21. Golden Ratio How to generate the number, GSP script for dividing segments, rectangle and other shapes, the rabbit problem and references. http://jwilson.coe.uga.edu/emt669/Student.Folders/Frietag.Mark/Homepage/Goldenra

Phi: That Golden Number by Mark Freitag 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. x Squaring both sides we have 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.

22. The Golden Rectangle And The Golden Ratio The Golden Rectangle and the golden ratio. Note If your WWW browser cannot display special symbols, like ?2; http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

23. Constructing The Golden Rectangle The ratio, called the golden ratio, is the ratio of the length to the width of what is said to be The golden ratio can be noticed in the way trees grow, http://jwilson.coe.uga.edu/EMT669/Student.Folders/May.Leanne/Leanne's Page/Golde

Constructing the Golden Rectangle With respect to the Golden Ratio by Leanne May The ratio, called the Golden Ratio, is the ratio of the length to the width of what is said to be one of the most aesthetically pleasing rectangular shapes. This rectangle, called the Golden Rectangle, appears in nature and is used by humans in both art and architecture. The Golden Ratio can be noticed in the way trees grow, in the proportions of both human and animal bodies, and in the frequency of rabbit births. The ratio is close to 1.618. Whoever first discovered these intriguing manifestations of geometry in nature must have been very excited about the discovery. A study of the Golden Ratio provides an intereting setting for enrichement activities for older students. Ideas involved are: ratio, similarity, sequences, constructions, and other concepts of algebra and goemetry. Finding the Golden Ratio. Consider a line segment of a length x+1 such that the ratio of the whole line segment x+1 to the longer segment x is the same as the ratio of the line segment, x, to the shorter segment, 1. Thus

24. The Golden Ratio Extension of the number. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

25. 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/

Internet Store and Ecommerce Solution Provider Free Web Site Free Web Space and Site Hosting Web Hosting ... High Speed Internet if(window.ivnRotate) window.ivnRotate1 = new window.ivnRotate('ivnRotate1',0,document.awsSearch1.Keywords) Popular Searches: Home Page Art Gallery of Mark Ivan Welcome Thanks for viewing my gallery, hope you enjoy your visit. Featured Artwork Old Bridge Many centuries ago, there was a bridge spanning the gap from the mainland to the dwelling on the great rock... Original size: 9x12 in./23x31 cm Favorite Links National Gallery of Art - D.C. Gallery displaying one of the finest collections of art from all periods. Albright-Knox Gallery - Buffalo, NY gallery displaying modern American and European art. Copenhagen Art Gallery - Denmark gallery displaying the work of contemporary Scandinavian artists. Finderz Gallery - Gamesroom displaying free games to play on the internet.

26. USATODAY.com - Sheboygan, Known For Brats, Also Rates High For a "golden ratio" for each metropolitan area, using U.S. Census Bureau figures and other factors, such as cost of living and the ratio of http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

27. Deep Secrets A new theory that uses diagrammatic geometry to reveal a possible connection between the Great Pyramid, the golden ratio and the ancient Egyptian Royal Cubit. http://www.sover.net/~rc/deep_secrets/

Introduction The Hexagon Measuring the Earth The Great Pyramid ... Links Deep Secrets The Great Pyramid, The Golden Ratio and The Royal Cubit This site provides a new, and perhaps for some a controversial, explanation for the rationale behind the exterior and interior design parameters of the Great Pyramid of Giza. Learn here the historical significance of both the "golden ratio" and the equal-sided pentagon (and pentagram); a new theory for the derivation of the ancient Egyptian Royal Cubit; a diagrammatic method by which the square root of any number can be derived; how to diagrammatically derive a trigonometric table; a relatively easy to follow presentation of Euclid's derivation of the 36 angle ; and now a newly added section detailing the derivation diagrams for the interior design parameters of the Red, Bent, Khafre, and Great Pyramids. Introduction As one delves into the exterior design details of the Great Pyramid, two striking numerical correlations emerge from the data, and they compel the serious student either to explain these correlations as being nothing more than coincidence or to deal with their implications. These findings are: 1) that the pyramid's cross-section, as defined by its slant height of 611.5 feet divided by one half the length of a side (= 377

28. Golden Ratio Provides a golden ratio GreekFace activity for 5th grade and up, plus a link for extra information. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

29. The Golden Ratio This ratio was named the golden ratio by the Greeks. In the world of mathematics, Phidias widely used the golden ratio in his works of sculpture. http://www.geom.uiuc.edu/~demo5337/s97b/art.htm

The Golden Ratio 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.

30. 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/

Web and Palm OS Applications for Health Care LMRP Tool 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.

31. The Golden Mean The Golden Mean. The Golden Mean (or Golden Section), represented by the If you then take the ratio of any two sequential numbers in this http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

32. Math Forum: Ask Dr. Math FAQ: Golden Ratio, Fibonacci Sequence The golden ratio/Golden Mean, the Golden Rectangle, and the relation between the Fibonacci Sequence and the golden ratio. http://mathforum.org/dr.math/faq/faq.golden.ratio.html

Ask Dr. Math: FAQ G olden R atio, F ibonacci S equence Dr. Math FAQ Classic Problems Formulas Search Dr. Math ... Dr. Math Home Please tell me about the Golden Ratio (or Golden Mean), the Golden Rectangle, and the relation between the Fibonacci Sequence and the Golden Ratio. The Golden Ratio The golden ratio is a special number approximately equal to 1.6180339887498948482. We use the Greek letter Phi to refer to this ratio. Like Pi, the digits of the Golden Ratio go on forever without repeating. It is often better to use its exact value: The Golden Rectangle 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

33. Math Forum - Ask Dr. Math Archives: High School Fibonacci Sequence/Golden Ratio Fibonacci sequence in nature, Golden Mean, golden ratio 12/6/1994 The Relation of the golden ratio and the Fibonacci Series 1/28/1996 I am trying http://mathforum.org/library/drmath/sets/high_fibonacci-golden.html

Ask Dr. Math High School Archive Dr. Math Home Elementary Middle School High School ... Dr. Math FAQ TOPICS This page: Fibonacci sequence, golden ratio Search Dr. Math See also the Dr. Math FAQ golden ratio, Fibonacci sequence Internet Library golden ratio/ Fibonacci HIGH SCHOOL About Math Analysis Algebra basic algebra ... Trigonometry Browse High School Fibonacci Sequence/Golden Ratio Stars indicate particularly interesting answers or good places to begin browsing. Appearances of the Golden Number Why does the irrational number phi = (1 + sqrt(5))/2 appear in so many biological and non-biological applications? Calculating the Fibonacci Sequence Is there a formula to calculate the nth Fibonacci number? Congruum Problem I have found a reference to Fibonacci and his congruum problem. But something has me stumped... Fibonacci sequence in nature, Golden Mean, Golden Ratio I need examples of where the Fibonacci sequence is found in nature and how it relates to the Golden Mean. Fibonacci Series I was helping an Algebra student with a "bonus" problem recently. It asked something about drawing a spiral using the Fibonacci series. What is this series? Does it draw a spiral? Golden Ratio Do you have any topics that I can use in my term paper about the golden ratio?

34. 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/

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 bracelets earrings and altar pieces.

35. Cynthia Lanius' Lessons: The Golden Ratio Mathematics lessons for elementary, middle, and high school including geometry. http://math.rice.edu/~lanius/Geom/golden.html

Cynthia Lanius Thanks to PBS for permission to use the Pyramid photo. Golden Ratio 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

36. Division In Mean And Extreme Ratio The base angle of the largest trinalges of most representations of Sri Yantra are about 52 degrees, close to the base angle of the Great Pyrmaid of Cheops, which is 51deg50'. With such a base angle, the ratio of the hypotenuse to half the base is phi, the golden ratio. http://alumni.cse.ucsc.edu/~mikel/sriyantra/golden.html

Division in Mean and Extreme Ratio The base angle of the largest trinalges of most representations of Sri Yantra are about 52 degrees, close to the base angle of the Great Pyrmaid of Cheops , which is 51deg50'. With such a base angle, the ratio of the hypotenuse to half the base is phi, the Golden Ratio The design was investigated with the largest two triangles having this base angle. The construction continues similar to the 7x7 grid method. The result is striking, for apart from the fact that the error (at Z and W) is not noticeable, the overall shape is very simlar to examples from the literature . The error is only .3616% of length of the diameter. A small change in base angle results in large error - a 53 degree angle has an error of 9.125%! 1. Draw a rectangle of 2 x 1 units (ABCD) for construction of the large pyramid- angled triangles on base DC. The centre of DC is E. 2. Draw the diaganol DB. It's length is sqr-root 5, by Pythagoras. 3. Draw a circle of radius one centered at point B. Extend the diagonal. 4. Bisect the extended diaganol, creating two line segments of length sqr-root 5 plus 1, divided by 2. This length is phi!

37. Golden Ratio - Wikipedia, The Free Encyclopedia The golden ratio is an irrational number, approximately 1.618, that possesses Shapes defined by the golden ratio have long been considered aesthetically http://en.wikipedia.org/wiki/Golden_ratio

Golden ratio From Wikipedia, the free encyclopedia. It has been suggested that this article or section be merged with Golden Mean Discuss This article is about the mathematical ratio. For the Aristotelian concept of "golden mean" see Nicomachean Ethics The golden ratio is an irrational number , approximately 1.61803..., that possesses many interesting properties. Shapes defined by the golden ratio have long been considered aesthetically pleasing in Western cultures, reflecting nature's balance between symmetry and asymmetry and the ancient Pythagorean belief that reality is a numerical reality, except that numbers were not units as we define them today, but were expressions of ratios. The golden ratio is still used frequently in art and design. The golden ratio is also referred to as the golden mean golden section golden number divine proportion or sectio divina Contents History A startlingly quick proof of irrationality Alternate forms Mathematical uses ... edit History The golden ratio was first studied by ancient mathematicians due to its frequent appearance in geometry . The golden ratio may have been understood and used by the Egyptians. The discovery of irrational numbers, numbers that cannot be represented as an exact ratio of two

38. American Phi Music, story and poetry of the golden ratio. http://members.aol.com/loosetooth/phi.html

39. Golden Ratio - Wikipedia, The Free Encyclopedia The golden ratio is still used frequently in art and design. The golden ratio is also referred to as the golden mean, golden section, golden number, http://en.wikipedia.org/wiki/Golden_mean

Golden ratio From Wikipedia, the free encyclopedia. (Redirected from Golden mean It has been suggested that this article or section be merged with Golden Mean Discuss This article is about the mathematical ratio. For the Aristotelian concept of "golden mean" see Nicomachean Ethics The golden ratio is an irrational number , approximately 1.61803..., that possesses many interesting properties. Shapes defined by the golden ratio have long been considered aesthetically pleasing in Western cultures, reflecting nature's balance between symmetry and asymmetry and the ancient Pythagorean belief that reality is a numerical reality, except that numbers were not units as we define them today, but were expressions of ratios. The golden ratio is still used frequently in art and design. The golden ratio is also referred to as the golden mean golden section golden number divine proportion or sectio divina Contents History A startlingly quick proof of irrationality Alternate forms Mathematical uses ... edit History The golden ratio was first studied by ancient mathematicians due to its frequent appearance in geometry . The golden ratio may have been understood and used by the Egyptians. The discovery of irrational numbers, numbers that cannot be represented as an exact ratio of two

40. 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

Ask Dr. Math High School Archive Dr. Math Home Elementary Middle School High School ... Dr. Math FAQ TOPICS This page: Fibonacci sequence, golden ratio Search Dr. Math See also the Dr. Math FAQ golden ratio, Fibonacci sequence Internet Library golden ratio/ Fibonacci HIGH SCHOOL About Math Analysis Algebra basic algebra ... Trigonometry Browse High School Fibonacci Sequence/Golden Ratio Stars indicate particularly interesting answers or good places to begin browsing. Appearances of the Golden Number Why does the irrational number phi = (1 + sqrt(5))/2 appear in so many biological and non-biological applications? Calculating the Fibonacci Sequence Is there a formula to calculate the nth Fibonacci number? Congruum Problem I have found a reference to Fibonacci and his congruum problem. But something has me stumped... Fibonacci sequence in nature, Golden Mean, Golden Ratio I need examples of where the Fibonacci sequence is found in nature and how it relates to the Golden Mean. Fibonacci Series I was helping an Algebra student with a "bonus" problem recently. It asked something about drawing a spiral using the Fibonacci series. What is this series? Does it draw a spiral? Golden Ratio Do you have any topics that I can use in my term paper about the golden ratio?

Page 2     21-40 of 111    Back | 1  | 2  | 3  | 4  | 5  | 6  | Next 20