WE ARE THE INCUNABLISTS.. BEWARE OF YOUR PATH... THIS OFFER MAY BE NULL OR VOID AT ANYTIME.. NOT FEASIBLE IN CERTAIN STATES EXCEPT RHODE ISLAND..WE ARE THE ONGS HATTERS... WAL-MART IS EVIL...ROBERT CRUMB IS GOD..etc. The Edge... there is no honest way to explain it because the only people who really know where it is are the ones who have gone over Hunter S. Thompson 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~ I believe the future is only the past again, entered through another gate. Sir Arthur Wing Pinero 1 visitor in the last 15 minutes: Members - 1 Guest - Anonymous Topic Replies Last Comment Started By Dan Winter Reprints 9/20/03 12:27 am Geo-Egg 9/19/03 8:28 pm Phi Harmonics 9/18/03 10:14 pm Fractal Geometry 9/18/03 10:00 pm Spirals in Nature: The Magical Number behind Hurricanes 9/18/03 9:41 am Snow Crystal Photo Selection 3/13/03 9:55 am 12/8/02 10:33 am Entropy 11/7/02 10:22 am Pale Rider Searched for Golden Mean/Bodes Law 9/28/02 9:27 am Golden Blossoms, Pi Flowers

62. A Posse Ab Esse htm. The golden mean. http//www.floweroflife.org/spiral01.htm. ExperiencingSacred geometry without Intellectually Understanding It. http://groups.msn.com/Aposseabesse/goldenmean.msnw

var nEditorialCatId = 279; MSN Home My MSN Hotmail Shopping ... Money Web Search: document.write(''); Groups Groups Home My Groups Language ... Help A posse ab esse Aposseabesse@groups.msn.com What's New Join Now A posse ad esse Messages ... Tools The Golden Mean The Golden Mean is a ratio that is present in the growth patterns of many thingsthe spiral formed by a shell or the curve of a fern, for example. The Golden Mean or Golden Section was derived by the ancient Greeks. Like "pi", the number 1.618... is an irrational number. Both the ancient Greeks and the ancient Egyptians used the Golden Mean when designing their buildings and monuments. http://galaxy.cau.edu/tsmith/KW/golden.html 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

63. Kosmic Plenum Phi and geometry. http//www.dromo.com/fusionanomaly/goldenmean.html. http//home.att.net/~vmueller/prop/theo.html.golden Section or golden mean, Modulor, Square http://groups.msn.com/KosmicPlenum/thegoldenmean.msnw

var nEditorialCatId = 279; MSN Home My MSN Hotmail Shopping ... Money Web Search: document.write(''); Groups Groups Home My Groups Language ... Help Kosmic Plenum KosmicPlenum@groups.msn.com What's New Join Now The Kosmic Plenum Messages ... Tools The Golden Mean The Golden Mean is a ratio that is present in the growth patterns of many thingsthe spiral formed by a shell or the curve of a fern, for example. The Golden Mean or Golden Section was derived by the ancient Greeks. Like "pi", the number 1.618... is an irrational number. Both the ancient Greeks and the ancient Egyptians used the Golden Mean when designing their buildings and monuments. http://galaxy.cau.edu/tsmith/KW/golden.html 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

64. Sacred Geometry The design of TARA chapel is based on the laws of sacred geometry. It sstrongest components are harmony and the golden mean proportions. http://homepages.paradise.net.nz/rainersh/sacred_geometry.htm

Sacred Geometry at Tara Sanctuary (The ideas on this Web Page came from a paper called: "The Tara Chapel at Mana is based on Sacred Geometry of Bio Harmonic Architecture" written by the architect of Tara Sanctuary Reinhard Kanuka-Fuchs) The design of TARA chapel is based on the laws of sacred geometry. It's strongest components are harmony and the golden mean proportions. With it's purpose of practising unity in Meditation, Song, Dance and Prayer the harmonic proportions are essential. From the outside harmony is expressed in a multitude of equilateral triangles touching various important points of the building, connecting them. The unity principle can also be demonstrated by a series of concentric circles with the centre of gravity in the centre of the small "soul eye" windows above the annexes The centre of the chapel is a point of gravity, union and essence and it radiates symmetrically out in all directions touching annexes and octagon corners. In the same way bells radiate sound in all directions from the gravity centre of the bell framing. The law of the golden section as expressed in the beauty of the human form, can be seen in various aspects of nature. It is present in the harmonious properties of the human voice as brilliances appearing as high frequencies in the golden mean (Fibonacci) proportions of 3000, 5000, 8000 Hertz. Throughout the building the golden mean ratio of 1:1.618 can be found, pleasing to the eye and soul, our sense of harmony and beauty. It is creating a space of divine acoustics, where the sound seems to ascend. Drawing IV accentuates examples of the golden ratio in various parts of the chapel and bell tower.

65. THE FIBONACCI SEQUENCE, SPIRALS AND THE GOLDEN MEAN young Frenchman, scholar who is torn between his enjoyment of geometry and mathematics famousratio with a long and honored history; the golden mean of Euclid http://www.math.temple.edu/~reich/Fib/fibo.html

THE FIBONACCI SEQUENCE, SPIRALS AND THE GOLDEN MEAN The Fibonacci sequence exhibits a certain numerical pattern which originated as the answer to an exercise in the first ever high school algebra text. This pattern turned out to have an interest and importance far beyond what its creator imagined. It can be used to model or describe an amazing variety of phenomena, in mathematics and science, art and nature. The mathematical ideas the Fibonacci sequence leads to, such as the golden ratio, spirals and self- similar curves, have long been appreciated for their charm and beauty, but no one can really explain why they are echoed so clearly in the world of art and nature. The story began in Pisa, Italy in the year 1202. Leonardo Pisano Bigollo was a young man in his twenties, a member of an important trading family of Pisa. In his travels throughout the Middle East, he was captivated by the mathematical ideas that had come west from India through the Arabic countries. When he returned to Pisa he published these ideas in a book on mathematics called Liber Abaci , which became a landmark in Europe. Leonardo, who has since come to be known as

66. The Equiangular Spiral Spira Mirabilis the same geometry, though changed magnitude. The wonderful properties of thespiral are further enhanced by its connection to golden mean and Fibonacci http://online.redwoods.cc.ca.us/instruct/darnold/CalcProj/Sp98/GabeP/Spiral.htm

Gabriel Peterson The Equiangular Spiral: Spira Mirabilis Gabriel Peterson Math 50C: Multivariable Calculus Abstract The purpose of this article is to develop the parametric equation for the plane curve of the equiangular spiral – also known as the logarithmic spiral or the logistique – from its geometric definition. Through analysis, it was found to be where a is an arbitrary constant and a is a constant angle made between the radial vector to any point on the curve and the tangent line at that point. Introduction Most readers will have had at least some informal introduction to the elegant beauty of the spiral prior to reading this. Certainly, most will have witnessed the sublime geometry of a spiral in the vortex of water rushing down a drain, the tempest of a hurricane, the hypnotic pattern of a magician’s spiral, the shape of a snail’s shell, the inscrutable movement of the arms of a spiral galaxy like our own... The formal mathematical study of spirals – as did so many other rich intellectual traditions present today – began with the ancient Greeks. Building upon the work of Conon of Samos, Archimedes of Syracuse wrote a definitive early work on the subject in 250 BC entitled On Spirals.

67. THREE TABLES OF THE GRAIL The golden mean is based on the division of space by root rectangle derivatives,and it in terms of area instead of length was the basis of ancient geometry. http://freespace.virgin.net/peter.morley/lighter/a1-3tables.htm

Laurence Gardner. Bloodline of the Holy Grail APPENDIX I THREE TABLES OF THE GRAIL Tradition relates that "Three Tables bore the Grail; they were round, square and rectangular. Each had-the same perimeter, and the number of the Three was Two-One.' This ambiguous description of Tables has served to perpetuate the image of the Grail being an object, such as a cup or platter. The Tables have been likened to those of King Arthur, Grail Castle, and the Last Supper. However, the 2-1 specification is an inherent tabular proportion of the Golden Mean, and has little to do with tables in the utility sense. The Golden Mean is a geometric progression employed by the Greek mathematician, Euclid, in the 1st century BC. In practice, however, it dates back far beyond Euclid to the time of Plato. The Golden Mean has been used as an architectural standard for proportionment, and is used today in sophisticated artwork, framing and design. Roughly speaking, it is a proportion of 5:8, but the precise mathematical ratio is .618:1. The subject is fully covered in Nigel Pennick's Sacred Geometry ch2, pp 25-28.

68. "The Eye Of Horus/Ra" , "Sacred Geometry" And Pyramids - Unexplained - IN SEARCH 202 hold the key to Freemasonry in their Sacred geometry . were often designedand constructed according to the golden Section aka golden mean, to ensure http://istina.rin.ru/eng/ufo/text/290.html

Russian In search for truth : Unexplained Parapsychology and Magic Astrology :ž Unknown Earth :ž Ancient civilizations :ž Space exploration :ž Aliens ... :ž Forum Search Mail system 15Mb! @boxmail.biz [Register] Constructor Free Hosting Game server ... "The Eye of Horus/Ra" , "Sacred Geometry" and Pyramids "The Eye of Horus/Ra" , "Sacred Geometry" and Pyramids Known as the "udjat" or "wedjet" by the Ancient Egyptians, the eye was the emblem of the falcon-headed Horus [Ancestor of Kings and Sky God] and Ra [the Sun God and chief deity of the Ennead, the Gods of Heliopolis]. As Atum-Ra in the Ennead he was the Creator-God. The udjat, symbolising the Sun, was thought to protect the pharaoh [there is one at each corner of Tutankhamun's sarcophagus], and was used as an amulet against evil. But there is more to this emblem "than meets the eye" [pardon the pun!] Question:- what do a) Ray Brown's crystal [described in "carib"], b) the reverse of the Seal of the USA, and c) St Piran's Church, Perranzabuloe, Cornwall, have in common? Answer:- they all feature the "all-seeing eyes" of an omnipotent deity. Although, the third image is early Medieval its features bear an uncanny resemblence to the giant Olmec heads in Mexico! Images a) and b) feature pyramids, and I said in "carib" that the three in the crystal were linked to Giza. Pyramids, traditionally, are said to represent solar rays, seen by the Egyptians as the source of light and fertility. In the Armarna art of Akhenaton and Tutankhamun [possibly father and son], they protectively touch these pharaohs and their queens in a triangular formation. Maurice Cotterell in The Tutankhamun Prophecies [London, 1999] makes an interesting link between statues of those kings and pyramid design. If their navels represent the apex, he argues, then the eye on the capstone of the "solar-eye pyramid" [such as the one on the Seal], is Ra's. The pyramid-shaped skirts worn by the kings are decorated with solar rays, hence the most common interpretation of those structures. One example of a capstone bearing the udjat-eye [plus invocations to Ra] was once on the Pyramid of Ammenemes III, Dahshur.

69. Links mathematics Pythagoras` constant, golden mean, Natural logaritmic base e, Archimedesconstant Pi, EulerMascheroni constant Sacred geometry Home Page. http://milan.milanovic.org/math/links/links.html

Link Page PASCAL TRIANGLE Links: Pascal Triangle This Java applet graphically presents the Pascal triangle modulo an integer number p. Developed by Sergey Butkievich, Department of Mathematics, The Ohio State University ... Math Forum web pages on Pascal`s triangle Probably the best place to find out all about Pascal`s triangle ... Pascal`s Triangle and related triangles Contens: Links, Puzzles, Related Triangles, Clown Problem ( Catalan Numbers ), Tchebychev Polynomials, Bessel Polynomials, Stirling numbers ... KryssTal: Pascal`s Triangle Pascal`s Triangle and its uses in probability. The Binomial Theorem used for algebraic expansions and finding roots ... Pascal`s Triangle Image Generator Generate nice pictures with Pascal`s triangle ... Chinese Mathematics: Binomial Theorem and the Pascal Triangle So called ` Pascal ` triangle was known in China as early as 1261. In 1261 the triangle appears to a depth of six in Yang Hui and to a depth of eight in Zhu Shijiei in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in ... New Theory on the Typographical Roots of the Hindu Arabic Numbers and Brahmi Scripts The Hindu Arabic numbering is named for Hindus who appear to have invented it, and the Arabs who transmitted it to the West.The Hindu Arabic 1-2-3-4 numbers are based traces with angles: The number one has one angle.The number two has twoadditives angles. The number three has three aditives angles.The number four has four additive angles. The number four get closed due to cursive hand write....

70. Geoman Text adds two of the three fundamental polygonal shapes in plane geometry, the equilateraltriangle, and the pentagram, both in the golden mean relationship to the http://www.geoman.com/geomantext.html

G E O M A N A T O M Y James L. Fournier The new Vitruvian Man I discovered, which I have called Geoman, adds two of the three fundamental polygonal shapes in plane geometry, the equilateral triangle, and the pentagram, both in the golden mean relationship to the same circle represented with the square in Leonardo daVinci's Vitruvian Man. In Leonardo's drawing there are two of the four simplest shapes in plane geometry. These are the circle representing unity, or one, and the square representing four. I had noticed that the relationship between the circle and the square in Leonardo's drawing is the golden mean ratio. Thus the length of one side of the square is 1.618 times the radius of the circle. I found this by measuring Leonardo's drawing, but D'Arcy Thompson had also demonstrated by statistical analysis that on average the distance from the ground to a person's navel is the golden mean of their overall height. I also knew that the navel, our center, the center that we grow from, is also our center of mass, the point which we would spin about weightless in space, which is also the center that we find when we meditate and find our "center" (yellow in the diagram). Each of the three shapes shares the same edge length as the square, and thus each is in the golden mean relationship to the radius of the circle. The key to the success of the diagram is that the tip of the equilateral triangle protrudes through the base of the square, counter to the medieval teaching that the arm span is equal to the diagonal to the feet. Instead, the two points where the triangle meets the ground represent the centers of the feet, and the tip of the triangle represents the pointed toes as if in a pirouette.

71. Loving Unified Field Geometry - Mountain Man's UseNet Archive looks like Betsy Ross s pent stars within stars, created by 10 golden mean spiralsin a pent nest circle. (Top down view DNA). Waves in this geometry can add http://www.mountainman.com.au/news96_2.html

Mountain Man's UseNet Archive Loving Unified Field Geometry for Softies by Dan Winter Web Publication by Mountain Man Graphics, Australia in the Southern Summer of 1995 Loving Unified Field Geometry for Softies by Dan Winter Date: 3 Jan 1996 From: Dan Winter To: sci.physics Subject: Quanta and Consciousness The Heart, Fractals and the Universe >> The quanta of consciousness is recursion.. >> as is the branching, the quantum collapse to center >> called gravity occurs only in the presence of >> fractal pattern compression, optimized by golden mean/phi >> (idealized translation vorticity).. >> fractality defines/limits spin density/ mass >> awareness-distributed as spin-onsets with recursion in harmonic >> system, dodeca(dna/earthgrid/zodiac) permits cross scalar >> info transfer in as above/so below, pressure fractal.. >> if time is spin measured and the time spiral is fractal(mayan), >> then when does it become self aware? "You Couldn't Get a Better Squeeze".. Loving Unified Field Geometry for Softies. by Dan Winter 12/24/95 On the side of the box containing a well designed crank operated Tomato Juicer, is printed the motto of today's inspiration: "You Couldn't Get a Better Squeeze". The news for preservers of sweet memories is juicy. Properly applied pressure, sorts waves into preserveable order. The key operating component of the Tomato juicer is a human operated turning spiral helix engraved on a cone vortex. What emerges from the apex of the cone in the shade of living blood, is a harvest of sweetness.

72. BRUCE RAWLES FAVORITE SACRED GEOMETRY (& OTHER) LINKS The geometry Junkyard Steven FInch of Mathsoft s page on The golden mean TheDivine Proportion Robert Conroy Structural Elements of Nature and their http://www.intent.com/bruce/links.html

Links to Sacred Geometry and related sites Source Books and it's relation to the golden ratio and much more! Jonathan Quintin's Sacred Geometry website Michael S. Schneider - author of a MARVELOUS book on sacred geometry, A Beginner's Guide to Constructing the Universe - The Mathematical Archetypes of Nature, Art, and Science - A Voyage from 1 to 10 David Fideler - The Pythagorean Sourcebook and Library The School of Pythagoras ... John Boyd-Brent - The Circle and the Square and the Square Root of Two Links to mathematical sites VRML Polyhedra models with Shockwave - a marvelous and extensive site!!! more wonderful live Polyhedra (zonohedra) animations some wonderful POV-Ray ray tracing polyhedra models ; here is a sample showing a small stellated dodecahedron Poly is a fabulous 3D app that rotates polyhedra in real time, and simultaneously morphs from 2d net (foldup pattern) to folded 3D shape; lots of polyhedra! A must see! Fractal Explorer The Geometry Center has a wealth of interesting info; my favorite interactive application is... ...QuasiTiler 3.0 (from The Geometry Center) ; try changing the "Dimension = " parameter under "Generating Plane") The Geometry Junkyard Steven FInch of Mathsoft's page on The Golden Mean The Divine Proportion Robert Conroy - Structural Elements of Nature and their compounds the Platonic and Archimedean solids ... Fibonacci Numbers and Nature : an excellent tutorial on Fibonacci numbers with nice animations Jim Plank - Origami Page (Modular) Gerald de Jong - Portfolio (geometrical wire frames from expandable/compressable members which dynamically readjust as they are stretched or compressed) Anders Sandberg - Platonic Solids and Their Symmetries Some Random Thoughts about the Occult Correspondences of the Platonic Solids and Their Symmetries mathematicians: Pythagoras ... World of Escher - Recreational Mathematics - Roger Penrose target=new

73. Sacred Geometry Home Page mineral intelligence embodied within crystalline structures follows a geometry unfalteringin ratio (aka phi ratio aka sacred cut aka golden mean aka divine http://www.intent.com/sg/

Sacred Geometry Home Page by Bruce Rawles In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. These inevitably follow geometrical archetypes, which reveal to us the nature of each form and its vibrational resonances. They are also symbolic of the underlying metaphysical principle of the inseparable relationship of the part to the whole. It is this principle of oneness underlying all geometry that permeates the architecture of all form in its myriad diversity. This principle of interconnectedness, inseparability and union provides us with a continuous reminder of our relationship to the whole, a blueprint for the mind to the sacred foundation of all things created. The Sphere (charcoal sketch of a sphere by Nancy Rawles) Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. There is no point of view given greater or lesser importance, and all points on the surface are equally accessible and regarded by the center from which all originate. Atoms, cells, seeds, planets, and globular star systems all echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm. The Circle The circle is a two-dimensional shadow of the sphere which is regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. All other symbols and geometries reflect various aspects of the profound and consummate perfection of the circle, sphere and other higher dimensional forms of these we might imagine.

74. SAPAAN: Vol. 1 Spring 2003 - Hidden Geometry In Music Of Bach And Schoenberg: By architectural and geometric proportions of these works illuminating a consistentuse of arithmetic, geometric, harmonic, and golden mean proportions amid these http://www.sapaan.com/vol1/saggau.htm

Home About SAPAAN Archives Submissions ... Contact Us SAPAAN Vol.1 Spring 2003 Hidden Geometry in Music of Bach and Schoenberg: Reflection, Rotation, Proportion Jonathan Saggau Abstract 1. Bach 1.1 Architectural Proportions. The first iteration of the nadir pitch C2 at time point 117 is at the golden section of the movement. The Apex of section A is at its golden mean. Pitch Bb3 at time point 24 of section A is at the golden mean of local apexes at time points 14 and 30; the same Bb3 also bisects section A. Pitch C2 at the nadir of section B is at the geometric mean at time point 69 (time points in this case counted without the repeats) of time points 48 and 96 quarter notes. (sqr. ~69) x 96 48 Pitch E2 at the nadir of section A is at the geometric mean at time point 69 (repeat included) of time points 48 and 96. Notice that the geometric mean proportions meet at the midpoint of the piece. Local apex D4 at time point 15 of section A bisects the onset and apex (time point 30) of section A.

75. 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.

76. The Math Forum - Math Library - Golden Ratio/Fibonacci Great Pyramid. It can also be called the Great golden Pyramid, becauseits geometry is that of the golden mean. Pictures and diagrams http://mathforum.org/library/topics/golden_ratio/

Browse and Search the Library Home Math Topics Arithmetic/Early Number Sense/About Numbers : Golden Ratio/Fibonacci Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Fibonacci Numbers and the Golden Section - Ron Knott Information about the Fibonacci series, including a brief biography of Fibonacci, the numerical properties of the series, and the ways it is manifested in nature. Fibonacci numbers are closely related to the golden ratio (also known as the golden mean, golden number, golden section) and golden string. Includes: geometric applications of the golden ratio; Fibonacci puzzles; the Fibonacci rabbit binary sequence; the golden section in art, architecture, and music; using Fibonacci bases to represent integers; Fibonacci Forgeries (or "Fibonacci Fibs"); Lucas Numbers; a list of Fibonacci and Phi Formulae; references; and ways to use Fibonacci numbers to calculate the golden ratio. more>> The Fibonacci Series - Matt Anderson, Jeffrey Frazier, and Kris Popendorf; ThinkQuest 1999 more>> Aesthetics, dynamic symmetry, equations, the Divine Proportion, the Fibonacci sequence, the Golden rectangle, logarithmic spirals, formulas, links to other MathSoft pages mentioning the Golden Mean, and print references. Also available as MathML more>> Golden Ratio, Fibonacci Sequence - Math Forum, Ask Dr. Math FAQ

77. Human Form From Sacred Geometry Pyramid in Cairo, Egypt embodies the golden mean which is the ratio that is usedin Nature to generate growth patterns in space. Sacred geometry studies such http://saturn.vcu.edu/~chenry/

SACRED GEOMETRY New Discoveries Linking The Great Pyramid to the Human Form Professor, Department of Sculpture Virginia Commonwealth University Richmond, Virginia This site is best viewed on Microsoft Internet Explorer 4.0 or higher with screen set to 1024 X 768 pixels, 24 bit ...16 million colors. Set ... View/Text Size ... to Meduim Click on thumbnails to view larger images. For more than twenty years, I have been studying the image generating properties of reflective spheres stacked in 52 degree angle pyramids. The 52 (51.827) degree angle slope of the sides of The Great Pyramid in Cairo, Egypt embodies the Golden Mean which is the ratio that is used in Nature to generate growth patterns in space. Sacred Geometry studies such primal systems which reveal the unity of the cosmos by representing the relationships between numbers geometrically. The Vesica Piscis is one of the most fundamental geometrical forms of this ancient discipline and it reveals the relationship between the The Great Pyramid and the 2 dimensional expansion of a circle of one unit radius R as shown in Figure 1. This relationship is more completely described in The New View Over Atlantis by John Michell published by Thames and Hudson. Figure 1 Vesica Piscis in 2 Dimensions In the early 1970s, I became very interested in the three dimensional representation of this geometry and I visualized this as a three dimensional pyramid inside two intersecting spheres shown in Figure 2.

78. Sacred Geometry Rome. Sacred geometry. Phi is the golden ratio (proportio divina or sectio aurea),also called the golden mean, golden section, golden number or divine proportion http://www.mcuniverse.com/Sacred_Geometry.1313.0.html

Angels Assorted Ideas Dolls Holiday Crafts ... Rome Sacred Geometry Phi and the Fibonacci Sequence feature prominently in the book are are first mentioned in Chapter 8 and then in more detail in Chapter 11. Phi Phi is 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 read more about this in Wikpedia's entry about Phi The Fibonacci Number The Fibonacci Sequence is 0-1-1-2-3-5-8-13-21 and is achieved by starting with and 1, and then adding the two previous numbers. Read more about this in Wikpedia's entry about the Fibonacci Sequence More Sacred Geometry Links The Golden Number Net provides extensive information and examples of Phi and the Fibonacci sequence. Ellie Crystal's site also has a big section on sacred geometry Books about Sacred Geometry The Golden Ratio : The Story of PHI, the World's Most Astonishing Number Assorted books about Sacred Geometry Assorted books about the Fibonacci Numbers Newsletter ... To Top Page updated: Thursday, April 22, 2004 Home Crafts Graphic Design Marlies ... Resources

79. Sacred Geometry Exercise-Nautilus Shell Spiral The nautilus shell spiral is a logarithmic spiral similar to other spirals suchas the golden mean or phi spiral, but with slightly different proportions. http://www.sacredarch.com/sacred_geo_exer_shell.htm

The Nautilus Shell Spiral Sunflower Mandala Snowflake Pattern Six-Around-One The shell of the chambered nautilus is a symbol of beauty and proportional perfection. In this exercise you will experience the essence and energy of the spiral displayed in the unfolding of the nautilus shell. The proportion of this nautilus shell is consistent through all of the relationships of the shell, so once you discover the secret ratio, you will see clearly why this particular gem of nature is such a treasure. The nautilus shell spiral is a logarithmic spiral similar to other spirals such as the Golden Mean or phi spiral, but with slightly different proportions. A close approximation of a Golden Mean spiral, based on the Fibonacci whole number sequence is illustrated below. The spiral of the chambered nautilus as well as other logarithmic spirals can be found throughout the human body and nature. The drawing of the inner ear and the photo image of a star cluster nebula shown to the right are just two examples which can be seen with a microscope or a telescope. There are many examples which can be seen without magnification. See what you can find. This beautiful spiral can be easily drawn on a piece of grid paper with a pencil. Refer to the drawings below as you work.

80. Crop Circles And Sacred Geometry twelve retainers. It is also a common symbol in Islamic geometry, and its of greatfascination to ancient and modern geometers is the golden mean since it http://www.lovely.clara.net/crop_circles_sacredgeo2.html

CONNECTING SACRED GEOMETRY AND CROP CIRCLES It is significant that as our alienation from all forms of spiritual and universal wonder increases, symbols bearing the hallmarks of an ancient, harmonious philosophy have suddenly begun manifesting in cereal crop. Even to the hardened skeptic crop circle designs reveal a facility by their makers of creating a visual harmony that is pleasing to the eye, much like an ancient temple or a classical painting. The proportions are balanced, the shapes rhythmic, their outlying elements forming part of an unseen whole. Upon close scrutiny even the small 'grapeshot' circles that flank certain formations lie at their given remote locations not by fluke but by engineered and premeditated design, markers and clues for the observer to follow and uncover. Not surprising, then, to find sacred geometry lying at the heart of the fundamental blueprints of many formations, sometimes blatantly, sometimes veiled like a secret waiting to be uncovered only by the most persistent of minds. But just as with sacred geometry and other esoteric principles, crop circles have been marginalized by practically the entire scientific community since they challenge the current worldview simply because science is at odds to explain them.

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