101. Divine Proportion The Easy Way - Golden Section Photoshop Plugin Tool to draw the golden section, golden spiral, divine proportion and other fibonacci number compositions. http://powerretouche.com/Divine_proportion_tutorial.htm

How to get the divine proportion/golden section into your composition Now you can instantly draw the golden sections, or other divine proportions, as an aid to composition. This plugin can draw fibonacci sequences such as the golden sections golden spiral and the golden triangles . In addition it also can draw the harmonious triangles and the rule of thirds - based on composition through identity. The best way to use the plugin is to output the drawing to a transparent top layer you can move around for cropping. see list Divine proportion Golden section, golden spiral, Golden Section plugin - Tutorial Benefits of the Golden Section plugin Draws the fibonacci sequences: Golden Section, Golden Spiral and Golden Triangles. Draws the two common harmonies: Rule of Thirds and Harmonic Triangles. Freely adjust the rectangle to any size within the image boundaries. Rotate or flip the divisions any way you like.

102. Read This: The Golden Section Read This! The MAA Online book review column review of The golden Section, by Hans Walser. http://www.maa.org/reviews/golden.html

Search MAA Online MAA Home Read This! The MAA Online book review column The Golden Section by Hans Walser Reviewed by Underwood Dudley In the first sentence of his Foreword, the author says, "The Golden Section has turned up, since antiquity, in many aspects of geometry, architecture, music, art, and even philosophy." Before getting around to what is in his book I want to comment on this. It might be misleading. As most readers of MAA Online know, the golden section is that which results when a line segment is divided into two pieces such that the ratio of the whole to the larger is the same as the ratio of the larger to the smaller. That is, if the segment has length 1 (which it may as well) and the larger piece has length x , then 1/ x x x). This gives x = .618033988. The reciprocal of this, 1.618033988 , has been denoted by a variety of symbols, but I think is the most common and the one I will use. Professor Walser prefers t , which is also fine, and lets r denote - 1. The number has many properties, including

103. Golden Ratio -- From MathWorld Proportions golden Section or golden Mean, Modulor, Square Root Page of Mueller Home Site Showing Proportioning Systems (golden Section, Modulor, DIN A, and how to Construct Them. http://www.astro.virginia.edu/~eww6n/math/GoldenRatio.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Constants Golden Ratio ... 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"). The term "golden section" ( goldene Schnitt ) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik (Livio 2002, p. 6). The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. The symbol ("phi") was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works (Livio 2002, pp. 5-6). has surprising connections with continued fractions and the Euclidean algorithm for computing the greatest common divisor of two integers . It is also a so-called Pisot Number Given a rectangle having sides in the ratio is defined such that partitioning the original

104. The Golden Proportion, Beauty, And Dental Aesthetics Device for design, study of beauty in nature, art, science. http://www.goldenmeangauge.co.uk/golden.htm

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105. The Golden Mean By Jerry Bonnell And Robert Nemiroff - Project Gutenberg Start here to download the Project Gutenberg eBook of The golden Mean by Jerry Bonnell and Robert Nemiroff. http://www.gutenberg.org/etext/744

Project Gutenberg Online Book Catalog Quick Search Author: Title Word(s): EText-No.: Advanced Search Recent Books Top 100 Offline Catalogs ... In Depth Information The Golden Mean by Jerry Bonnell and Robert Nemiroff Read online Help on this page New Search Bibliographic Record Creator Bonnell, Jerry Creator Nemiroff, Robert Title The Golden Mean Note To a million digits Language English LoC Class QA: Science: Mathematics Subject Mathematics EText-No. Release Date No Formats Available For Download Edition Format Encoding ¹ Compression Size Download Links ² Plain text none 1011 KB main site mirror sites Plain text zip 480 KB main site mirror sites ¹ If you need a special character set, try our online recoding service ² If you are located outside the U.S. you may want to download from a mirror site located near you to improve performance. Click on mirror sites to select a mirror site. If you have P2P software installed that understands magnetlinks click on Most recently updated: 2005-09-13 09:46:15

106. The Archdome - Golden Mean Design golden Mean The Archdome enfolds the golden spiral (also known as the Fibonacci spiral). Scientists have studied the dome and have come to a number of http://www.archdome.com/goldenmean.html

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.

107. ACD Systems The golden Mean Photography Part I golden Spiral ACD Digital Photography Tips. http://www.acdsystems.com/English/Community/ColumnsArticles/PhotoTips/photo-2005

ACD Language Sites: English Deutsch Espa±ol Fran§ais Italiano Shopping Cart Products ACDSee 8 Photo Manager FotoSlate 4 Photo Print Studio ... Home Community ACD Community: Articles Newsletters Contests Product Forums ACD Digital Photography Tips Community Enjoy digital photography tips . Enter Photo Contest (s) to win ACD software. Sign up for digital photography tips newsletters Wacky Photo Story, April 30, 2005 Lyn Carlin of Moving Images Photography Melbourne, Australia Here is a polocrosse photo taken at the Victorian finals 2004 in Melbourne. The ball is soft and air filled and the game is played a bit like polo. Its a desperate fight to grab the ball in the racket and hurl it to a team mate who can then drive it through the goal posts. Click to enlarge As the photographer it was a day that tested my nerves and the durability of my Canon D10 and 100 to 400 zoom. The field has no fences around it so to get the good shots I had to stand on the edges and shoot as galloping horses headed straight for me. On one occasion I had two horses locked together in a tustle galloping at me straight over the boundry line and only saw my lens up their snouts at the last instant....however due to the amazing skill of these ponies one went a foot to the left of me and the other a foot to my right.... and no that particular shot was blurred... The day also proved testing for my equipment as it was summer and the field was throwing up choking white dust that no only tricked the camera exposure, hid the subject till the last minute but covered my camera. There were flies dust, sweat and heat all day......would I do it again....yep....

108. IOnOne | Art | Architecture | Golden Section IOnOne architecture golden section online magazine of architectural design and urbanism. Guide to exibitions, digital architecture and design, http://www.ionone.com/arcgolds.htm

art architecture painting music startup.file golden section divine proportion, golden ratio, PHI construction search for golden section Divine Proportion by Luca Pacioli golden section by Runion A Study in Mathematical Beauty Mathematical History Golden Number Fibonacci Ratios Geometry: Euclid and Beyond Essays on Number in Architecture link@ Technical University Hamburg-Harburg proportion : Claude Debussy The Golden Section by Hans Walser Since antiquity, the Golden Section has played a significant role in many parts of geometry, architecture, music, art, and philosophy. But it also appears in the newer domains of technology and fractals. In t his way, the Golden Section is no isolated phenomenon but rather, in many cases, the first and also the simplest non-trivial example in a sequence of generalizations leading to further developments. It is the purpose of this book, on the one hand, to describe examples of the Golden Section, and on the other, to show some paths to further extensions. read more da Vinci proportions The Last Supper Vitruvian Man (The Proportions of the Human Figure), 1490

109. ArtLex On The Golden Mean The golden mean / section defined with images of examples from throughout history, great quotations, and links to other resources. http://www.artlex.com/ArtLex/g/goldenmean.html

G olden Mean or Golden Section golden mean or golden section - A proportional relation ( ratio ) obtained by dividing a line so that the shorter part is to the longer part as the longer part is to the whole. Another way to describe this: a proportion between the two dimensions of a plane figure or the two divisions of a line, in which the ratio of the smaller to the larger is the same as the ratio of the larger to the whole: a ratio of approximately 0.618 to 1.0 The Golden Mean produces a harmonic effect called eurythmy found in nature as well as in a wide variety of works of art and design Artists of various periods and cultures have found that dimensions determined by this formula are aesthetically appealing. Other images of the Golden Mean: The Parthenon , Athens, superimposed with a diagram demonstrating the use of the Golden Mean in the Parthenon's design. See architecture and Greek art Architect Charles E. Jeanneret, known as "Le Corbusier" (French, 1887-1965), often used golden rectangles in his designs for buildings. One of these is the United Nations building in New York. The upright part of the L has sides in the golden ratio, and there are distinctive marks on this taller part which divide the

110. Golden Rectangle: Information From Answers.com golden rectangle The large rectangle BA is a golden rectangle. If we remove square B , what is left, A , is another golden rectangle. http://www.answers.com/topic/golden-rectangle

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping golden rectangle Wikipedia golden rectangle The large rectangle BA is a golden rectangle. If we remove square B , what is left, A , is another golden rectangle. A golden rectangle is a rectangle with dimensions which are of the Golden Ratio side s of the same proportions when sectioned in a particular manner. That is, sectioned into two shapes : firstly a square with one side being one of the lesser sides of the surrounding golden rectangle ; and secondly a rectangle composed of the remainder . The new, smaller rectangle is thus a golden rectangle itself, and one of its longer sides will be the other lesser side of the surrounding rectangle, the other being one of the sides of the new square. The rectangle looks like this: See also Golden spiral Fibonacci Fibonacci numbers External links Golden Ratio at MathWorld http://mathworld.wolfram.com/GoldenRatio.html The Golden Mean and the Physics of Aesthetics http://uk.arxiv.org/abs/physics/0411195

111. The Golden Mean Explains the theory behind the golden mean and how it can be constructed out of the Fibonacci series. http://www.vashti.net/mceinc/golden.htm

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.

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