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Golden Ratio

How and where the Golden Ration is found. Madi 7W
by

Madison Harding

on 13 September 2012

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Transcript of Golden Ratio

THE GOLDEN RATIO The triangle that is shown in blue is 'The Ancient Triangle' it consists of the dimensions as following: sloping height, the perpendicular height and the measurement of half the base.These are the dimensions and measurements of the Golden Ratio. They may have designed this triangle to have an approximately perfect angle degree of 51.50 as the sloping angle degree of the Great Pyramid is 51.50 approximately. Another Aspect of the Golden Ratio is this equation. If you created a rectangle that was according to the dimensions of the pyramids it would fit perfectly inside the rectangle. The height of the Great Pyramid is approximately 146.5 meters in its original state and the base is 230.4. So 230.4 ÷ 146.5 = 1.57269625. This is only an approx. estimation and there is only a difference of 0.045337742 to the perfect Golden ratio Number. To the Egyptians the Golden Ratio was sacred as it was a perfect number. For this reason they used the Golden Ratio when designing and building The Great Pyramids. They used the Sacred Ratio in their Pyramids, the early stages of this was when the Ancient Egyptians discovered that a circles diameter is constant, later helping them to incorporate into their pyramids. This discovery was said to be found in the Fourth Dynasty and for their time was an extraordinary feat. Another Aspect of the Golden Ratio The Golden Ratio is found in music in several areas for example, the design of a musical instrument, octaves and musical notes and sequences. Below is a diagram of the design of a violin, the coloured lines show the proportions that the Golden Ratio is incorporated. Stradivari was aware of the Golden Number when creating his famous violins and designed the f-holes according to the Golden Ratio.

Almost every aspect of the violin's design is near perfect up to its scroll and even its whole body. The Golden Ratio in the design of a violin. Surprisingly the Golden Ratio can also be found in written pieces of music, for example Beethoven's Fifth Symphony. The Golden Ratio in the Fifth can be found exactly at the golden mean point 0·618 in bar 372 of 601 and again at bar 228. Below is the bar that shows the Golden Ratio in Beethoven's Fifth Symphony it is at the point of phi and repeats twice throughout the song. The real question is 'did he do this on purpose, or by accident' as he may have decided that is sounded the most pleasing and did not know of the existence of the Golden Ratio, or that is was also found in Music. The Golden Ratio in Beethoven's Fifth Symphony In mathematics, the Golden Ratio is made up of two quantities. The Golden Ratio occurs when these two quantities are added together and the ratio of this sum to the largest quantity is equal to the ratio of the largest quantity to the smallest quantity.

In other words the definition means that when you divide an objects length by its base you get the Golden Number. The Golden Ratio number is 1.6180339887 - this is an abbreviated version as the real number is infinite. This creates a spiral, which appears in nature, art, the human body and much more.

Artists use the Golden ratio in their masterpieces and Mother Nature utilises the Golden Ratio in her own artworks. Why? The reason is the Golden Ratio produces objects people consider to be most pleasing to the eye. Definition of Golden Ratio The Golden Ratio in an equation The symbol for the Golden Ratio is represented in several ways in mathematics for example: and the symbol shown below in the algebraic equation. This algebraic equation expresses the Golden Ratio (Phi). This equation uses a as the smaller quantity and b as the larger one. The equation is also explained in the definition. ϕ Did you know that the Golden Ratio can be found in the real world, it's not just a stale algebraic equation? The Golden Ratio can be seen in many of Leonardo Da Vinci's artworks for example the Mona Lisa, Michelangelo's the Statue of David and even the length of your arm. Diagrams of the Golden Ratio There are many different names for The Golden Ratio these include:
Φ Phi, The Golden Section, The Golden Number, The Golden Mean, Fibonacci proportion, Divine proportion, Divine section, Fibonacci Sequence or even the Sacred Ratio by the Ancient Egyptians. The Golden Ratio is linked to several things such as Architecture, Music, Art and Nature. Golden Ratio - Did you Know? The Golden Ratio in the Ancient World The Golden Ratio is not a recent mathematical discovery, in fact the Ancient Egyptians used this ratio to design and create their Great Pyramids. How they discovered this is unknown but there are many theories as to how they discovered this complex and difficult equation to built there stunning pyramids in near perfect proportion. IN THE GREAT PYRAMIDS 230.4 ÷ 146.5 = 1.572696246 The Golden Ratio is found in almost several aspects of the piano. Since the piano has thirteen notes in an octave, eight notes are found in a scale, the third and the fifth notes are the base of all chords. The scale of a piano goes from C to C and have eight whole tones for the complete musical scale. This scale has thirteen white keys and eight black keys and is split into two groups of three and two. So this comes to the final equation of the Golden Ratio in Piano, which is: which almost equals Phi (ϕ) which is 0.61803 etc. Golden Ratio in Piano 8 ÷ 13 = 0.61538 This is a design of a violin. The coloured lines show where the golden ratio is found in the design of a violin. The overall violin shape also fits the Golden Ratio, even down to the scroll and tuning pegs. The Egyptians were equipped with a knowledge far past there time. I believe a great example of this is the discovery of the Golden Ratio in their pyramids. From the facts I have found I feel that the Egyptians had a profound understanding of this complex equation and process and astonishingly achieved it with very basic tools. I think that the Egyptians did built the Great Pyramid to the proportions of the Golden Ratio but were quite advanced in their knowledge, much past their time. On the other hand I believe that while having an advanced knowledge for their time, they also had a basic understanding of the Golden Ratio principle. Maybe the Egyptians did not know the existence of the Golden Ratio, but found this design of pyramids, most pleasing to the eye. Also the Golden Ratio may have been a coincidence to appear in the Great Pyramid, the Golden ratio may in fact be a modern discovery. Contrary to this, I still believe that they possibly designed the Great Pyramid to the Golden Ration proportions, this is because we have no way of knowing what happened in the past if it was not recorded. Furthermore, since none of our egyptology scientists were present in the Egyptian time period it is almost impossible to have proof that they did know of the Golden Ratio apart from theories and possibilities. This is why I feel that they designed the Great Pyramid to the Golden Ration proportions Reflection and Evaluation These are the dimensions of the Great Pyramids. Please take into consideration that these measurements are approximate as they are to the dimensions of my model. Dimensions Base = 230.4
Sloping Height = 186.54 (the degree of 51.50)
Perpendicular Height = 146.5
Golden Ratio/Phi = 230.4 ÷ 146.5
= 1.57269625 The Ancient Triangle
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