The Handbook of Technical Analysis + Test Bank_ The Practitioner\'s Comprehensive Guide to Technical Analysis ( PDFDrive )

Fibonacci Number and Ratio Analysis

As it turns out, there is only one ratio that satisfies the following condition

where the ratios of the lengths are:

BC/ABAC/BC=

That unique ratio is 1.618 (to three decimal places), which is also referred to

as the Golden Section. This mysterious property has inspired mankind since its

discovery, and as a consequence, many monuments and works of art have incor-

porated various aspects of the Golden Section within their construction. This ratio

is also purportedly found in nature as an underlying fabric of creation.

10.2.2 the simple mathematical Derivation of phi (Φ)

We can easily derive the value of Φ mathematically by extrapolating the ratio in

the limit of two adjacent numbers in a Fibonacci series. Here is one of the many

mathematical methods that may be employed to derive this ratio.

As seen earlier, a Fibonacci sequence may be defined as:

F F Fnnn+ 1 =+ − 1

Let us now divide across by Fn, giving us:

( ) ( ) ( )

( ) ( )

F /F F /F F /F

F /F 1 F /F

1 1

1 1

nnnnnn

nn nn

+ −

+ −

=+

=+

(1)

Figure  10.3 The Lucas‐Based Fibonacci Ratio (Fn/Fn−1) versus the Lucas Number

Sequence.

Figure 10.4 The Golden Ratio (or Section).