**A bit history**

Leonardo of Pisa (Fibonacci) introduced the succession that bears his name, in a treatise on mathematics in 1202 in his work Liber Abaci in old Latin language, this succession is the key to form the quadrants and then the spiral, although it was discovered by the Hindu mathematician Pingala about the year 200.

Fibonacci sequence Is an infinite mathematical sequence of integers numbers.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 …

For our calculations of the FDM and the spiral the Fibonacci sequence is used up to 34.

Each new element is calculated by adding the previous two elements to it.

(0 + 1) = 1; (1 + 1) = 2; (1 + 2) = 3; (2 + 3) = 5 ……

X0 = 0 i x1 = 1; If n> 1 xn = xn-2 + xn-1

The quadrants are created based on the golden ratio, which uses the golden number 1.618 … and its inverse 0.618.

Many things of nature fulfill the sequence, we do not know why, there is much mysticism about this, focusing on the scientific fact, it was decided to start testing with Fibonacci for the signatures, because a signature is a natural spontaneous form of each person, and the Fibonacci succession always appears in natural and spontaneous phenomenon, leaving the building of temples, churches and biological things, today use it secretly in predictions of the stock market, to anticipate tendencies of the graphs, for example.

More info about this https://en.wikipedia.org/wiki/Golden_ratio

According to our research, we must draw the spiral in a special way for our case.

Usually when using Fibonacci in drawing, the spiral is first drawn and then the shape of the spiral is use for drawn, but we start with a signature that is already drawn, so we cannot do this, and we have to draw the spiral on the signature shape and last define the quadrants.

The spiral is calculated inversely to what Fibonacci tells us, Fibonacci indicates that it should be done from the center to the outside, but from what I said before, it cannot be and here it is calculated, from the outside towards the center, this Inverts the quadrants and the largest dimension is the first quadrant.

This is the ordination quadrants with our Fibonacci spiral. Only we use the Q1, Q2, Q3 and Q4 quadrants Q5, Q6 and Q7 is not used.

This is an example with black rectangles, so that the position of the points is ideal, the position follows a color code, to position the maximum points points up, right, down and left.

For the null quadrants (without points) or manually turn null (see corresponding video) the points are placed in a predetermined position by the software and can not be moved.

**Explanation about results table.**

The graphics show **8 points (F0 to F7)** in function to **%Values Fibonacci Fan**, NEGA defined before a **vanishing point**, **on same position, depending on whether the spiral is Horizontal or Vertical**, to create fan segments towards the points, and search the segment with maximum length, this is result 100% in our case is segment to F3 point in KNOW-2 and F2 in QUEST-4, and calculates the other segments percentages relative to this in the list, on Questioned & Know.

The **Differential Fibonacci Fan** result is calculated over two values the **Gradient** and **%Gradient**. This results not can to be showed on the graphic because are two final values (shadowed yellow), the value lists are used for calculating this.

The **Gradient** is the differential numeric values between **Questioned – Know** on list, is showed on real number format (not percentage%). The final result about Gradient (shadowed yellow), is calculated with the differential between maximum value and minimum value on the list.

The **%Gradient** is numeric percentage between **Questioned / Know** on list. The final result about %Gradient (shadowed yellow), is statistical arithmetic average of the value list.

**Final Results**

**Accuracy Matching **

Is calculated on value list Gradient, this result is *Absolut value (1.0 – Gradient)* and this value will be 100% if two signatures are identical geometrical shapes.

**Trust collation**

Is calculated with this formula **% Gradient / Fibonacci Coefficient**

*.*

**Fibonacci Coefficient** is a secret that we will not publish, is based in Accuracy Matching value, it has been calculated empirically testing with more signatures, provided by the association that collaborates with me.

We never sign totally the same, if the two signatures are totally equal, this coefficient will be zero, because **if two signatures are very equal one of them is a forgery**. The **Fibonacci coefficient** is the one that regulates this until a limit, from which it is considered that the signatures have a proportional similarity, and then the final value of the **Trust collation** is higher, although it will always be between 60% and 100%, below or above these values, **Trust collation** shall be calculated 0.0%. For this, totally identical graphics does not mean here is a positive thing.

**Fibonacci similarity **

Is statistical arithmetic average between **Accuracy Matching value and Trust collation value. **

**This is explained in PDF quick user manual about NEGA Acpc.**

**This final result is a mathematical value, this means that the expert must decide whether to act accordingly to the result, the mathematics are exact and if we obtain for example 79.9%, mathematically will be indeterminate for NEGA (orange) , because is within the range 60% to 79%, for to be valid would be > = 80% but, the machines fortunately do not think like us, and then you’d have to ask yourself with another type of analysis or method if you think it’s worth considering 79.9% = 80%.**