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Golden Ratio: more books (52)

Fractal Universe and the golden ratio structural and rhythmic unity of the world - ("Relata Refero") / Fraktalnaya Vselennaya i zolotoe otnoshenie Strukturnoe i ritmicheskoe edinstvo mira - ("Relata Refero") by Yakimova N.N., 2008
Mathematical Constants: E, Pi, Golden Ratio, Brun's Constant, Catalan's Constant, Feigenbaum Constants, de Bruijn-Newman Constant
The Golden Ratio, The Story of Phi the World's Most Astonishing Number - 2002 publication by Maro Lvo, 2002-01-01
Golden Ratio the Story of Phi the Worlds by Mario Livio,
Irrational Numbers: Golden Ratio
The Golden Ratio The Story of PHI the Worlds Most Astonishing Number 2003 publication. by Mario Livio, 2003
Alishev C. x. Bulgarian-Kazan and the Golden ratio in the XIII-XVI in / Alishev S.Kh. Bolgaro-kazanskie i zolotoordynskie otnosheniya v XIII-XVI v by Alishev S., 2009
Variance amplification and the golden ratio in production and inventory control [An article from: International Journal of Production Economics] by S.M. Disney, D.R. Towill, et all 2004-08-18
The Return of Sacred Architecture: The Golden Ratio and the End of Modernism
Golden Ratio by MarioLivio, 2002
Golden Section: An entry from Macmillan Reference USA's <i>Macmillan Reference USA Science Library: Mathematics</i> by Philip Edward Koth, William Arthur Atkins, 2002
Fibonacci Trading, Chapter 1: Fibonacci Numbers and the Golden Ratio by Carolyn Boroden, 2008-02-25
The Golden Mean or Ratio[(1+sqrt(5))/2] by Jerry Bonnell, 2010-07-06
Golden ratio geometry: A book of research by Joan Moore, 1996

lists with details

Golden Ratio Conjugate -- From MathWorld
Number Theory Constants Continued Fraction Constants Number Theory Constants GoldenRatio. golden ratio Conjugate. The quantity, (1). where is the golden ratio.
http://mathworld.wolfram.com/GoldenRatioConjugate.html
Golden Ratio
11374 84754 08807 53868 91752 12663 38622 23536 93179 31800 60766 ConstructionsYou can actually construct the golden ratio with a compass and straight edge.
http://www.geocities.com/robinhuiscool/Goldenratio.html

Extractions: Most things in nature follow the golden ratio pattern. Look at your own fingers for example. Measure the length of the longest finger bone. Then measure the shorter one next to it. Divide the longer one by the shorter one. You should get a number close to 1.168. All parts of the human body are poportional to the golden ratio. If you face is in this ratio you are said to be beautiful. The golden ratio is an irrational number, therfore it can't be written as a regular fraction. You could however, get a close estimate. One way, is by dividing Fibonacci numbers. Fibonacci numbers basically follow the pattern 1,1,2,3,5,8,13,21.... each number is the sum of the two before it. 2+3=5,5+3=8,8+5=13 and so on. See a list of the first 1,000 Fibonacci Numbers
Art Gallery Of Mark Ivan
A virtual art gallery containing the Phyconic art works of the artist Mark Ivan and showing how this art is created using the golden ratio.
http://sidewalksalon.bizhosting.com/
Math Forum: Ask Dr. Math FAQ: Golden Ratio, Fibonacci Sequence
The golden ratio/Golden Mean, the Golden Rectangle, and the relation between theFibonacci Sequence and the golden ratio. golden ratio, Fibonacci Sequence.
http://mathforum.org/dr.math/faq/faq.golden.ratio.html

Extractions: A Golden Rectangle is a rectangle in which the ratio of the length to the width is the Golden Ratio. In other words, if one side of a Golden Rectangle is 2 ft. long, the other side will be approximately equal to Now that you know a little about the Golden Ratio and the Golden Rectangle, let's look a little deeper. Take a line segment and label its two endpoints A and C. Now put a point B between A and C so that the ratio of the short part of the segment (AB) to the long part (BC) equals the ratio of the long part (BC) to the entire segment (AC): The ratio of the lengths of the two parts of this segment is the Golden Ratio. In an equation, we have
Math Forum - Ask Dr. Math Archives: High School Fibonacci Sequence/Golden Ratio
Browse High School Fibonacci Sequence/golden ratio. golden ratio 01/03/1998 Doyou have any topics that I can use in my term paper about the golden ratio?
http://mathforum.org/library/drmath/sets/high_fibonacci-golden.html
Golden Ratio Design
Local doctor designs medical database applications for the Palm, as well as providing other Web design services. Includes samples of sites and PERL scripts, links, and news on spring peepers.
http://www.tonywitte.com/

Extractions: The Golden Ratio or Golden Mean is a number revered since antiquity that appears with suprising frequency in natural designs and great works of art. At Golden Ratio Design we believe well-designed computer applications and web tools are recognizable for their simplicity and elegance. We bring this concept to web-based and Palm OS applications for health care clinical desion making and productivity. The Palm OS is the dominant operating system for handheld computing, and for good reasons: simplicity, utility, dependability and a wide range of available software. As a physician dealing with volumes of critical information on a regular basis, the value of handheld computing has been very apparent to me. I have created a few applications for the Palm OS of use to the medical community, and am at work on other applications placing needed databases literally in the palm of the clinician's hand. LabCode NCD - Medical Necessity coding tool using latest Medicare medical necessity requirements included in the 23 lab test National Coverage Decisions. LabCode LMRP - Medical Necessity coding tool using latest local medical review policy medical necessity requirements.
Cynthia Lanius' Lessons: The Golden Ratio
golden ratio. 1.61803398874989484820. This ratio, called the golden ratio, notonly appears in art and architecture, but also in natural structures.
http://math.rice.edu/~lanius/Geom/golden.html

Extractions: Thanks to PBS for permission to use the Pyramid photo. If you need a definition If you were going to design a rectangular TV screen or swimming pool, would one shape be more pleasing to the eye than others? Since the early Greeks, a ratio of length to width of approximately 1.618, has been considered the most visually appealing. This ratio, called the golden ratio, not only appears in art and architecture, but also in natural structures. Estimate the ratio of the length to width in the rectangles below: length width Answers Golden Ratio Table of Contents Introduction Find golden rectangles. Build golden rectangles. Confirm the ratio using algebra. Back to the ... Email any comments to lanius@math.rice.edu URL http://math.rice.edu/~lanius/Geom/golden.html
The Golden Ratio
Explanation, presence in biology, art, and ancient art.
http://www.geocities.com/jyce3
Sacred Geometry Jewelry And Healing Tools By Gretchen McPherson
Jewelry and power objects based on Platonic solids, Archimedian solids, and the golden ratio. Necklaces, pendants, earrings, altar pieces by artist Gretchen McPherson.
http://www.lotuslazuli.com/

Extractions: lotus lazuli is a collection of sacred geometry jewelry and power objects handcrafted by jewelry artist, gretchen mcpherson The Platonic solids tetrahedron, octahedron, cube, icosahedron and dodecahedron , as well as Archimedian solids, the Merkaba, Flower of Life, fibonacci sequence, phi spiral and golden ratio are the major motifs employed. A 3-dimensional labyrinth is created within each shape, directing the energy flow of carefully chosen semi-precious and precious stones held inside its net. Math, spirituality and beauty meet in these unique necklaces pendants earrings and altar pieces.
ThinkQuest : Library : The Golden Ratio
Welcome to this site! When you think of math, do you think of beauty?Do you think of stuff like pinecones and sunflowers? What
http://library.thinkquest.org/C005449/home.html

Extractions: Index Math Geometry When people think of math, do they think of beauty? Do they think of things like pinecones and sunflowers? What does Leonardo da Vinci have to do with this? What do the Greeks, Romans, and people of the Renaissance have in common? They all a mathematics concept in common: the Golden Ratio. The most irrational number in the world is a basis for many things: math, art, architecture, biology, and this site explains how. Visit Site 2000 ThinkQuest Internet Challenge Students Andrei Grupul Scolar H. Coanda, Rm.Valcea, Romania Shujun Thomas Jefferson High School for Science and Technology, Great Falls, VA, United States Melissa Potomac Falls High School, Potomac Falls, VA, United States Coaches Randy Potomac Falls High School, Alexandria, VA, United States Emilia Potomac Falls High School, Rm. Valcea, Romania Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site.
Golden Ratio
The golden ratio. Although Euclid does not use the term, we shall callthis the golden ratio. The definition appears in Book VI but
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Golden_ratio.html

Extractions: Although Euclid does not use the term, we shall call this the golden ratio . The definition appears in Book VI but there is a construction given in Book II, Theorem 11, concerning areas which is solved by dividing a line in the golden ratio. As well as constructions to divide a line in the golden ratio, Euclid gives applications such as the construction of a regular pentagon, an icosahedron and a dodecahedron . Here is how the golden ratio comes into the construction of a pentagon. First construct an isosceles triangle whose base angles are double the vertex angle. This is done by taking a line AB and marking C on the line in the golden ratio. Then draw a circle with centre A radius AB . Mark D on the circle so that AC CD BD . The triangle ABD has the property that its base angles are double its vertex angle.
The Golden Rectangle And The Golden Ratio
The Golden Rectangle and the golden ratio. a/b = (a+b)/a This fraction, (a+b)/a,is called the golden ratio (or golden section or golden mean).
http://www.jimloy.com/geometry/golden.htm

Extractions: Go to my home page click here for the alternative Golden Rectangle and Golden Ratio page This diagram shows a golden rectangle (roughly). I have divided the rectangle into a square and a smaller rectangle. In a golden rectangle, the smaller rectangle is the same shape as the larger rectangle, in other words, their sides are proportional. In further words, the two rectangles are similar. This can be used as the definition of a golden rectangle. The proportions give us: a/b = (a+b)/a This fraction, (a+b)/a, is called the golden ratio (or golden section or golden mean). Above I have defined the golden rectangle, and then said what the golden ratio is, in terms of the rectangle. Alternatively, I could have defined the golden ratio, using the above equation. And then a golden rectangle becomes any rectangle that exhibits this ratio. From our equation, we see that the ratio a/b=1/2+sqr(5)/2 -1/2+sqr(5)/2 or 0.61803398875 . . .) is called the golden ratio. Also, other mathematical quantities are called phi. The golden ratio is also called tau. Some people call the bigger one (1.61803398875 . . .) Phi (an uppercase phi) and the smaller one (0.61803398875 . . .) phi.
American Phi
Music, story and poetry of the golden ratio.
http://members.aol.com/loosetooth/phi.html
Math Forum - Ask Dr. Math Archives: High School Fibonacci Sequence/Golden Ratio
A list of questions gathered pertaining to Fibonacci and golden ratio.
http://mathforum.org/dr.math/tocs/golden.high.html
Fibonacci Numbers & The Golden Ratio Link Web Page - About This Page
About This Page. Welcome to Dawson Merrill s Fibonacci and golden ratio Link webpage. If asked to sum up the golden ratio in a word, I would reply, Growth .
http://pw1.netcom.com/~merrills/aboutthispage.html

Extractions: About This Page Welcome to Dawson Merrill's Fibonacci and Golden Ratio Link web page. Please note that unless otherwise stated each link takes you off my page to an Internet site, the author of which deserves all the credit for his or her efforts. It is my hope that I am maintaining a single point of focus for all mathematicians, scientists, researchers, hobbyists, and explorers everywhere in providing a well organized link to the appropriate Internet resource. I want to take this opportunity to thank Dr. Gerald Alexanderson of Santa Clara University who first planted the seed and watered the thirst for my personal pursuit of the Golden Ratio. It began in a phone conversation when I was a teenager in 1980. Although not comprehending much of what Dr. Alexanderson said while on the phone, I feverishly scribbled down as much and as fast as I could. Then after the call, putting pencil, compass, and straightedge to paper, I began to catch a glimpse of the beauties of which he spoke. Ever since, it has been my life's most inspiring and enthralling quest. I'd also like to thank Dr. Ron Knott
Index
Mathematical calculations; explanations of Phi, the golden ratio and Golden Rectangles; examples from art, architecture, music and nature.
http://www.geocities.com/cyd_conner

Extractions: Columbia University Library, D.E. Smith Collection I created this site as my term project for the 2000/2001 Elementary Math curriculum course at Queen's University. I have made every attempt to reference the graphics and text which I have gleaned from various sources. Many of these resources are web-based and I have included links to the sites. However, due to the ever-changing nature of the Web, some of these links may be broken and I apologize in advance for any inconvenience. Most of the links are green , and the button in the upper left corner of each page will always take you back to familar territory! Click here to enter
Guardian Unlimited | Online | 1.618 Is The Magic Number
It s the golden ratio and, arguably, it crops up in more places inart, music and so on than any number except pi. The golden ratio!
http://www.guardian.co.uk/online/science/story/0,12450,875198,00.html

Extractions: Sign in Register Go to: Guardian Unlimited home UK news World news Archive search Arts Books Business EducationGuardian.co.uk Film Football Jobs Life MediaGuardian.co.uk Money The Observer Online Politics Shopping SocietyGuardian.co.uk Sport Talk Travel Audio Email services Special reports The Guardian The weblog The informer The northerner The wrap Advertising guide Crossword Dating Headline service Syndication services Events / offers Help / contacts Information Living our values Newsroom Reader Offers Style guide Travel offers TV listings Weather Web guides Working at GNL Guardian Weekly Money Observer Home Web watch Ask Jack Feedback ... Life Think of any two numbers. Make a third by adding the first and second, a fourth by adding the second and third, and so on. When you have written down about 20 numbers, calculate the ratio of the last to the second from last. The answer should be close to 1.6180339887... What's the significance of this number? It's the "golden ratio" and, arguably, it crops up in more places in art, music and so on than any number except pi. Claude Debussy used it explicitly in his music and Le Corbusier in his architecture. There are claims the number was used by Leonardo da Vinci in the painting of the Mona Lisa, by the Greeks in building the Parthenon and by ancient Egyptians in the construction of the Great Pyramid of Khufu.
The Golden Ratio
The golden ratio. Throughout history, the ratio for length to the eye.This ratio was named the golden ratio by the Greeks. In the world
http://www.geom.uiuc.edu/~demo5337/s97b/art.htm

Extractions: Throughout history, the ratio for length to width of rectangles of 1.61803 39887 49894 84820 has been considered the most pleasing to the eye. This ratio was named the golden ratio by the Greeks. In the world of mathematics, the numeric value is called "phi", named for the Greek sculptor Phidias. The space between the collumns form golden rectangles. There are golden rectangles throughout this structure which is found in Athens, Greece. He sculpted many things including the bands of sculpture that run above the columns of the Parthenon. You can take a slide show visit to the Parthenon which is pictured above. Phidias widely used the golden ratio in his works of sculpture. The exterior dimensions of the Parthenon in Athens, built in about 440BC, form a perfect golden rectangle. How many examples of golden rectangles can you find in the below floorplan of the Parthenon? You may want to print the diagram and measure the distances using a ruler. Following are more examples of art and architecture which have employed the golden rectangle. This first example of the Great Pyramid of Giza is believed to be 4,600 years old, which was long before the Greeks. Its dimensions are also based on the Golden Ratio. The website about the pyramid gives very extensive details on this.
Pentagram & The Golden Ratio
The Pentagram The golden ratio. Johann Kepler (1571-1630). The ratio has become known as the golden ratio or golden section.
http://www.contracosta.cc.ca.us/math/pentagrm.htm

Extractions: and this is the golden ratio Notice also the diagonals of the pentagon form another regular pentagon in the center of the figure with, of course, the potential for additional diagonals to be drawn, thus generating the golden ratio again as well as another regular pentagon further inside the figure. Presumably this could continue indefinitely. The golden ratio also appears in comparing consecutive elements of certain kinds of sequences, most notably, the
The Golden Ratio And Aesthetics
It was Euclid who first defined the b golden ratio /b , and ever sincepeople have been fascinated by its extraordinary properties.
http://plus.maths.org/issue22/features/golden/

Extractions: Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Issue 22 November 2002 Contents Features More or Less In a spin The golden ratio and aesthetics The best medicine? Career interview Career interview: Medical statistician Regulars Plus puzzle Pluschat Mystery mix Reviews 'The Golden Ratio' 'Euclid's Window' 'Elements of Grace' and 'Copernican Notes' 'Calculus' ... poster! November 2002 Features Mario Livio is a scientist and self-proclaimed "art fanatic" who owns many hundreds of art books. Recently, he combined his passions for science and art in two popular books, The Accelerating Universe , which appeared in 2000, and The Golden Ratio reviewed in this issue of Plus . The former book discusses "beauty" as an essential ingredient in fundamental theories of the universe. The latter discusses the amazing appearances of the peculiar number 1.618... in nature, the arts, and psychology. Here he gives us a taster.

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