Geometry.Net - Math_Discover: Golden Ratio


Home - Math_Discover - Golden Ratio

e99.com Bookstore

Images

Newsgroups

1-20 of 111 1 | 2 | 3 | 4 | 5 | 6 | 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

Golden Ratio
Custombuilt massage tables, massage chairs, spa equipment, and other products.
http://www.goldenratio.com/
Steve, Jeanette, And Marc's Final Project
Project with art references and object construction lessons.
http://www.geom.uiuc.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.
The Golden Ratio
Extension of the number.
http://www.cs.arizona.edu/icon/oddsends/phi.htm
Golden Ratio
Provides a golden ratio GreekFace activity for 5th grade and up, plus a link for extra information.
http://www.markwahl.com/golden-ratio.htm

Extractions: Scroll below for a neat 2-page Golden Ratio activity (It will take some extra time to finish loading while that happens, read on). Select each page of it at a time and print it for use with students. 2) Or, if you have been searching for any of the following keywords, a click on one will take you to an excellent book resource A Mathematical Mystery Tour ) for weeks of personal, home, or classroom learning about the Golden Ratio and Fibonacci Numbers: 3) Or you can go to this website and see a selection of creative books, links, and information on math learning that goes beyond these topics: Mark Wahl Learning Services and Books Now, the Golden Ratio . It has fascinated layman and mathematician for centuries. It seems like magic that it turns up in such different arenas as pine cones earth-moon and planet relationships, the Cheops Pyramid in Egypt, the
Fibonacci Numbers & The Golden Ratio Link Web Page
A long list of links to pages about Fibonacci and his numbers, the golden ratio and applications in art and science.
http://pw1.netcom.com/~merrills/fibphi.html
Golden-ratio.co.uk
News, tour dates, biography, discography, lyrics, and photographs.
http://www.golden-ratio.co.uk
The Golden Ratio
Examines the uses/occurances of phi in biology, art, and ancient times.
http://library.thinkquest.org/C005449
The Golden Ratio
Gives and intro to the golden ratio and its presence in biology, art, and ancient art.
http://www.geocities.com/jyce3/
PHI, The Golden Ratio
Provides a definition of Phi, and explains some mathematical background as well as a listing of 1000 digits of the number.
http://astronomy.swin.edu.au/pbourke/analysis/phi/

Extractions: May 1990, Updated January 1995 Definition Break a line segment into two such that the ratio of the whole to the longest segment is the same as the ratio of the two segments. From the diagram below. The condition can expressed as a/b = 1/a. This can be rearranged and expressed as a quadratic. There are two solutions, phi-1 and -phi where This is the original Greek definition, often phi-1 is used instead. Solution of a quadratic Normally the quadratic for which phi is the quoted solution is The solutions being phi and phi-1 Relationships x , x , x ..... x i ..... where x i = x i-1 + x i-2 The ratio This tends to phi as i tends to infinity. That is, the ratio of consecutive terms in such a series approaches phi, this is true independent of the starting points of the series. The zero order series starts with 1 and 1 as below. 1 1 2 3 5 8 13 21 34 55 89 etc the ratio of consecutive pairs are 1 0.5 0.67 0.6 0.625 0.6154 0.619 0.6176 0.6182 etc
Golden Ratio
Essay and brief introduction by Edwin M. Dickey.
http://www.ite.sc.edu/dickey/golden/golden.html

Extractions: The simple elegance of the algebraic expression stands out in glaring contrast to the mind numbing English language expression of the same idea. Why do we study algebra? Because it provides us with an effective and efficient means of communicating certain ideas. Given the definition of the Golden Ratio in algebraic language, one can now investigate methods of finding the numbers satisfying the statement through other representations. The algebraic analysis takes the form of solving the equation: . This can be done by multiplying the equation by 1 + x and solving the resulting quadratic equation using the quadratic formula. This type of analysis yielding two solutions: is familiar to algebra teachers. The graphical analysis of the original problem can be accomplished by again manipulating the original equation into the form x^2 + x - 1= and graphing the relation y = x^2 + x - 1. To solve the equation one can "zoom in" on the point where the curve crosses the x-axis (where the curve y = x^2 + x - 1 crosses the line y = 0). Figure 2 illustrates how the computer algebra system
The Golden Ratio And The Fibonacci Numbers
A presentation of the relationship between the golden ratio and the Fibonacci Numbers from the proceedings of the Friesian School.
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
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
Inter.View To George Cardas
An interview with George Cardas, describing his use of the golden ratio in highend audio equipment cables.
http://www.tnt-audio.com/intervis/cardase.html

Extractions: Let us take a segment a of lenght 1. Another segment b is said to be the Golden Section of a if it solves the following equation: b + b - 1 = that is to say the two segments respect the following proportion: a : b = b : (a-b) . In simpler words, given the fact that a has lenght 1, b must be 0.618 approx. Historically the Golden Ratio was well known to the Egyptians who used it for building their pyramids but it achieved wider popularity thanks to the Greek geometers.
Fibonacci Numbers, The Golden Section And The Golden String
The Golden section and Geometry The golden section is also called the golden ratio, the golden mean and the divine proportion.
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Golden Ratio -- From MathWorld
The golden ratio, also known as the divine proportion, golden mean, Livio, M. The golden ratio The Story of Phi, the World s Most Astonishing Number.
http://mathworld.wolfram.com/GoldenRatio.html

Extractions: 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
Sacred Geometry For Fun And Personal Growth
A summary of sacred geometry, covering Pythagoras, the golden ratio, cymatics and creation through sound, plus a practical geometry workshop, geometric graphics, and a meditation for higher consciousness.
http://geometry.wholesomebalance.com

Extractions: Sacred geometry is a vast and exciting subject. This website will give you a good summary, with some practical exercises and tools to get started, plus further resources to guide you onward. To start with, mathematics is a wonderful clean subject. It is not subject to opinion, nor does it rely on heated debates as to what the correct answer is. And geometry specifically is pure beauty! It is a great synthesizer, merging the linear, rational aspect of math through the left-side of the brain with the graphical, artistic aspect of pattern and beauty through the right brain. It unites the mind and the heart (called the "intelligence of the heart" by the ancient Egyptians), spirit and matter, science and spirituality. These are all apparently separate halves of the Whole. Plato said in the Republic (VII, 527 d, e) that it is through geometry that one purifies the eye of the soul, "since it is by it alone that we contemplate the truth." Mother nature uses geometry everywhere you look, from the spirals of the nautilus shell, sunflower centre and spiral galaxies to the hexagon symmetry of snowflakes, flower petals and honeycomb.
The Golden Section - The Number And Its Geometry
What is the golden section (or Phi)? We will call the golden ratio (or Golden number) after a greek letter Phi (
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Welcome To The Golden Ratio
This is an informative site on an interesting aspect of Geometry The golden ratio.
http://members.tripod.com/~ColinCool/mathindex.html
The Golden Ratio
Gives and intro to the golden ratio and its presence in biology, art, and ancient art
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

1-20 of 111 1 | 2 | 3 | 4 | 5 | 6 | Next 20