81. AntKnee Cure-Rated PolyLovely Shareware Program for Constructing Nested Polyhedra; golden mean@;Sacred geometry Coloring Book - for children and adults; taken fromt the Flower http://www.antknee.demon.co.uk/antknee/ver1summary/p2u_sacredgeometry.htm

a Sacred Geometry Systems of hidden numbers and formulas. Templates from nature and belief systems and language founded on numeric relationships. Greeks, Jews, Egyptians, Arabians, the Stock Market, Designers, Painters, Musicians. This subject has been around for a while - ever since Islamic people divided a circle in two and further still. I recently used one of the sacred geometric forms to undertake some music and the results were mind bogglingly good. Indian ragas.....murals....check out the links below for your next big project. Most of these links can be found at www.sacredgeometry.com - an excellent site. - extensive list of articles and examples. Formative Sacred Geometry the Egyptian Neters - article on cosmic laws and how they may be defined and described by numbers. Linking The Great Pyramid to the Human Form - acticle on primal systems which reveal the unity of the cosmos by representing the relationships between numbers geometrically. QDC Solutions: Sacred Geometry - articles and links to speculations and realisations of where we fit in the fractal.

82. Untitled Document Golden Ratio of successive Fibonacci number ratios is the golden mean. the relation among thegolden Ratio, Fibonacci HSM Coxeter s Introduction to geometry, published by http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/KURSATgeometrypro/goldenrat

The Golden Mean I believe that this geometric proportion served the Creator as an idea when He introduced the continuous generation of similar ojects from similar objects. J. Kepler (1571-1630) We start with a problem in aesthetics. Consider a line segment. What is the most "pleasing" division of this line segment into two parts? Some people might say at the halfway point. Others might say at the one-quarters point. The "correct answer" is, however, none of these, and is found in Western art from the Ancient Greeks ownward (art theorists speak of it as the principle of "dynamic symmetry"): A geometric definition can be given in terms of the above figure. Let the ratio x = BC/AB. The Numerator and Denominator can then be taken as AB = a and BC = x without loss of generality. Now define the position of B by Plugging in gives or which can be solved using the Quadratic Equation to obtain This quantity known as the Golden Ratio, Divine Proportion, etc. The quantity where is the Golden Ratio. The golden ratio conjugate is sometimes also called the Silver Ratio. Click on the icon for a GSP scritp to divide a segment in golden ratio.

83. Mathematics Links and golden Spiral. The golden mean 3 Another investigation of the algebraand geometry of the golden mean. The golden Section Constructing http://www.msad51.org/GHS/mathlinks.html

athematics inks Curves Golden Mean Fractals Number Theory ... Geometer's Sketchpad Return to Mathematics athematical urves Famous Curves Applet Index Use Java applets to experiment with the graphs of different curves Xah: Visual Dictionary of Special Plane Curves A visual dictionary of special plane curves Famous Curves Index Witch of Agnesi A really nice discussion of this special parametric curve. Witch of Agnesi A gif animation of the curve known as the Witch of Agnesi. Return to Mathematics Links olden ean The Golden Mean, Rectangle, ... The Golden Mean #1 A nice summary of the golden ratio and its derivation. The Golden Mean #2 Some "golden geometry", Penrose tilings, and Golden Spiral. The Golden Mean #3 Another investigation of the algebra and geometry of the Golden Mean. The Golden Section Constructing the Golden Section The Golden Rectangle Constructing the Golden Rectangle and Golden Spiral The Golden Rectangle Animated Animations illustrating the Golden Rectangle and Golden Spiral The Fibonacci Numbers The Fibonacci Numbers and Golden section in Nature An interesting and well illustrated site investigating the occurrance of the golden ratio in nature.

84. The Golden Ratio : The Story Of PHI, The Worlds Most Astonishing Number why so many people see the golden mean in ancient The golden Ratio The Story ofPHI, the Worlds serious lovers of proportion and geometry, architects, mystics http://www.sciencesbookreview.com/The_Golden_Ratio__The_Story_of_PHI_the_Worlds_

The Golden Ratio : The Story of PHI, the Worlds Most Astonishing Number The Golden Ratio : The Story of PHI, the Worlds Most Astonishing Number by Authors: MARIO LIVIO Released: 23 September, 2003 ISBN: 0767908163 Paperback Sales Rank: List price: Our price: You save: Book > The Golden Ratio : The Story of PHI, the Worlds Most Astonishing Number > Customer Reviews: Average Customer Rating: The Golden Ratio : The Story of PHI, the Worlds Most Astonishing Number > Customer Review #1: Remarkable Catalyst for Thought Author Mario Livio has added another wonderful book that bridges the gap between writings meant for the academic and for the layperson. "The Golden Ratio", was not quite as accessible as some other books that I have read, but it is certainly worth the extra effort even if many of the proofs found at the books end remain a mystery. The book spent a great deal of time disproving the myths of application that have been attributed to the remarkable relationships of the number PHI. Like the more familiar PI it is a decimal that has yet to be proven to ever repeat itself, and it demonstrates its presence both widely and in fascinating manners. Whether or not Mozart used the number or Leonardo DaVinci did, or even if a building long considered to be predicated upon the number truly is or is not, does not detract from the wonders of this numbers appearance.

85. Re: Posting PROBLEM FIXED - Golden Mean - Architecture Forum make rational some choices has produced any theories, from epicicles, to welds andpassing through golden mean. Aesthetical or sacred geometry theories in the http://www.designcommunity.com/discussion/13916.html

Design Community Architecture Discussion Message - Re: Posting PROBLEM FIXED - Golden Mean Responses Architecture Forum Architecture Students Architecture Scrapbook ... ArchitectureWeek Posted by Manuel Oliveros on February 03, 2002 at 09:49:53: In Reply to: Re: Posting PROBLEM FIXED - Golden Mean posted by Paul Malo on February 03, 2002 at 07:56:34: JW, we even don't know what happens truly in a weld, how to say about ideal sizes for families or indiviudals? The need to apparently make rational some choices has produced any theories, from epicicles, to welds and passing through golden mean. Aesthetical or sacred geometry theories in the past were well practiced for the plan and elevation design of many beautiful items, it seems, and so may bear some true value in this sense. But of course only as tools, for it was always design in the end what made it more or less beautiful. By completely discarding such theorizations one would ignore history and maybe would be losing some tool, but it would be equally wrong to discard the programmatic statement (written or not) of a building as an useful tool to ascertain if fit to use. ArchitectureWeek Search Buildings Architects ... Library Search GreatBuildings.com

86. List Of Mathematical Topics (G-I) At Opensource Encyclopedia geometry Géometrie Algébrique et Géométrie Analytique geometry of numbers Goldbach sweak conjecture golden angle golden mean golden mean http://wiki.tatet.com/List_of_mathematical_topics_(G-I).html

Free world wide web encyclopedia wiki.tatet.com (encyclopedia DB was kindly granted by Wikipedia Encyclopedia Sites Home List of mathematical topics (G-I) List of mathematical topics A-C D-F G-I J-L M-O P-R S-U ... Mathematicians G G2 (mathematics) G-delta set Gabriel's horn Galilean transformation ... Gumbel, Eric H H infinity H-principle H-space Haar integral ... Hypothesis testing I IACR Icosagon Icosahedron Icosidodecahedron ... List of mathematical topics %28G I%29 in directory Related sites Rooms with a View Philippe Schwartz Photographies Topica Real Estate Agent Directory ... come to egypt This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article "List of mathematical topics (G-I)"

87. Golden Ratio -- From MathWorld as the divine proportion, golden mean, or golden section, is a number often encounteredwhen taking the ratios of distances in simple geometric figures such as http://mathworld.wolfram.com/GoldenRatio.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Number Theory Constants Continued Fraction Constants ... Lambrou Golden Ratio The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagram decagon and dodecagon . It is denoted or sometimes (which is an abbreviation of the Greek "tome," meaning "to cut"). is a Pisot-Vijayaraghavan constant . It also has surprising connections with continued fractions and the Euclidean algorithm for computing the greatest common divisor of two integers Given a rectangle having sides in the ratio is defined such that partitioning the original rectangle into a square and new rectangle results in a new rectangle having sides with a ratio Such a rectangle is called a golden rectangle , and successive points dividing a golden rectangle into squares lie on a logarithmic spiral . This figure is known as a whirling square . The legs of a golden triangle are in a golden ratio to its base and, in fact, this was the method used by Pythagoras to construct

88. 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://ccins.camosun.bc.ca/~jbritton/goldengeom/goldengeom.html

Some Golden Geometry Here are instructions for constructing the Golden Rectangle, a rectangle whose sides measure 1 and 1.618... Construct a square. Bisect the square. Draw a line from one end of the bisecting line to one of the opposite corners. Extend the baseline of the square. Using the diagonal line as the radius, drop an arc from the corner of the square down to the baseline. Draw a line from the point of intersection of the arc and the baseline, perpendicular to the baseline. Extend the top edge of the square to meet this line and form a rectangle. This rectangle is referred to as the Golden Rectangle On to the The Golden Spiral or to the Penrose Tilings Original webpage by Rashomon

89. Mathsoft: Well-known Constants: The Golden Mean, φ as n approaches infinity, the limit of the sequence of successive Fibonacci numberratios is the golden mean. Nested Rectangles. Here is a geometric connection. 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 Approximation of Functions ... 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

90. Golden Mean 3 Again If a straight line is cut in extreme and mean ratio, then as the wholeis to the greater segment, the greater segment is the lesser segment. http://facultystaff.vwc.edu/~trfanney/golden-mean-WOWslides/gm3.html

Page 1: Intro Page 2: Euclid Page 3: Repeating geometry Page 4: Golden Rectangle ... Page 11: Golden mean and Fibonacci Numbers Again: If a straight line is cut in extreme and mean ratio, then as the whole is to the greater segment, the greater segment is the lesser segment.

91. 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:

92. Links Section. The golden mean and a geometric expansion of a line in theproportions of the golden Section, presented by T. Smith. Another http://home.att.net/~vmueller/links/links.html

The Links Software Links JavaScript Sources Art Links Leonardo DaVinci ... Golden Section in Nature, Art, Architecture, Music, etc. Software Links: 3d modeling and rendering: form*Z RenderZone by auto*des*sys, Inc. in Columbus, Ohio. Various image editing and layout / publishing tools: Adobe Systems, Inc. back to top JavaScript Sources: Voodoo's Intro to JavaScript by Stefan Koch. Lots of Links to Other JavaScript Sites back to top Art Links: back to top Leonardo DaVinci Leonardo DaVinci, Selected Drawings , collected by David M. Reuteler Leonardo DaVinci Links Leonardo DaVinci synopsis in the Windows To The Universe Project by the University of Michigan, funded by NASA (the space agency). back to top Sandro Botticelli: Sandro Botticelli (Hungarian Site) and at the Uffizi in Florenz, Italy. Uffizi Room 10 (Botticelli) Botticelli links Botticelli Designs for Dante. back to top Peter Paul Rubens: Baroque Art Index of the University of Haifa Library Some paintings by P. P. Rubens in the Museo Prado in Madrid, Spain back to top Baroque Art: MEHAP Baroque Links Baroque Ring Site List Baroque at the Paris Webmuseum.

93. THREE TABLES OF THE GRAIL The golden mean is a geometric progression employed by the Greek mathematician,Euclid, in the 1st century BC. In practice, however http://www.aquavitic.freeserve.co.uk/lighter/bloodline/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.

94. Cesme.utm.edu/resources/framewks/geo1.htm euclidean like the golden Section which provides extensive information on what Euclidean Geometryreally is. The golden Section, also known as the golden mean and the http://cesme.utm.edu/resources/framewks/geo1.htm

95. 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) May 2004 Persons interested in the Heart Tuner, click here for statements from Rollin McCraty of the Institute of Heart Math Dr. Gary Schwartz of the University of Arizona, and Vinny Pinto, moderator of the ... e-group on Yahoo REWARD Meru Foundation is offering substantial rewards and "finders' fees" for information that leads to the collection of the $140,000 in court costs and interest owed to it by Mr. Daniel E. Winter. If you have done business with Mr. Winter, or have information with regard to his business and/or business partners, please contact reward@danwinter.com for further information. Meru Foundation is also accumulating evidence for possible future legal action (US and world-wide) with regard to Mr. Winter's (and those acting with and for him) new plagiarism and disparagement. If you have purchased copies of Mr. Winter's illicit works, if you have attended presentations by Mr. Winter, or those working with and for him, or if you have other first-hand knowledge or physical evidence of the new and quite obvious works of plagiarism and disparagement, please contact action@danwinter.com. Dear Friends

96. Excerpts From Sworn Statements Of Witnesses a nearperpendicular manner. It has nothing to do with the golden meangeometry which he is claiming. It is impossible for rotation http://www.danwinter.com/depoexcerpts.html

EXCERPTS FROM SWORN STATEMENTS OF EXPERT WITNESSES AND FACT WITNESSES The excerpts below are from sworn statements of witnesses, taken prior to June 1998 when USDJ Charles Siragusa issued his Findings of Fact, Conclusions of Law, and Order Sworn Testimony of Expert and Fact Witnesses Excerpted from Affidavits and Depositions, as noted Compiled by Cynthia Tenen, Meru Foundation, November 1997 Copies of the original documents available on request [The following persons were scheduled to be expert witnesses on our behalf in our lawsuit against Mr. Daniel Winter. We have sworn affidavits and depositions from them; below are some quotations from the body of their testimony, and their conclusions.] Louis H. Kauffman, Ph.D. Mathematics: Full Professor, University of Illinois at Chicago. One of world's foremost experts in topology and knot theory. From the Affidavit of Louis H. Kauffman, Ph.D., 11 November 1994: Quotation: Page 2, line 21 through Page 3, line 9: "I have examined Mr. Winter's book, "Alphabet of the Heart," and his CD-ROM for Macintosh, "The Language of Geometry Animated," as well as Macintosh disks which were the precursors of the CD-ROM and contain much of the same material. In my opinion it is abundantly clear that Mr. Winter was inspired by Mr. Tenen's work to create a three dimensional computer image (using the program Aldus Super 3-D) that copies as best he could manage Mr. Tenen's design for a "flame letter" that projects the different letters of the Hebrew alphabet. I am fully aware that this flame letter is Mr. Tenen's individual design, as I had the honor of watching him evolve this design over the decade of the 1980's."

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