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Example of Golden Ratio

This is a famous geometric expression, also known as the "golden mean", which dates back in mathematical expression to Euclid.

The basic equation is:

a+b = a = phi, leading to phi = 1+ the square root of 5 divided by two, giving the 'golden ratio', a figure given as 1.6180339887 a b

The concept has fascinated mathematicians artists, architects, and mystics for millennia. The golden ratio is considered aesthetically pleasing, and the basis of famous architectural designs. The golden ratio is also applied to other geometric shapes, like the pentagram, octagon and dodecahedron.

Examples of Golden Ratio:

http://en.wikipedia.org/wiki/Golden_ratio
http://www.geom.uiuc.edu/~demo5337/s97b/art.htm
http://simple.wikipedia.org/wiki/Golden_ratio
http://www.geom.uiuc.edu/~demo5337/s97b/

Image Example of Golden Ratio:

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.
3. Use that line as the radius to draw an arc that defines the long dimension of the rectangle.
The golden section is a line segment divided according to the golden ratio: The total length a + b is to the longer segment a as a is to the shorter segment b.
         


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