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Topic: Golden ratio


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  Math Forum: Ask Dr. Math FAQ: Golden Ratio, Fibonacci Sequence
A Golden Rectangle is a rectangle in which the ratio of the length to the width is the Golden Ratio.
The ratio of the lengths of the two parts of this segment is the Golden Ratio.
The Golden Ratio is the ratio of BC to AB.
mathforum.org /dr.math/faq/faq.golden.ratio.html   (497 words)

  
  Golden ratio - Wikipedia, the free encyclopedia
The philosophy of Summum, a sect of about 200,000 adherents that has incorporated the golden ratio into the design of their Summum Pyramid winery in Utah, maintains that because it is the human mind that interprets the characteristics and qualities of the golden ratio, it should be considered in its relation to the human psyche.
Nevertheless, some of these ratios are observed to be quite close to the golden ratio in the shape of the organs or parts which closely follow some basic geometrical shape (such as the Nautilus shell, whose construction proceeds in a logarithmic spiral).
From a mathematical point of view, the golden ratio is notable for having the simplest continued fraction expansion, and of thereby being the "most irrational number" worst case of Lagrange's approximation theorem.
en.wikipedia.org /wiki/Golden_ratio   (3564 words)

  
 Golden Mean Golden Section Golden Ratio Math Art Poster Posters Tshirt Tshirts Math Art
A series of images capturing the Golden Mean and the Golden Rectangle, from ancient times to the modern day, available as Posters, math Tshirts, and Sweatshirts, for those interested in math, art, and the relationship between mathmatics and art.
The ratio generally expressed as 1 : 1.618 (an approximation) has come to be described as the Golden Ratio, or the Golden Mean.
In Leonardo Da Vinci's drawing studies, the human face itself was shown to be expressive of the golden ratio of the Golden Mean.
mathematicianspictures.com /sp_Golden_Mean.htm   (360 words)

  
 Golden ratio
This idea that Plato began the study of [the golden ratio] as a subject in itself is not in the least inconsistent with the supposition that the problem of Euclid II, 11 was solved by the Pythagoreans.
The first known calculation of the golden ratio as a decimal was given in a letter written in 1597 by Michael Maestlin, at the University of Tübingen, to his former student Kepler.
The result that the quotients of adjacent terms of the Fibonacci sequence tend to the golden ratio is usually attributed to Simson who gave the result in 1753.
www-groups.dcs.st-and.ac.uk /~history/HistTopics/Golden_ratio.html   (1650 words)

  
 Nature's Golden Ratio, Alaska Science Forum
Geometrically, it can be defined as the ratio obtained if a line is divided so that the length of the shorter segment is in the same proportion to that of the longer segment as the length of the longer segment is to the entire line.
Soon, many of the masters began to proportion their canvases according to the golden ratio, and it is still the shape most preferred today for anything from window blinds to table tops.
The same golden ratio that appears as a rectangle in human constructs often is expressed in nature forms as an elegant spiral.
www.gi.alaska.edu /ScienceForum/ASF7/716.html   (709 words)

  
 Golden Section and Rule of Thirds (Golden Mean, Golden Ratio, Golden Spiral, Golden Proportion, Golden Triangles).
Golden Section and Rule of Thirds (Golden Mean, Golden Ratio, Golden Spiral, Golden Proportion, Golden Triangles).
It affects the ratio (1:1.618) of a picture size, as well as the placement of the main subjects in the photo.
This ratio is close to the 35mm ratio, so you don't need to change the size of the photo in most cases.
photoinf.com /Golden_Mean/Eugene_Ilchenko/GoldenSection.html   (373 words)

  
 CameraHobby - e-Book on the Golden Ratio, Chapter 16
One of the most interesting graphic forms of the Golden Ratio is the nautilus shell and the way the shell starts from a central origin and then spirals outward around itself until it reaches the horn or opening of the shell where the cephalopod's head is located.
Egyptians used the Golden Ratio for their pyramids and the layout of the three great pyramids of Giza use the curve of the Golden Ratio that is predominant in a nautilus shell.
The Golden Ratio pops up over and over again for what humans consider to be attrative and it is becoming more and more clear to me that it is a natural phenomenon so pervasive that Pythagoras called it a universal beauty so many thousands of years ago.
www.camerahobby.com /Ebook-GoldenRatio_Chapter16.htm   (1419 words)

  
 Reference.com/Encyclopedia/Golden ratio
He took Leonardo's suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system.
The golden ratio is also apparent in the organisation of the sections in the music of Debussy's Image, Reflections in Water, in which the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the φ position.
The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected.
www.reference.com /browse/wiki/Golden_ratio   (4744 words)

  
 1.618 is the magic number | Technology | Guardian Unlimited Technology
The golden ratio is also difficult to pin down: it's the most difficult to express as any kind of fraction and its digits - 10 million of which were computed in 1996 - never repeat.
The symbol of their cult was the five-pointed star, and the ratio of the length of the side of each triangular point to its projected base is the golden ratio.
Perhaps the most surprising place the golden ratio crops up is in the physics of fl holes, a discovery made by Paul Davies of the University of Adelaide in 1989.
technology.guardian.co.uk /online/science/story/0,12450,875198,00.html   (1004 words)

  
 Golden Ratio
The study of the Golden Ratio allows teachers and learners to explore a well-known problem through four important representations as well as to incorporate technology in a manner that illuminates different aspects of the problem.
golden section, when the longer of the two segments formed is the mean proportional between the shorter segment and the whole line.
The ratio of the shorter segment to the longer segment is called the golden ratio" (Eves, 1983).
www.ite.sc.edu /dickey/golden/golden.html   (1253 words)

  
 Golden Ratio
The Golden Ratio, also known as the divine ratio or proportion, is a ratio known for its relevance to art and aesthetics.
This ratio is also present in a variety of natural phenomena, particularly in the growth patterns of plant and animal life.
The Golden Ratio was derived by the ancient Greeks.
www.logicville.com /sel7.htm   (153 words)

  
 Golden Ratio
The blue triangle has its sides in the golden ratio with its base, and the red triangle has its base in the golden ratio with one of the sides.
As was seen with the whirling rectangles, the ratio of consectutive Fibonacci numbers begins to apporximate the Golden Ratio.
The values for the computed ratios for n = 1 to 40 are found in column E of the spreadsheet.
jwilson.coe.uga.edu /emt669/Student.Folders/Frietag.Mark/Homepage/Goldenratio/goldenratio.html   (2304 words)

  
 The golden ratio and feng shui
The golden ratio is a very important concept in feng shui due to the way it implies aspects of balance and perfection of shapes.
The golden ratio is a rule that can be often found in many elements of the nature as well as in artificial objects made by man. This way, it can help achieving the desired harmony by being used along with feng shui balancing elements and objects.
The golden ratio is a numeric value which was discovered by Euclid and shows a mathematical relationship which appears as a constant.
www.fengshuicrazy.com /feng-shui-basics/the-golden-ratio-and-feng-shui.php   (973 words)

  
 Naked Golden Ratio
The most pleasing of all numbers, the golden ratio has properties which have delighted and inspired thoughtful people throughout the ages.
The golden ratio also famously plays a central role in many of the world's greatest pieces of architecture, such as the Egyptian Pyramids and the Greek Parthenon.
This symbol was the sacred symbol of the Pythagoreans.
www.nakedgeometry.com /goldenratio.html   (165 words)

  
 The Golden Section - the Number and Its Geometry
Euclid used this phrase to mean the ratio of the smaller part of this line, GB to the larger part AG (ie the ratio GB/AG) is the SAME as the ratio of the larger part, AG, to the whole line AB (ie is the same as the ratio AG/AB).
The ratio itself is mentioned in several places and, since Euclid seems to have collected already known methods and facts then the golden ratio would have been known well before his time too.
The ratio of the length of a face of the Great Pyramid (from centre of the bottom of a face to the apex of the pyramid) to the distance from the same point to the exact centre of the pyramid's base square is about 1·6.
www.mcs.surrey.ac.uk /Personal/R.Knott/Fibonacci/phi.html   (4627 words)

  
 Leonardo Da Vinci Golden Mean, Leonardo Da Vinci Golden Ratio
Leonardo Da Vinci Golden Mean, Leonardo Da Vinci Golden Ratio
In Leonardo Da Vinci's painting of the Mona Lisa, a Golden Rectangle frames central elements in the composition, and a Golden Triangle is evident as a composition framing element.
In Leonardo Da Vinci's Last Supper fresco, the Golden Ratio (rear wall and windows) and other relationships based on Fibonacci Numbers (foreground, table and disciple's feet) may be found in the relationship of elements in the composition.
mathematicianspictures.com /LEONARDO_DA_VINCI_GOLDEN_RATIO_GOLDEN_MEAN/Leonardo_Da_Vinci_Golden_Ratio_Golden_Mean.htm   (296 words)

  
 Phi Golden Ratio Phi Golden Mean
Prevalent in the major works of Leonardo Da Vinci and underlying many of his design compositions, is the Golden Ratio ("Golden Mean"), a ratio of approximately 1:1.618, found in nature and creation, and inherent in the Fibonacci sequence.
The Golden Rectangle, the Golden Triangle, and the Golden Pyramid, all based on the Golden Ratio are all appear prominent in the work of Leonardo Da Vinci.
Phi Golden Ratio Phi Golden Mean, Phi Golden Ratio Violin, Phi Golden Mean Violin, Phi Golden Ratio Violin, Phi Equation, Phi Equations, Phi Infinite Nested Radicals, Phi Poster, Phi Posters, Phi T shirt, Phi T shirts, Phi Tshirt, Phi Tshirts, Phi T-shirt, Phi T-shirts, Phi Golden Ratio nature butterfly, Phi Golden rectangle nature butterfly
mathematicianspictures.com /PHI_GOLDEN_RATIO_GOLDEN_MEAN/Phi_Golden_Ratio_Golden_Mean.htm   (206 words)

  
 Golden Ratio
Statues of human bodies considered most perfect by the Greeks had many Golden Ratios.
It turns out that the "perfect" (to the Greeks) human face has a whole flock of Golden Ratios as well.
You’ll be measuring lengths on the face of a famous Greek statue (with a broken nose) by using the instructions on this page.
www.markwahl.com /golden-ratio.htm   (554 words)

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