Also known as the Golden Ratio, the Fibonacci sequence was introduced by Leonardo Pisano Bogollo (1170-1250), an Italian mathematician from Pisa, and can be listed as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610……
The sequence can be infinitely extended and contains many unique mathematical properties:
1. After 0 and 1, each number is the sum of the two prior numbers (1+2=3, 2+3=5, 5+8=13 8+13=21 etc…).
2. A number divided by the previous number approximates 1.618 (21/13=1.6153, 34/21=1.6190, 55/34=1.6176, 89/55=1.6181). The approximation nears 1.6180 as the numbers increase.
3. A number divided by the next highest number approximates .6180 (13/21=.6190, 21/34=.6176, 34/55=.6181, 55/89=.6179 etc….). The approximation nears .6180 as the numbers increase. This is the basis for the 61.8% retracement.
4. A number divided by another two places higher approximates .3820 (13/34=.382, 21/55=.3818, 34/89=.3820, 55/=144=3819 etc….). The approximation nears .3820 as the numbers increase. This is the basis for the 38.2% retracement. Also, note that 1 – .618 = .382
5. A number divided by another three places higher approximates .2360 (13/55=.2363, 21/89=.2359, 34/144=.2361, 55/233=.2361 etc….). The approximation nears .2360 as the numbers increase. This is the basis for the 23.6% retracement.
Among of the key numbers mentioned, 1.618 refers to the Golden Ratio or Golden Mean. The inverse of 1.618 is .618. These ratios can be found throughout nature, architecture, art, and biology.