Space+&+Scale


 * //The Golden Section //**

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean. Other terms encountered include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias. The golden ratio is often denoted by the Greek letter phi, usually lower case (φ). Throughout history, the Golden ratio has been considered the most pleasing to the eye. The Golden Section is a ratio or proportion based on a phi (φ = 1.618033988749895... ).  It can be derived with a number of geometric constructions, each of which divides a line segment at the unique point where: the ratio of the whole line (A) to the large segment (B) is the same as the ratio of the large segment (B) to the small segment (C)    In other words, A is to B as B is to C. This occurs only where A is 1.618 ... times B and B is 1.618 ... times C.

The figure illustrates the geometric relationship that defines this constant.

   Construction of a golden rectangle: 1. Construct a unit square (red). 2. Draw a line from the midpoint of one side to an opposite corner. <span style="color: #808080; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">3. Use that line as the radius to draw an arc that defines the long dimension of the rectangle.

<span style="color: #808080; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">This ratio has been used by mankind for centurias

<span style="color: #808080; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px;">Its use may have started as early as with the Egyptians in the design of the pyramids,

<span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"> <span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">

<span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"><span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">The Greeks recognized it as "dividing a line in the extreme and mean ratio" and used it for beauty and balance in the design of architecture

<span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"><span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">

<span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"><span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"><span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">The Renaissance artists knew it as the Divine Proportion and used it for beauty and balance in the design of art

<span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">

<span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">It was used in the design of Notre Dame in Paris and continues today in many examples of art, architecture and design. <span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"> <span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"> <span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"> Today architects are still frequently using the golden section in their work. In the United Nations building, the ratio of width of the building compared with the height of every ten floors is Golden <span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"> <span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">The CN Tower in Toronto, the tallest tower and freestanding structure in the world, contains the golden section in its design. The ratio of its total height of 553.33 meters to the height of the observation deck at 342 meters is 1.618. <span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;"><span style="color: #808080; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 14px; text-align: justify;">It also appears in the physical proportions of the human body, movements in the stock market and many other aspects of life and the universe.

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