The Golden Ratio, also known as the divine ratio or proportion, is a ratio
known for its relevance to art and aesthetics. This ratio is also present
in a variety of natural phenomena, particularly in the growth patterns of
plant and animal life. Some of the examples are the spirals formed by
nautilus shells, and the growth patterns of ferns. The Golden Ratio was derived by the ancient Greeks.
It is an irrational number with a value
f =
(1 + sqrt(5))/2 or 1.618...
Since the ancient
times,
artists and architects discovered that by utilizing this ratio, one could
create a feeling of aesthetics in their works. Both the ancient Greeks and the ancient Egyptians
used the Golden Ratio when designing their buildings and monuments.
An example of an ancient structure using this ratio is the Parthenon. Artists such as Leonardo da Vinci and George Seurat used the ratio in their paintings.
Some interesting properties of the golden
ratio is:
1/f = 1/f  1 =
0.618 ...
f^2 = f + 1 =
2.618 ...
Several geometric figures embodies the
golden ratio. These include the isocahedron, dodecahedron, pentagon,
pentagram, decagon, golden rectangle and golden
triangle.
More Mathematical Recreations
