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# The Golden Ratio

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### The Golden Ratio

1. 1. Table of Contents Name Page No. What is the Golden Ratio? 1 What is the idea behind the Golden Ratio? 2 What is the symbol for the Golden Ratio? 3 Who discovered the Golden Ratio? 4 What are five other names for the Golden Ratio? 5 Golden Ratio in Nature 6 Golden Ratio in works of Art 7 Golden Ratio in Architecture 8 Golden Ratio in Human Body 9 Bibliography 10
2. 2. What is the Golden Ratio? o The Golden Ratio is or equal to: 1.61803398874989484820 (etc.) o The golden ratio is a special number approximately equal to 1.618. o It appears many times in geometry, art, architecture and other areas. o In the Golden ratio only the first few numbers will be shown. For example: 1.618.
3. 3. What is the idea behind the Golden Ratio? The Idea behind the Golden Ratio is that: o If you divide a line into two parts the longer part divided by the smaller part is also equal to the whole length divided by the longer part then you will have the golden ratio.
4. 4. What is the Symbol for the Golden Ratio? The symbol for the Golden Ratio is:
5. 5. Who discovered the Golden Ratio? o A sculptor named Phideas was known to apply the 'golden ratio' prior to Pythagoras. o Pythagoras was known to observe the phenomenon of the golden ratio, which is in fact an aesthetic proportion. o Plato also observed it and applied it to his philosophy, and certainly one senses it in his ideas of perfection and the 'solids' which he attempted to apply to the cosmos. o Kepler tried to apply Plato's solids and ended up creating his own solids and discovering the elliptical nature.
6. 6. What are five other names for the Golden Ratio? Five other names for the Golden Ratio: o golden mean o golden number o divine proportion o divine section o golden proportion
7. 7. Golden Ratio in Nature o The most common example is that of the Nautilus shell. o The shell is composed of concentric spirals, and in this case, the ratio of each spirals' diameter to the next smaller spiral is equal to phi.
8. 8. Golden Ratio in works of Art o The Dutch artist Mondrian explicitly used the golden ratio in his paintings. He used horizontal and vertical black lines that outlined blocks of colour (in white, red, blue and yellow). o The proportion of the golden ratio could be found in many of the rectangles. o As well, the area covered by certain colours compared to others also respects the golden ratio.
9. 9. Golden Ratio in Architecture o When the basic phi relationships are used to create a right triangle, it forms the dimensions of the great pyramids of Egypt, with the geometry shown below creating an angle of 51.83 degrees, the cosine of which is phi, or 0.618.
10. 10. Golden Ratio in Human Body o 5 appendages to the torso, in the arms, leg and head. o 5 appendages on each of these, in the fingers and toes o 5 openings on the face. o 5 senses in sight, sound, touch, taste and smell.
11. 11. Bibliography Internet Sources: o http://www.goldennumber.net/architecture/ o http://www.goldennumber.net/human-body/ o http://eyephi.com/phi-the-golden-ratio/history- of-phi-the-golden-ratio/ o http://mathworld.wolfram.com/GoldenRatio.html o http://www.goldennumber.net/golden-ratio- history/