Harmonic Numbers Harmonic numbers are the "Davinci Code" of most liquid financial markets. The numbers are derived from the Fibonacci summation series which starts with 0 and adds 1. Each succeeding number in the series adds the previous two numbers thus we have 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 to infinity. If you divide 55 by 89 you have the golden mean - .618. If you divide 89 by 55 you have 1.618.
.382 is the difference of 1.00 - .618 = .382
.618 is the golden mean (phi) and the square root of .382
.786 is the square root of .618
1.27 is the square root of 1.618 - it is also the hypotenuse of a right triangle
1.618 is difference of the square root of 4 minus .382 (2 - .382 = 1.618)
Fibonacci retracement is fundamentally based on a single number, which is Golden Ratio 1.618 or 0.618. <---
(1/1.618 = 0.618 .just from different side of perspective)
This single magic mysterious number does all the trick and covers the entire Fibonacci numbers or Levels.
0.618x0.618 =0.382
0.382x0.618 =0.236
0.236x0.618= 0.146
So, here is the full sequence of Fib numbers(levels) from 0.1 to 1.0
0.146 1- 0.854
0.236 1- 0.764
0.382 1- 0.618
0.5 mid point
0.618 1- 0.382
0.764 1- 0.236
0.854 1- 0.146
(1.236 = 1+ 0.236 = 0.382+ 0.854 = 0.618x 2 = 2- 0.764)
(1.618 = 1+ 0.618 = 0.764+ 0.854 = 1/ 0.618 = 2- 0.382)
0.5 is not a fib number to be precise, but it is as important as fib.
At the same time, there is a Gap between 0.382 and 0.618, PLUS
(0.382 + 0.618)/2
(0.236 + 0.764)/2
(0.146 + 0.954)/2
= 1 /2
= 0.5
which means that the middle point of
0.382 and 0.618
0.236 and 0.764
0.146 and 0.854
is 0.5, and obviously it is also the middle point of 0 and 1.
These numbers cover fair range between 0 to 1.0.
It's as simple as that, just +or -. based on 0,618=Golden Ratio
