2-- Proportion and progression
 

The word of proportion in the field of arts and designs represents the ratio of a quantity (length, area, etc.). For example, when there is a rectangular, the ratio of the lengths of the vertical and horizontal sides is called proportion. When the ratio is larger, it means a thin rectangular. When it is close to one, it means a rectangular close to a square. When we speak about a human figure like "That person has a good proportion", the word of proportion represents the ratio of head and height and the ratio of the body thickness and height (fatness). It means that the person is good looking.

(1) Golden ratio

The proportion has been studied since the age of Greeks. The golden ratio is especially famous among them. The proportion between the height of the roof and the length of the beam is a golden ratio as seen in the Parthenon shrine of Athens. The golden ratio is also said to be contained in the ratio of the important dimensions of Milo's Venus' statue. The golden ratio often appeared in the pictures of the modern times and the modern ages as well. A example of the nice looking "Pentagram" touching a pentagon from insides is illustrated in Figure 229. The ratios of AB:BD, AC:AD, and BC:CD of the "Pentagram" are all in the Golden ratio. Thus, the Greek people loved this star very much as sacred beautiful shapes. The reason that sacredness was felt in the golden ratio because the golden ratio contains a irrational number and it is f »1:1.618. In other words, it is a very complicated number, and is not easy to be treated arithmetically. But it is obtained easily geometrically with a beautiful ratio.
 
 

227 228   229 230   Figure 227: The Pantheon shrine (the outside frame which contains the roof is the golden rectangle). Figure 228: Composition by four golden rectangles. Figure 229: The star-shaped "Pentagram", which the Greeks loved. Figure 230: Composition which shows relations between the golden rectangles and squares.

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