mathematical concepts of the golden ratio were known throughout the history. Keywords: Golden Ratio, Golden Triangle, Regular pentagon, Fibonacci. Golden Ratio, Fibonacci Numbers, and the Golden Spiral — Troy Henderson. The heavens are telling of the glory of God; and their expanse is declaring the. way or the most common definition is that of finding the golden section of a straight line. This problem was originally solved in Euclid's elements. Let a line AB of.

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The universal ratio of beauty is the 'Golden Ratio', found in many structures. This ratio comes from Fibonacci numbers. In this article, we explore this concept. since Fibonacci numbers and the golden ratio are topics not usually covered in a University numbers in terms of powers of the golden ratio and its reciprical. Geometrical Substantiation of Phi, the Golden Ratio and Abstract Golden Proportion or Golden Ratio is usually denoted by the Greek letter.

The golden ratio is not derived from Fibonacci series, it comes from finding two segments of a line in which the ratio of the line to the biggesbsegment equals the ratio of thte biggest segment to the smallest one. Again Phi is the 21st letter of the Greek alphabets and the number, 21, is the 8th member of the Figure 1. Pacioli was a contemporary of Da Vinci's, and the book contains dozens of beautiful illustrations of three-dimensional geometric solids and templates for script letters in calligraphy. Mark Baker says: The degree to which you rely on the golden ratio is up to you, but even the slightest application of its proportions can really add appeal to your designs. As the author of this site since , I've changed my views and the information on this site as well. The resulting face will look something more like this:

The proportion The main contribution of the paper is to study about the known as the Golden Mean has always existed in mathematics validation and substantiation of the Equation of Phi based on and in the physical universe and it has been of interest to classical geometric relations.

The technique can be considered as mathematicians, physicists, philosophers, architects, artists and an interesting strategy to prove the Equation of Phi. In the early days of the 19th century it was I. Basically golden ratio is always considered as the most many mathematicians. It is unknown exactly when the idea was pleasing proportion to human eyes and many work has been first discovered and applied by mankind. The presence of both done, also going on where the ratio concept are analyzed.

Pi and Phi in the design of the Pyramids represents that the Human detection, human face detection and recognition, Egyptians were aware of the ratio. The Greeks based the design emotion detection, beauty detection of an image, biological of the Parthenon example of Doric architecture, the main inspired robot structure design, locomotion analysis of human temple of the goddess Athena built more than years BC and animals are some of the fields where the golden section on this proportion.

Phidias, a Greek sculptor and proportion are being used [5]. In Elements, Euclid - BC referred a line by dividing at the 0. Euclid also established a A. Golden Section link of the number with the construction of a pentagram [2].

The Fibonacci pattern was ascertained around AD. The For a line segment, golden section can be considered as a exceptional and unique property of the numerical series was point where the line is divided into two sections containing a established by Leonardo Fibonacci - AD , an unique property such as the ratio between the bigger segment Italian born mathematician, but its quiet clear that he even and the shorter segment should be equal to the ratio between realized its relation to the Phi and the Golden Proportion [2].

The ratio is The concept was first called the Divine Proportion in the early approximately 1. According to the theory, the artworks of the five Platonic solids.

This Vinci was the first man who called it the Sectio Aurea, means relation can be shown by the following equation, Golden Section in Latin. The Renaissance artists used the Golden Mean largely in their various paintings and sculptures 1. From the most primitive time it is often been the Divine Proportion. Consequently, the idea has been incorporated into many art The term Phi was not used before the 's until the works, architectural design and mathematical analysis.

American mathematician Mark Barr used the Greek letter Phi to designate this proportion. Again Phi is the 21st letter of the Greek alphabets and the number, 21, is the 8th member of the Figure 1.

A line segment AC is divided at the golden section point B. Fibonacci series. Golden Rectangle series. It is a particular rectangle where the ratio The characteristics of Phi have some interesting theological between the length and width is exactly the same as the value implications.

ABCD is a golden rectangle shown in Figure 2. A in the 19th century [5]. Fechner was the first person who fixed straight line MN can be considered through the golden section his analytical gaze upon this task as early as the s.

It appeared in rectangle.

Another straight line, IJ, can be drawn between the Roger Penrose's discovery of Penrose Tiles in the 's, two golden sections of the two sides AD and BC that will make which first allowed surfaces to be tiled in five-fold symmetry another smallest square, MGJC, and another golden rectangle, [1] [2]. It appeared again in in the aluminium-manganese GNBJ.

This process can be continued for ever which will alloy Al6Mn , known as quasi-crystals, which was newly create smaller to smallest golden rectangles. The two lines MN discovered form of matter [2] [5]. Based on the different position of thee golden section of Golden rectangle is alsoo known as whirling square a line, there can be at most four golden means m in a golden rectangle because of the speciaal property of subdividing into a rectangle.

The proportionally the other possible golden mean points of thee golden rectangle, decreasing squares produce a spiral by using the arcs having ABCD. The two diagonals intersect at the point O which is called the sink centre of the spiral and all other diagonals ofo the smaller golden rectangles must lie on these two diagonalss. In Figure 3 the largest arc, AE, of the spiral has the radius equal to the edge of the big square AFED and the point F is representing as the centre of that arc.

The second biggest square, CGME, have thhe second arc of the golden spiral while the radius is equal to the side of that square and the point Figure 2.

M is its centre. This process can be continued and this will construct the spiral shape calledd the golden spiral. There are some common techniques to t draw a golden rectangle. Firstly, a perpendicular line havinng the length equal C. Fiigure 4 shows the two types of at the golden section point N.

Based on Figure length of p. So, the biggest possible golden rectangle, ABCD, 4 a and b , equation 1 can be b written as, can be drawn where the length of the rectanngle is same as the base line. Secondly, one of the segments of the base line 1.

Based on this L-shaped form, a golden rectangle can be drawn [5]]. In Figure 2 the bigger segment, AN, of the base line is foldedd at 90o angle with the smaller segment, NB.

Thiirdly, a square can be considered to draw a golden rectanglee. Considering the midpoint of the base of the square as the cenntre of a circle and the length between the upper corner and thhe midpoint as the radius, an arc can be drawn that will interseect the base line of the square. Drawing a rectangle based on thhe new intersecting point and the square will make a golden rectaangle [1] [2] [5]. The arc MB intersects at the point B with the extensioon of the base line Figure 4.

So, using the intersecting point the connstructed rectangle becomes the golden rectangle, ABCD. These pentagon and pentagram is possible to characterized using u the golden triangle. The decagram and decagon also yield a series of golden triangles by connecting the centre point withh any two adjacent edges [1] [5]. Figure 3. Static rectangles do not produce a series of visually pleasing ratios of surfaces while subdividing. On the other hand, dynamic rectangles produce an endless amount of visually pleasing harmonic subdivisions and surface ratios.

Any of these rectangles can easily be drawn into reciprocal triangles. Figure rectangles etc. The easiest way to start using the golden ratio is to implement it within your typographical graphic design elements.

Using the golden ratio, you can determine the best size for the headings by multiplying by 1. Since the headline text is the bigger element, you would divide by 1. Naturally, a simple way to incorporate the golden ratio into a design is to crop photos or any other images you may use into a golden rectangle shape. For example, you could crop a photo to golden proportions in such a way that the main focal point of the image is at the center of the corresponding golden spiral.

For example, say you had an image in your design that was 2 inches wide and you wanted to pair it with a smaller picture. A 2 inch image divided by 1. You could also add a larger image to the design, which would require you to multiply your 2 inch photo by the golden ratio to end up with roughly 3. But unlike the rule of thirds grid, you can move the golden rectangle around to suit your needs.

A common trick in web design is to use the golden ratio to divide space between the body of the website and the sidebar. The same technique can still apply to print design—but you have to be careful.

Web designers are working within a horizontal medium, and much of print design is vertically oriented. The advantage to working in print is that the size of the media itself can be measured out according to the golden ratio.

However, there are also times when print designers are constrained to a standard size and unable to use custom print options. Thankfully, you can still apply the golden ratio to the layout of any print template; you just have to be smart about it.

The good thing about presentation folders and other print materials that open up is that they give you both a vertically and horizontally aligned canvas to work with. Whenever you open up a presentation folder, the combined interior creates one big horizontal rectangle.

You could also implement the same kind of sidebar idea that web designers use by having a custom-made info flap inside the folder. Even the position of your printed design elements inside the folder can have an aesthetic appeal to the viewer if you place them according to the golden proportion. We gathered up some of the best tools and apps to help you incorporate the golden ratio into your design. The degree to which you rely on the golden ratio is up to you, but even the slightest application of its proportions can really add appeal to your designs.

If you want to be extra sure your design is up to snuff, try measuring it up to both the golden ratio and the rule of thirds. If your design satisfies both, you could have something great on your hands.

This work by Company Folders, Inc. With his team of designers and experts, he helps customers put forth the best possible impression with high-quality collateral.

Thanks for posting golden ratio.

Plz, if u have some more knowledge about g-lden ratio and related graphic design knowledge,Send me. Thanks for everyrhing. After reading this.. Makes sense though, and i didnt realize the history behind it. Is there a plugin of some kind that will set up or reference the Golden Ratio?

Id like to recommend it to my associate designers if it does exist. Yes, there are several plugins that reference the Golden Ratio.

Happy designing! I really appreciate your efforts for creating such a great golden ration designs. It really helped me in designing,. Nice work, but a bit unaccurate, The golden ratio was well known centuries before Fibonacci was even born.

The golden ratio is not derived from Fibonacci series, it comes from finding two segments of a line in which the ratio of the line to the biggesbsegment equals the ratio of thte biggest segment to the smallest one. What a great article, thank you Vladimir. The National Geographical have just released an interesting book about the Golden Ratio in their our mathematical world series.

Also there is a great Android App which lets us find our own example of the Golden Ratio — https: We are the standard bearer of online folder printing delivering absolute quality infused with the design knowledge of an advertising agency. Learn More. We guarantee the quality of our products for a lifetime. See Details. New Here? Visit our store: See Products. Shares 8K.