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The Golden Ratio

The most pleasing of all numbers, the golden ratio has properties which have delighted and inspired thoughtful people throughout the ages.  Also known as the Divine Proportion, it was venerated by Da Vinci, Seurat, Frank Lloyd Wright, and many others who drew upon the spiritial power of its geometric properties.  The golden ratio also famously plays a central role in many of the world's greatest pieces of architecture, such as the Egyptian Pyramids and the Greek Parthenon.
   
The Greek sculptor Phidias (c. 450 BCE) created sculptures of humans of which many proportions in the figures were golden.  The ratio is now given the short name "phi," which is the first letter in Phideas’ name.


A square may again be removed from a golden rectangle;
the remaining portion is another golden rectangle.
The process may be continued infinitely.


The Divine Proportion



A five-pointed star is called a pentagram.  When inscribed inside a pentagon, the figure contains the golden ratio is many many ways.  This symbol was the sacred symbol of the Pythagoreans.


Learn the mathematics and see more golden figures in the Naked Geometry Book.
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