(0),1,1,2,3,5,8,13,21,34,55,89,144,233,377...
The Golden Ratio of 1.618 is derived from the Fibonacci Sequence (above). The Fibonacci Sequence is found by starting with one. The next number is the sum of the two numbers that immediately preceded it: Starting with 1, 0+1=1, 1+1=2, 1+2=3, and so on.
The Golden Ratio is found by dividing any number in the Fibonacci Sequence by the number preceding it. At first the ratio is not quite exact, but eventually it plateaus at 1.618: 5/3=1.666; 13/8=1.625; 89/55=1.618; 377/233=1.618...
[click here to see it in action]
This number is not only signifcant in regard to the Fibonacci Sequence, however. When a rectangle with sides measuring lengths of successive numbers in the Fibonacci Sequence (233 and 144, for example) is divided to make a square, it creates a new rectangle with sides that have a ratio of 1.618, which can then be divided to make a new rectangle with sides in a ratio of 1.618... Connecting the dividing points then creates the Golden Spiral.
The Golden Spiral is found in everything from the arms of spiral galaxies to the pattern of leaves on a sunflower stem to the shape of a nautalis shell. It is even postulated to be the measure of the spiral in strands of DNA.
In terms of sacred geometry, even buildings of great antiquity demonstrate the Golden Ratio. In the Great Pyramid, the shape of the King's Chamber is a Golden Rectangle. Some contend this to be coincidence  a product of the natural stability of shapes that exhibit the Golden Ratio. That may satisfy some that the pyramid builders had no knowledge of the Golden Ratio, but it also denotes the inherent sacredity of the number, that it should be the best ratio for all structures, complex or otherwise.
The Golden Ratio is truly the Macrocosm within the Microcosm; the universe in the shell of a snail.
