 # Fibonacci & the Golden Ratio

This week we will explain how to create straight lines of support and resistance based on the golden number of the Fibonacci sequence.

Fibonacci was the nickname of the Italian Mathematician Leonardo de Pisa, who lived between the years 1170 and 1250 a.C. Considered one of the most renowned mathematicians in history, he is better known for two major accomplishments, the first was the introduction of arabica numbers (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) in Europe, which substituted roman numerals, and for discovering an infinite sequence of numbers initiated from 0 and 1 where each number is the sum of the two numbers before, known as the Fibonacci sequence.

The sequence is very simple, it begins with two numbers, 0 and 1. Adding these two, 0 + 1, gives you the next number in sequence, which is once again 1. Adding the last two numbers in the sequence, 1 + 1, we get 2. With 2 + 1 we get 3 and this goes infinitely:  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 5, 89, 144, 233, 377, 610, etc.

This sequence was discovered by Fibonacci to solve a problem of how many pairs of bunnies could be generated by a single pair within the course of a year. For those that don’t know the subject, the theory is that a single pair of bunnies will give birth to another pair of bunnies every month, given that the bunnies won’t die off and that the new pair of bunnies will take one month to reproduce, it’s possible to get to this sequence of numbers where each new number in the sequence will be the new number of the bunny population at the end of the month.

From the countless curiosities related to this sequence, it’s imperative to mention that it’s also found in the human body proportions, in the spiral-shaped galaxy, in the snail shell, in plant growth, in the ocean waves, in atoms and numerous other places in nature, which suggests that this is a sequence of numbers in equilibrium, that is present in everything we study and know.

Therefore, there wouldn’t be reasons not to apply Fibonacci’s discovery in the financial markets. In this post, we will embrace the utility of the golden number in the Fibonacci sequence when projecting prices in our graphs, so we can find support and resistance logics, what are in harmony with the law that governs everything else.

The golden number, better known as PHI (because of the greek sculptor Phidias) and represented by the same greek letter F, is a reason already known by men since Pythagoras, because it is present in all that we admire as beauty or harmon, from aesthetics to music. Its value is of 1.618033988749895 (rounded, the sequence of decimals is infinite). It just so happens that the last number of the Fibonacci sequence divided by the second to last, we get PHI. Since the sequence is infinite, the larger the two numbers that we use for this division, the closest the result is to PHI, for example:

F(n-1)
F(n-2)
F
34
21
1,6190476190476190476190476190476
89
55
1,6181818181818181818181818181818
610
317
1,6180371352785145888594164456233
1548008755920
956722026041
1,6180339887498948482045863457769

In the graphs we round the value of PHI to 1.618. That is, 0.618 more than 1, or 61.8%. Heading the opposite way, we have 1 – 0.618 or 0.382, or 38.2%.

Having these two percentages, we trace straight lines of support and resistance besides those that already exist and are well defined, finding price values that are in harmony, that tend to follow this proportion. It’s well-noted in the examples above, the correlation leans to PHI, but it is a rounding of this golden number, never it exactly.

The image below shows how the Fibonacci correlations are used in the graphics for the stock market, the blue lines are based on the percentages of 38.2% and 61.8% analyzed above, the red line of 50% divides the analysis proportionately at half and the white lines show the support and resistance that already existed and that were used as a base for the application of the Fibonacci correlation. The largest part of the text above explains how it makes sense to use Fibonacci in the technical analysis of the stock market.

## Its practical use is simple and even if you don’t have much interest in mathematics, it’s worth utilizing Fibonacci in your graphs, to understand the movement of past prices, or to make predictions of future possibilities.

This week we will explain how to create straight lines of support and resistance based on the golden number of the Fibonacci sequence.

Fibonacci was the nickname of the Italian Mathematician Leonardo de Pisa, who lived between the years 1170 and 1250 a.C. Considered one of the most renowned mathematicians in history, he is better known for two major accomplishments, the first was the introduction of arabica numbers (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) in Europe, which substituted roman numerals, and for discovering an infinite sequence of numbers initiated from 0 and 1 where each number is the sum of the two numbers before, known as the Fibonacci sequence.

The sequence is very simple, it begins with two numbers, 0 and 1. Adding these two, 0 + 1, gives you the next number in sequence, which is once again 1. Adding the last two numbers in the sequence, 1 + 1, we get 2. With 2 + 1 we get 3 and this goes infinitely:  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 5, 89, 144, 233, 377, 610, etc.

This sequence was discovered by Fibonacci to solve a problem of how many pairs of bunnies could be generated by a single pair within the course of a year. For those that don’t know the subject, the theory is that a single pair of bunnies will give birth to another pair of bunnies every month, given that the bunnies won’t die off and that the new pair of bunnies will take one month to reproduce, it’s possible to get to this sequence of numbers where each new number in the sequence will be the new number of the bunny population at the end of the month.

From the countless curiosities related to this sequence, it’s imperative to mention that it’s also found in the human body proportions, in the spiral-shaped galaxy, in the snail shell, in plant growth, in the ocean waves, in atoms and numerous other places in nature, which suggests that this is a sequence of numbers in equilibrium, that is present in everything we study and know.

Therefore, there wouldn’t be reasons not to apply Fibonacci’s discovery in the financial markets. In this post, we will embrace the utility of the golden number in the Fibonacci sequence when projecting prices in our graphs, so we can find support and resistance logics, what are in harmony with the law that governs everything else.

The golden number, better known as PHI (because of the greek sculptor Phidias) and represented by the same greek letter F, is a reason already known by men since Pythagoras, because it is present in all that we admire as beauty or harmon, from aesthetics to music. Its value is of 1.618033988749895 (rounded, the sequence of decimals is infinite). It just so happens that the last number of the Fibonacci sequence divided by the second to last, we get PHI. Since the sequence is infinite, the larger the two numbers that we use for this division, the closest the result is to PHI, for example:

Ex 1:
F(n-1) = 34
F(n-2) = 21 F=1,6190476190476190476190476190476 _____________________________

Ex 2:

F(n-1) = 89
F(n-2) = 55 F=1,6181818181818181818181818181818 _____________________________

Ex 3:
F(n-1) = 610
F(n-2) = 317 F=1,6180371352785145888594164456233 _____________________________

Ex 4:
F(n-1) = 1548008755920
F(n-2) = 956722026041 F=1,6180339887498948482045863457769

In the graphs we round the value of PHI to 1.618. That is, 0.618 more than 1, or 61.8%. Heading the opposite way, we have 1 – 0.618 or 0.382, or 38.2%.

Having these two percentages, we trace straight lines of support and resistance besides those that already exist and are well defined, finding price values that are in harmony, that tend to follow this proportion. It’s well-noted in the examples above, the correlation leans to PHI, but it is a rounding of this golden number, never it exactly.

The image below shows how the Fibonacci correlations are used in the graphics for the stock market, the blue lines are based on the percentages of 38.2% and 61.8% analyzed above, the red line of 50% divides the analysis proportionately at half and the white lines show the support and resistance that already existed and that were used as a base for the application of the Fibonacci correlation. The largest part of the text above explains how it makes sense to use Fibonacci in the technical analysis of the stock market.

## Its practical use is simple and even if you don’t have much interest in mathematics, it’s worth utilizing Fibonacci in your graphs, to understand the movement of past prices, or to make predictions of future possibilities.

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