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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

81. 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.

82. 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....

83. Mathcad Library: Constants
Press, 1987. K. Wiedman, The golden mean, part of Rashomon's Home Page.CS Ogilvy, Excursions in geometry, Dover, 1969. G. Markowsky
http://www.mathcad.com/library/Constants/goldrefs.htm
Well-Known Constants
Pythagoras'
Golden mean

Natural log

Archimedes'
... Home by Steven Finch Mathsoft Engineering and Education, Inc.
References for The Golden Mean
  • 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.
  • M. Boles, The Golden Relationship: Art, Math, Nature , 2nd ed., Pythagorean Press, 1987.
  • K. Wiedman, The Golden Mean , part of Rashomon's Home Page
  • C. S. Ogilvy, Excursions in Geometry , Dover, 1969.
  • G. Markowsky, Misconceptions about the Golden ratio, The College Math. J.
  • R. Knott, Fibonacci Numbers and the Golden Section (Surrey University).
  • Fibonacci Quarterly (virtually any issue).
  • 84. Sacred Geometry
    golden mean. The science of sacred geometry includes study of the Platonicsolids, numbers, and the golden mean ratio.. This is all
    http://www.inthelight.co.nz/spirit/research/Sacred Geometry/sacredgeometry.htm
    Sacred Geometry Page
    Details on this page is an extraction of some of the more interesting facts that have made an impression on me. See links for further research. PI The circumference of a circle is p (pi) times the diameter of the circle, where pi is approximately 3 1/7 (or 22/7 - these sacred numbers turn up frequently in Hindu texts and Rosicrucian literature), or 3.14, or about square root of 10. The value of pi is an irrational number, and pi to 39 decimal places is sufficient accuracy to calculate the circumference of the universe to within the radius of the hydrogen atom! Here it is to 100 decimal places (see here for 5000 decimal places):
    In Vedic Mathematics, Swami Sri Bharati Krsna Tirthaji Majaraja shows the vedic numeric code, and how a hymn in praise of the Lord Shri Krishna, the Lord Shri Shankara, is also the value of p /10 to 32 decimal places (and apparently a key to calculate it to any number of decimal place, which I do not know) - the Sanskrit is shown above, which you can decode in to syllables and the decoding key below. 1 ka, ta, pa, ya

    85. A Little Geometry
    Some golden geometry. Here are instructions for constructing the golden Rectangle,a rectangle whose sides measure 1 and 1.618 Construct a square.
    http://galaxy.cau.edu/tsmith/KW/goldengeom.html

    86. The 'Phi-Nest': Source To The Golden Section, Golden Mean, Divine Proportion, Fi
    Information on the golden Section, Divine Proportion, Fibonacci series and phi.Category Science Math Recreations Specific Numbers phi......F Phi - The golden Number - Ø A source to some of Net's phi-nest informationon the golden Section / mean / Proportion / Ratio / Number, Divine Proportion
    http://goldennumber.net/
    The
    Golden
    Number
    from T he
    Phi Nest™ Home
    Phi for Neo'phi'tes

    Fibonacci Series

    Golden Sectio
    ...
    Links

    Affiliates helping
    support this site: Save on purchases Earn on hosting Stock Market Investor Resources
    Phi: The Golden Number
    Dedicated to providing you with the p hi n est™ information on:
    The Golden Section , Ratio or Mean
    The Divine Proportion
    The Fibonacci Series
    and . . . Phi (
    Sites advancing the use of the golden section M athematical Connections in Nature, Science and Art An essay presented by the Rethinker's Movement Phi: The number 1.6180339887... Nest: A place providing secure lodging and development Phi Nest ™: A place providing secure lodging and development for insights into the pervasive appearance of Phi in life and the universe. Welcome, Bienvenue, Willkommen, Recepción, Benvenuto! Translate this site to your language of choice. Phi - The Golden Number A source to some of Net's "phi-nest" information on the Golden Section / Mean / Proportion / Ratio / Number, Divine Proportion, Fibonacci Series and Phi (1.6180339887...)

    87. Mathsoft: Well-known Constants: The Golden Mean, φ
    The golden mean, f. The most “aesthetically perfect” rectangle is picturedhere is. a constant which is called the golden mean or Divine proportion.
    http://www.mathsoft.com/mathresources/constants/wellknown/article/0,,1941,00.htm
    search site map about us  + news  + ... Feigenbaum Constants The Golden Mean, Natural Logarithmic Base, e Number Theory Constants Analytic Inequalities Discrete Structures ... Math Resources The Golden Mean,
    If the left-hand portion is of length u = 1, then the right-hand portion is of length v u , as drawn, is to the whole length u v , as the length v is to u . In symbols,
    u v
    The positive root of the resulting quadratic equation
    is
    a constant which is called the Golden mean or Divine proportion.
    The Fibonacci's Sequence
    We claim that the Golden mean is intricately related to Fibonacci's sequence:
    which can be used to model population growth.
    Continued Fraction
    f n
    All of the resulting fractions are ratios of successive Fibonacci numbers! This motivates the theorem that:
    In words, as n approaches infinity, the limit of the sequence of successive Fibonacci number ratios is the Golden mean.
    Nested Rectangles
    The length and width of the nth Golden rectangle can be written as linear expressions a b Logarithmic spirals are found throughout nature, for example, the shell of a chambered nautilus, the tusks of an elephant and patterns in sunflowers and pine cones. The Mathcad file logspira.mcd discusses how we obtained the diagram presented earlier and further topics.

    88. Sacred Geometry Of Sekhmet
    Swing the compass downward to see it cross the original line at its golden meanbalance. Upper circle will be Sekhmet's Celestial orb. 1. geometry showing the
    http://www.sangraal.com/sekhmet/sacredart/geometry.html
    Drawing the Face of the Goddess Sekhmet using the Geometry of the Square Root of Five and Phi ø by Lady Sekhmet I spent most of 1996 and 1997 working on recreating illustrations for a book on the physics of consciousness. It promised to be a remarkable workrelating the language of emotion to science and to geometrical principles. To be able to accomplish my task, I learned the principles of sacred geometry. Only after I completed my part did I discover the book would not be published and would never be published. For a long time, I stewed in anger, frustration, and disappointment. I was never paid for my efforts. Sekhmet comforted me. She indicated that all was not lost. The gift was in the doing. Did I not gain the secrets of sacred geometry? By going through the entire process of drawing fundamental shapes and relating them to universal concepts, did I not now comprehend everything the author was trying to impart and in fact create images with more precision, more clarity, and more beauty than the author's originals? So it was in September of 1998 that Sekhmet inspired me to create an image of Her based upon the double square. My process appears below:

    89. List Of Posted Documents
    bragged when he was first confronted about his lying that he knew that whathe was presenting (particularly with regard to the golden mean and the golden
    http://www.danwinter.com/
    usr="ctenen"; Tenen v. Winter 6:94-cv-7934
    CORRECTIVE NOTICE WEBSITE See List of Posted Documents English Translation (with footnotes)
    Dear Friends, www.danwinter.com has been transferred to the Plaintiffs, Stanley and Cynthia Tenen and Meru Foundation, by order of Hon. Judge Charles J. Siragusa, of the US Federal District Court for the Western District of New York in Rochester. The Court has taken this action because Mr. Winter has refused to respond to the Court. He has refused to show up for hearings, for depositions, and to show cause why he should not continue to be held in contempt of court for his many violations of the Court's orders. This is not a matter of censorship. There is an arrest warrant for Mr. Winter filed with the United States Federal Marshals' Service, and he is a fugitive. It is the Court's way of using its discretionary powers to encourage Mr. Winter to appear in Court in the United States, and for deposition, as he has been ordered to do. The idea is to get Mr. Winter's attention, not to censor him. (The three most recent Court Orders , listed and linked to below, make this clear.)

    90. Links To Other Sites And Information
    Home Phi for Neo'phi'tes Fibonacci Series Divine Proportion/ golden Section/ goldenMean Credit Cards Energy geometry History Life Human Hand Human Face Human
    http://evolutionoftruth.com/goldensection/links.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
    Links to Resources
    and Information
    Fibonacci Series and Golden Section - General Links
    Dr. Ron Knott's Fibonacci Numbers and the Golden section Site - One of the best and most complete sites on the Internet on this topic, and a winner of many awards. Fibonacci Quarterly Home Page - Research Magazine The life and numbers of Leonardo Fibonacci The Golden Mean Fascinating Fibonaccis - Mystery and Magic in Numbers The Golden Mean ... Golden Ratio
    Relationship to Divine Creation
    The Evolution of Truth (Main Site to the this site)
    Art and Architecture
    Fibonacci - The LIX Unit - In Astronomy and the Ancient Pyramids Fibonacci numbers and the Golden Section in Art, Architecture and Music Golden Section in Art, Architecture and Music The School of Pythagoras The School of Pythagoras ... Secrets of the Great Pyramid
    DNA and Phi
    Dan Winter on Super DNA and Physics of Phi
    Geometry
    A Little Geometry Sacred Geometry Home Page - The unique numbers in math
    Life
    Fibonacci - The Numbers of Life - An Overview
    Mathematics
    Fibonacci - The Golden Mean - Using trigonometry, limits, etc.

    91. "Unified Field" Physics? Based On Golden Mean Ratio By Alex Kaivarainen
    For example, I suppose, that the mechanism of influence of rigid structures withgeometry, following golden mean (I termed them Harmonizators ), on different
    http://soulinvitation.com/goldenphysics/
    "Unified Field" Physics? based on Golden Mean Ratio by Alex Kaivarainen comments from Dan Winter.. - see Alex K. new: COMPUTERIZED VERIFICATION OF NEW HIERARCHIC
    THEORY
    NEW OPTOACOUSTIC DEVICE:
    Comprehensive Analyzer of Matter Properties (CAMP)
    and its applications - at: alexKjuly02.pdf and also his Proposal to test and prove: Comprehensive Analyzer of Matter Properties (CAMP)-Alex Kaivarainen Note from Dan Winter: "I believe that the REASON the Golden Mean recursive wave ratio cascade is THE SOLE SOLUTION to COMPRESSION and "NON-LOCALITY" (true multiple-connected topologies)- is the coherent acceleration of phase velocities thru speed of light. True FUSION is only possible when waves nest in Golden Mean Ratio. Einstein while noting that acceleration was identical to gravity failed to note that recursive compression was identical to acceleration! (wave lengths and wave phase velocities both add and multiple in Golden Ratio)." New Link Added: Golden Ratio derived in Physics from Plank: Golden Ratio in the Hierarchy of Time - by John Deutsch
    Visual Tour of Golden Mean Unified Field Physics Model (from Dan Winter): This page offers the work of Alex Kaivarainen from Finland / Russia, on Golden Mean Ratio solutions in contemporary physics.

    92. Untitled Document
    10. Harmonics of Music and Thirteen Chakras, Like the golden mean Spiral, this Thisgeometry artistically symbolizes this relationship, and as such, may be a
    http://www.flora-balance.com/lightsource/sacred_geometry.htm
    lightSource
    Volume 1:
    A Sacred Geometry Experience Sacred Geometry is the blueprint of Creation and the genesis of all form. It is an ancient science that explores and explains the energy patterns that create and unify all things and reveals the precise way that the energy of Creation organizes itself. On every scale, every natural pattern of growth or movement conforms inevitably to one or more geometric shapes.
    As you enter the world of Sacred Geometry you begin to see as never before the wonderfully patterned beauty of Creation. The molecules of our DNA, the cornea of our eye, snow flakes, pine cones, flower petals, diamond crystals, the branching of trees, a nautilus shell, the star we spin around, the galaxy we spiral within, the air we breathe, and all life forms as we know them emerge out of timeless geometric codes. Viewing and contemplating these codes allow us to gaze directly at the lines on the face of deep wisdom and offers up a glimpse into the inner workings of the Universal Mind and the Universe itself.

    93. Golden Mean Tool Description
    Take a look at a small one I made out of mat board. Try this easyto-usegeometry to calculate the golden Section of your strips.
    http://www.spyrock.com/nadafarm/html/gmtoolkit.html
    A Golden Section Tool
    Consistent with the elegant simplicity of the Golden Proportion , there is a very simple "X" shaped tool that makes it possible to find, see and verify the Golden Proportion in the world around us. It is a very simple device modelled after a bronze tool used by architects in ancient Greece. Below you can find out what it looks like and how to make your own.
    Get two thin, straight strips of equal length of some rigid material such as mat board, tag board or thin wood slats . The longer they are, the bigger the measurements that you can make. My large Golden Section tool is made of thin oak strips about 3 ' long. Take a look at a small one I made out of mat board.
    Try this easy-to-use geometry to calculate the Golden Section of your strips. Mark the spot and drill or punch a hole in each strip at the same spot.
    Connect the two strips at the hole you have made. For my large oak version, I used a short screw with a wing nut so I can tighten and lock the tool in place while taking or finding measurements. For my small portable version, I used two strips of matboard and a brass stationery connector.
    Once your Golden Section Tool is finished, begin looking for the Golden Proportion in the world around you and in your own body. When you spread your Golden Section tool apart and take a measurement with one end, the other end will always be the Golden Proportion in relation to the former!

    94. Our Logo - The Golden Mean
    The golden mean. .618 1 1.618 The golden mean, or golden Ratio,has been around for a long time. But rarely do you hear any
    http://www.poordesign.com/pdgver3/logo/2logo.html

    HOME
    INFO OUR LOGO CLIENTS ... STAFF
    The Golden Mean
      The Golden Mean, or Golden Ratio, has been around for a long time.
      But rarely do you hear any discussion about its use as a design tool.
      That's the purpose of these pages to inform, and illustrate the use of this ratio (and others) as a means of breaking up space in a dynamic and aesthetically pleasing way.

    Constructing the Golden Mean

    General Info
    All the Math Dynamic Symmetry, ... Fibonacci 2
    Poor Design Group Inc.
    2845 Harriet Avenue South
    Minneapolis, MN 55408 USA
    Fax (612) 871-1530
    E-mail to jon@poordesign.com

    95. LycosZone Directory > Homework > Math > Geometry And Trigonometry
    What kind of geometry and Trigonometry Websites are you looking for?
    http://www.lycoszone.com/dir/Homework/Math/Geometry and Trigonometry/
    Search For: Lycos Zone Home Family Zone Teachers Zone What kind of Geometry and Trigonometry Websites are you looking for? Analytical Geometry
    Computational Geometry

    Euclids Elements and Postulates

    Fibonacci Numbers
    ...
    "GEOMETRY, INTEGRABILITY AND QUANTIZATION"
    "Proceedings of the International Conference on Geometry, Integrability and Quantization."
    Algebraic Curves
    A great resoucre to learn formulas for algebraic curves.
    Grade Level: 9-12
    Gallery of Interactive Geometry
    The Geometry Center is a mathematics research and education center at the University of Minnesota.
    Grade Level: 9-12
    Gallery of Interactive Geometry
    Eight interactive web events that illustrate various aspects of geometry.
    Grade Level: 9-12 Geometry This is where you'll find almost everything you'll ever need to know about Geometry. We have a special page on constructions and plenty of sample problems to help you understand the concepts. Grade Level: 6-8 Geometry Dictionary "This dictionary provides definitions for geometry, algebra and even some trig terms." Grade Level: 9-12 Geometry.net

    96. Democracy_steps
    the Fibonacci Sequence. Because I am well informed about the GoldenMean geometry and I was trained as an architect. I have many
    http://homepage1.nifty.com/starcage/english_democracy_steps.html
    DEMOCRACY STEPS (c)1993-1997 Akio HIZUME Democracy Steps (c)1993-1997 Akio HIZUME I made an outdoor sculpture called "The Democracy Steps ". One was realized in Yoshida, Saitama, JAPAN in 1993. Another was in the Hocking hills State Park, Ohio, U.S.A. in 1997.
    I can also design slope (ramp) for wheelchair using similar method. It is not ordinary staircase. It is even for both right and left legs, and for everyone whether whose step is long or short. It is based on the Fibonacci Sequence. This quasi- periodic rhythm is very comfortable for human mind and body.
    Peoples understand the effect of Golden Mean by their subconsciousness.
    If you climb it, you will relax. I believe that it should be the standard of gentle staircase. . I can design the most effective and reasonable flight of steps based on the Fibonacci Sequence. Because I am well informed about the Golden Mean Geometry and I was trained as an architect. I have many practical skill in order to find the best solution of the Democracy Steps for any slope.
    The Fibonacci Sequence is projection (shadow) of six dimensional lattice
    on one dimensional space.

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