goldenratio

goldenratio - Upon his election in 1981 as president of the...

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Upon his election in 1981 as president of the Republic of France, François Mitterrand had a major decision to make. 1 It was not a dilemma concerning the French economy nor was it a decision on where to deploy the French Legionnaire; rather, the decision concerned a more homely problem for France. One of the country’s great national treasures, the Louvre, was in disrepair. Looking for someone to resurrect the beautiful museum, in a controversial move, Mitterrand hired I.M. Pei, a Chinese American architect to restore the Louvre. His solution, to construct a series of glass pyramids, was considered unique and extraordinary for its time. What Pei really hit on, in actuality, was an ancient and mystical concept that defined great architecture of the past. This concept, called the golden ratio, has been missing in current architecture since the twentieth century. Attempts to understand and reproduce the magic of the golden ratio have largely been unsuccessful. The term “golden ratio” is actually one of many that describe this concept. The golden ratio is also known as the golden number, golden section, and divine proportion. It is written as phi (Φ) in the Greek alphabet. All, nevertheless, refer to the same number: 1.6180339887. 2 To arrive at the golden ratio, first begin with a square. A square can be divided into two equal parts by drawing a diagonal line from one corner to the opposite corner. The relationship between one side of the square to the diagonal line is 1: 2 Furthermore, placing two squares together creates a double square, or a rectangle. The relationship between the two differing sides of the rectangle is two to one. As with one square, a rectangle can be divided into two equal parts by drawing a diagonal line from one corner to the opposite corner. The relationship between one side of the rectangle to the diagonal line is 1: 5 From the double square arises the golden ratio. 3 According to Euclid, the first mathematician to define the golden ratio, this ratio comes from the definition of proportion. In Euclid’s definition, “A straight line is said to have been cut
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in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.” (Livio 3) In accordance with Euclid’s definition, from looking at Figure, if the ratio of the length of AC to the length of CB is equal to the ratio of the length of AB to the length of AC, then the line is said to be in proper ratio. This proper ratio is the mathematical basis for the golden ratio. The golden ratio is irrational because it does not have a fractional expression; it is neither a whole number nor a fraction that can easily be defined. From the golden ratio one can construct a golden rectangle, in which the ratio of the long side of a rectangle to its short side is equal to phi. A square added or subtracted from this golden rectangle can create a new golden rectangle. From these successive golden rectangles arises a golden spiral. Perhaps the most
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This note was uploaded on 02/10/2009 for the course AAH 2005 taught by Professor Grubiak during the Fall '08 term at Villanova.

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goldenratio - Upon his election in 1981 as president of the...

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