Home  - Math_Discover - Golden Ratio

Books Baby Camera Phones Computers Games DVD Electronics Kitchen Magazines Music Garden Software Tools Toys Video Apparel & Accessories Jewelry & Watches Musical Instruments Health & Personal Care Beauty Sports & Outdoors Office Products

e99.com Bookstore

Images

Newsgroups

1-20 of 100    1  | 2  | 3  | 4  | 5  | Next 20

Golden Ratio:     more books (52)

The Golden Ratio: The Story of PHI, the World's Most Astonishing Number by Mario Livio, 2003-09-23 The Golden Ratio and Fibonacci Numbers by R. A. Dunlap, 1998-03 The Return of Sacred Architecture: The Golden Ratio and the End of Modernism by Herbert Bangs M.Arch., 2006-11-14 The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty by Mario Livio, 2003-08-04 The Diet Code: Revolutionary Weight Loss Secrets from Da Vinci and the Golden Ratio by Stephen Lanzalotta, 2006-04-03 The Golden Mean or Ratio [(1+sqrt(5))/2] to 20,000 places by null, 2009-10-04 Non-Standard Positional Numeral Systems: Unary Numeral System, Golden Ratio Base, Fibonacci Coding, Quater-Imaginary Base, Negative Base Golden Ratio the Story of Phi the Worlds by Mario Livio, 2002 Golden Ratio: Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search, Golden Spiral The Golden Ratio: The Story of Phi, the World's Most Astonishing Number   [GOLDEN RATIO] [Paperback] The Golden Ratio by Mario Livio, 2002 The Glorious Golden Ratio by Alfred S. Posamentier, Ingmar Lehmann, 2011-06 The Golden Ratio by Keith Flynn, 2007-02-15 Constants: Mathematical Constants, Physical Constants, Dimensionless Quantity, Avogadro Constant, Pi, Golden Ratio, Gas Constant

lists with details

1. The Golden Section - The Number And Its Geometry
   We will call the golden ratio (or Golden number) after a greek letter Phi ( ) here, although some writers and  
   http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html
   
   Extractions: A bit of history... Links on Euclid and his "Elements" ... More What is the golden section (or Phi)? We will call the Golden Ratio (or Golden number) after a greek letter, Phi ) here, although some writers and mathematicians use another Greek letter, tau ). Also, we shall use phi (note the lower case p) for a closely related value. A simple definition of Phi There are just two numbers that remain the same when they are squared namely and . Other numbers get bigger and some get smaller when we square them: Squares that are bigger Squares that are smaller is 4 is 9 is 100 One definition of Phi (the golden section number) is that to square it you just add 1 or, in mathematics: Phi = Phi + 1 In fact, there are

2. The Golden Ratio
   Gives and intro to the golden ratio and its presence in biology, art, and ancient art This site is devoted to the golden ratio. In this page, you will find information about the golden ratio, Fibonacci  
   http://www.geom.umn.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.

3. Golden Ratio -- From MathWorld
   Order portable, salon, spa and stationary tables. Includes a description and a photo of each.  
   http://mathworld.wolfram.com/GoldenRatio.html
   
   Extractions: 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 also known as the divine proportion, golden mean, and golden section and is a Pisot-Vijayaraghavan constant . It 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 From the definition of the golden mean combined with the above figure

4. The Golden Ratio And The Fibonacci Numbers
   A presentation of the relationship between the golden ratio and the Fibonacci Numbers from the proceeding Category Science Math Recreations Specific Numbers phiThe golden ratio and The Fibonacci Numbers. Copyright (c) 1999 Kelley L. Ross, Ph.D.All Rights Reserved. The golden ratio and The Fibonacci Numbers, Note 1.  
   http://www.friesian.com/golden.htm
   
   Extractions: The Fibonacci Numbers The Golden Ratio ) is an irrational number with several curious properties. It can be defined as that number which is equal to its own reciprocal plus one: . Multiplying both sides of this same equation by the Golden Ratio we derive the interesting property that the square of the Golden Ratio is equal to the simple number itself plus one: . Since that equation can be written as , we can derive the value of the Golden Ratio from the quadratic equation, , with a = 1 b = -1 , and c = -1 . The Golden Ratio is an irrational number, but not a transcendental one (like ), since it is the solution to a polynomial equation. This gives us either or . The first number is usually regarded as the Golden Ratio itself, the second as the negative of its reciprocal. The Golden Ratio can also be derived from trigonometic functions: = 2 sin 3 /10 = 2 cos ; and = 2 sin /10 = 2 cos 2 . The angles in the trigonometric equations in degrees rather than radians are o o o , and 72 o , respectively. The Golden Ratio seems to get its name from the Golden Rectangle , a rectangle whose sides are in the proportion of the Golden Ratio. The theory of the Golden Rectangle is an aesthetic one, that the ratio is an aesthetically pleasing one and so can be found spontaneously or deliberately turning up in a great deal of art. Thus, for instance, the front of the Parthenon can be comfortably framed with a Golden Rectangle. How pleasing the Golden Rectangle is, and how often it really does turn up in art, may be largely a matter of interpretation and preference. The construction of a Golden Rectangle, however, is an interesting exercise in the geometry of the Golden Ratio

5. Fibonacci Numbers, The Golden Section And The Golden String
   Fibonacci numbers and the golden section in nature, art, geometry, architecture, music, geometry Category Science Math Specific Numbers Fibonacci Numbers Numbers and Nature Fibonacci and the original problem about rabbits where the seriesfirst appears, the family trees of cows and bees, the golden ratio and the  
   http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
   
   Extractions: a sequence of 0s and 1s which is closely related to the Fibonacci numbers and the golden section. There is a large amount of information at this site (more than 200 pages if it was printed), so if all you want is a quick introduction then the first link takes you to an introductory page on the Fibonacci numbers and where they appear in Nature. The rest of this page is a brief introduction to all the web pages at this site on 10 February 2003 Fibonacci Numbers and Nature Fibonacci and the original problem about rabbits where the series first appears, the family trees of cows and bees, the golden ratio and the Fibonacci series, the Fibonacci Spiral and sea shell shapes, branching plants, flower petal and seeds, leaves and petal arrangements, on pineapples and in apples, pine cones and leaf arrangements. All involve the Fibonacci numbers - and here's how and why.

6. Fibonacci Numbers And The Golden Section In Art, Architecture And Music
   Mathematics lessons for elementary, middle, and high school including geometry. considered the most visually appealing. This ratio, called the golden ratio, not only appears in art and architecture,  
   http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html
   
   Extractions: This section introduces you to some of the occurrences of the Fibonacci series and the Golden Ratio in architecture, art and music. Fibonacci in Films Fibonacci and Poetry Fibonacci and Music ... More The Golden section in architecture Even from the time of the Greeks, a rectangle whose sides are in the golden proportion (1 : 1.618 which is the same as 0.618 : 1) has been known since it occurs naturally in some of the proportions of the Five Platonic Solids (as we have already seen) and a construction for the golden section point is found in Euclid's Elements in this connection. This rectangle is supposed to appear in many of the proportions of that famous ancient Greek temple, the Parthenon, in the Acropolis in Athens , Greece but there is no original documentary evidence that this was how the building was designed. (There is a replica of the original building (accurate to one-eighth of an inch!) at

7. ThinkQuest Library Of Entries
   Created by Team C005449 { this site can be viewed with anybrowser } Click here to enter. media/splasherific.gif.  
   http://library.thinkquest.org/C005449/
   
   Extractions: The web site you have requested, The Golden Ratio , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to The Golden Ratio click here Back to the Previous Page The Site you have Requested ... click here to view this site Click image for the Site Site Desciption 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.

8. Math Forum: Ask Dr. Math FAQ: Golden Ratio, Fibonacci Sequence
   Please tell me about the golden ratio (or Golden Mean), the Golden Rectangle, and the relation between the Fibonacci  
   http://forum.swarthmore.edu/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

9. ThinkQuest Library Of Entries
   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: The web site you have requested, The Golden Ratio , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to The Golden Ratio click here Back to the Previous Page The Site you have Requested ... click here to view this site Click image for the Site Site Desciption 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.

10. Golden Ratio
    How to generate the number, GSP script for dividing segments, rectangle and other shapes, the rabbit Category Science Math Recreations Specific Numbers phi the segment A as the length of segment A is to the length of segment B. If we calculatethese ratios, we see that we get an approximation of the golden ratio.  
    http://jwilson.coe.uga.edu/emt669/Student.Folders/Frietag.Mark/Homepage/Goldenra
    
    Extractions: Most people are familiar with the number Pi, since it is one of the most ubiquitous irrational numbers known to man. But, there is another irrational number that has the same propensity for popping up and is not as well known as Pi. This wonderful number is Phi, and it has a tendency to turn up in a great number of places, a few of which will be discussed in this essay. One way to find Phi is to consider the solutions to the equation When solving this equation we find that the roots are x = ~ 1.618... or x= We consider the first root to be Phi. We can also express Phi by the following two series. Phi = or Phi = We can use a spreadsheet to see that these two series do approximate the value of Phi. Or, we can show that the limit of the infinite series equals Phi in a more concrete way. For example, let x be equal to the infinte series of square roots. But this leads to the equation which in turn leads to and this has Phi as one of its roots. Similarly, it can be shown that the limit of the series with fractions is Phi as well. When finding the limit of the fractional series, we can take a side trip and see that Phi is the only number that when one is subtracted from it results in the reciprocal of the number. Phi can also be found in many geometrical shapes, but instead of representing it as an irrational number, we can express it in the following way. Given a line segment, we can divide it into two segments A and B, in such a way that the length of the entire segment is to the length of the segment A as the length of segment A is to the length of segment B. If we calculate these ratios, we see that we get an approximation of the Golden Ratio.

11. Welcome To Golden Ratio
    Custombuilt massage tables, massage chairs, spa equipment, and other products.Category Business Healthcare Products and Services Massage  
    http://www.goldenratio.com/

12. What's New On The Golden Ratio Site
    Now open—golden ratio's Wellspring Institute—advancing the arts of wellnessand beauty. golden ratio Woodworks 1 800345-1129 PO Box 297 2896 Hwy.  
    http://www.goldenratio.com/whatsnew.html

13. The Golden Ratio
    Gives and intro to the golden ratio and its presence in biology, art, and ancientart. Introduction to the golden ratio and Fibonacci Numbers. Biology. Art.  
    http://www.geocities.com/capecanaveral/station/8228/

14. Steve, Jeanette, And Marc's Final Project
    Project with art references and object construction lessons.Category Science Math Recreations Specific Numbers phiOUR FINAL PROJECT. THE golden ratio The purpose of this web page is toprovide an introduction to the golden ratio and Fibonacci Sequence.  
    http://www.geom.umn.edu/~demo5337/s97b/
    
    Extractions: Steve Blacker, Jeanette Polanski, and Marc Schwach The purpose of this web page is to provide an introduction to the Golden Ratio and Fibonacci Sequence. Instead of simply supplying definitions and asking the student to engage in mindless practice, our idea is to have the student work through several activities to discover the applications of the Golden Ratio and Fibonacci Sequence. Enjoy! Please work through the following activities in the order given: Fibonacci Sequence Fibonacci in Nature Discover the Golden Ratio Golden Ratio in Art ... Worksheet Suggested Activities for Further Investigation (found on the web) Gain further practice in hand-constructing a golden rectangle golden spiral , and a golden section Here are some pretty descent activities you can work through for further understanding. Check out some of Dr. Math's responses to some excellent questions about the Golden Ratio and Fibonacci Sequence. For a slightly more rigorous look at the golden ratio, take a look at this page Here are some cool puzzles you can play with to pursue your investigations further.

15. 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 Answer Answer Answer Next: Find the objects around you that are closest to the golden ratio.

16. Cynthia Lanius' Lessons: Algebra Of The Golden Ratio
    golden ratio Algebra. golden ratio 1.61803, We used this property when we built therectangle, and now we will use it to confirm the value of the golden ratio.  
    http://math.rice.edu/~lanius/Geom/algebra.html
    
    Extractions: Algebra Golden Ratio 1.61803 We used this property when we built the rectangle , and now we will use it to confirm the value of the golden ratio. When we cross multiply the above proportion, we get l = lw + w or l - lw - w Solving the equation gives us l = w(1 + sqrt5) 2 Divide both sides by w: l = (1 + sqrt5) - - w 2 Enter this into a calculator, and you'll see the approximation of the golden ratio - Geometry Online Index Email any comments to lanius@math.rice.edu URL http://math.rice.edu/~lanius/Geom/algebra.html

17. 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

18. 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

19. Golden Ratio Conjugate -- From MathWorld
    golden ratio Conjugate, The quantity, (1). where is the golden ratio.The golden ratio conjugate is sometimes also called the silver ratio.  
    http://mathworld.wolfram.com/GoldenRatioConjugate.html

20. The Golden Ratio
    Extension of the number.Category Science Math Recreations Specific Numbers phiLast updated March 27, 1996 1.61803398874989484820458683436563811772030917980576286213544862270526046281890  
    http://www.cs.arizona.edu/icon/oddsends/phi.htm

1-20 of 100    1  | 2  | 3  | 4  | 5  | Next 20