
Fibonacci Ratio: In mathematics, the Fibonacci numbers are the numbers in
the following integer sequence:
0, 1, 2, 3, 5, 8, 13,
21, 34, 55, 89, 144,...(Sequence A000045 in OEIS)
By definition, the first two Fibonacci numbers are 0 and 1, and each subsequent
number is the sum of the previous two. Some sources omit the initial 0, instead
beginning the sequence with two 1s.
In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence
relation.
With seed values
Fibonacci Retracement: In technical analysis, Fibonacci retracement is created
by taking two extreme points (usually a major peak and trough) on a stock chart
and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%,
61.8% and 100%.
The Fibonacci sequence of numbers is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,
55, 89, 144, etc. Each term in this sequence is simply the sum of the two preceding
terms and sequence continues infinitely. One of the remarkable characteristics of
this numerical sequence is that each number is approximately 1.618 times greater
than the preceding number. This common relationship between every number in the
series is the foundation of the common ratios used in retracement studies.
The key Fibonacci ratio of 61.8%  also referred to as "the golden ratio" or "the
golden mean"  is found by dividing one number in the series by the number that
follows it. For example: 8/13 = 0.6153, and 55/89 = 0.6179. The Fibonacci sequence
of numbers is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Each
term in this sequence is simply the sum of the two preceding terms and sequence
continues infinitely. One of the remarkable characteristics of this numerical sequence
is that each number is approximately 1.618 times greater than the preceding number.
This common relationship between every number in the series is the foundation of
the common ratios used in retracement studies. The key Fibonacci ratio of 61.8%
 also referred to as "the golden ratio" or "the golden mean"  is found by dividing
one number in the series by the number that follows it. For example: 8/13 = 0.6153,
and 55/89 = 0.6179. The 38.2% ratio is found by dividing one number in the series
by the number that is found two places to the right. For example: 55/144 = 0.3819.
The 23.6% ratio is found by dividing one number in the series by the number that
is three places to the right. For example: 8/34 = 0.2352.
