What is the Fibonacci sequence?
The Fibonacci sequence is a series of numbers where a number is the sum of the last two numbers, starting with 0 and 1.
The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...
Written as a rule, the expression is:
Xn = Xn-1 + Xn-2
The Fibonacci Spiral and the Golden Ratio
The Fibonacci sequence is often displayed on a chart like the one in the heading of this article. Each of the squares illustrates the area of the next number in the sequence. Then the Fibonacci spiral is drawn inside the squares connecting the corners of the squares.
The squares fit perfectly because the ratio between the numbers in the Fibonacci sequence is very close to the golden ratio, which is approximately 1.618034. The larger the numbers in the Fibonacci sequence, the closer the ratio is to the golden ratio.
The spiral and the resulting rectangle are also known as the Golden Rectangle.
The origins of the Fibonacci sequence
Fibbonaci (Leanardo Pisano Bogollo, Fibonacci was his nickname) first introduced the series of numbers known as the Fibonacci sequence in his book Liver Abaci in 1202. Fibonacci was a member of an important Italian business family in the 12th and 13th centuries. Being part of a business family, mathematics was an integral part of the business. Fibonacci traveled throughout the Middle East and India and was captivated by the mathematical ideas of his travels. His book, Liver Abaci, was a speech on mathematical methods in trading that Fibonacci observed during his travels.
Fibonacci is remembered for two important contributions to Western mathematics:
He helped spread the use of Hindu number writing systems in Europe (0,1,2,3,4,5 instead of Roman numerals).
The seemingly insignificant series of numbers later named the Fibonacci Sequence in his honor.
Fibonacci discovered the sequence by asking the following question:
If a pair of rabbits is placed in an enclosed area, how many rabbits will be born there if we assume that each month one pair of rabbits produces another pair and that the rabbits begin to give birth two months after they are born?
Beginning: At the beginning, no rabbits are born, since the initial pair has not had time to be pregnant and to be born (0).
The first month: A pair of rabbits is born (1).
The second month: again, a pair of rabbits are born, since the new rabbits have not yet matured to have young (1).
The third month: two pairs of rabbits reproduce and one pair is not ready, so two pairs of rabbits are born (2).
The fourth month: Three pairs of rabbits reproduce and 2 pairs of rabbits are not ready, so three pairs of rabbits are born (3).
The fifth month: five pairs of rabbits produce and three are not ready, so five pairs of rabbits are born (5).
And so on.
Although the Fibonacci question about rabbits is an unrealistic scenario, the sequence can be observed in nature, as in the assemblage of sunflower seeds and other plants, and the shape of galaxies and hurricanes.
So how is it used?
What is the Fibonacci spiral?
It is an analysis tool that, using Fibonacci ratios, draws a spiral on the price chart of an asset and predicts support and resistance zones and time.
Fibonacci spirals connect price and time in such a way that each point of the spiral represents areas where corrections and trend changes occur. It is based on the application of a universal geometric law to the asset analyzed. The Fibonacci spiral is built by drawing concentric arcs whose radii correspond to the Fibonacci sequence.
To choose the center of the spiral, spirals should be drawn until we find that which best fits the market turning aspects in the past. Unlike the other Fibonacci study procedures, the precise procedures for drawing Fibonacci spirals used by experts is kept something of a secret. The broader initiative is to take extreme aspects of the market as the center and, from this point, the spiral based on the golden ratio will be drawn. Certain views during the spiral are thought of as strong views where prominent market events such as trend reversals, cost spikes, or strong support and resistance levels will take place. Fans of the Fibonacci spiral constantly speak of it as the most accurate method of forecasting market behavior based on time and critical cost levels and not just on the basis of costs.
There are various computer programs for calculating and drawing the Fibonacci spiral on a cost graph even though the precise calculations made are generally not made public.
The Fibonacci sequence is a series of numbers where a number is the sum of the last two numbers, starting with 0 and 1.
The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...
Written as a rule, the expression is:
Xn = Xn-1 + Xn-2
The Fibonacci Spiral and the Golden Ratio
The Fibonacci sequence is often displayed on a chart like the one in the heading of this article. Each of the squares illustrates the area of the next number in the sequence. Then the Fibonacci spiral is drawn inside the squares connecting the corners of the squares.
The squares fit perfectly because the ratio between the numbers in the Fibonacci sequence is very close to the golden ratio, which is approximately 1.618034. The larger the numbers in the Fibonacci sequence, the closer the ratio is to the golden ratio.
The spiral and the resulting rectangle are also known as the Golden Rectangle.
The origins of the Fibonacci sequence
Fibbonaci (Leanardo Pisano Bogollo, Fibonacci was his nickname) first introduced the series of numbers known as the Fibonacci sequence in his book Liver Abaci in 1202. Fibonacci was a member of an important Italian business family in the 12th and 13th centuries. Being part of a business family, mathematics was an integral part of the business. Fibonacci traveled throughout the Middle East and India and was captivated by the mathematical ideas of his travels. His book, Liver Abaci, was a speech on mathematical methods in trading that Fibonacci observed during his travels.
Fibonacci is remembered for two important contributions to Western mathematics:
He helped spread the use of Hindu number writing systems in Europe (0,1,2,3,4,5 instead of Roman numerals).
The seemingly insignificant series of numbers later named the Fibonacci Sequence in his honor.
Fibonacci discovered the sequence by asking the following question:
If a pair of rabbits is placed in an enclosed area, how many rabbits will be born there if we assume that each month one pair of rabbits produces another pair and that the rabbits begin to give birth two months after they are born?
Beginning: At the beginning, no rabbits are born, since the initial pair has not had time to be pregnant and to be born (0).
The first month: A pair of rabbits is born (1).
The second month: again, a pair of rabbits are born, since the new rabbits have not yet matured to have young (1).
The third month: two pairs of rabbits reproduce and one pair is not ready, so two pairs of rabbits are born (2).
The fourth month: Three pairs of rabbits reproduce and 2 pairs of rabbits are not ready, so three pairs of rabbits are born (3).
The fifth month: five pairs of rabbits produce and three are not ready, so five pairs of rabbits are born (5).
And so on.
Although the Fibonacci question about rabbits is an unrealistic scenario, the sequence can be observed in nature, as in the assemblage of sunflower seeds and other plants, and the shape of galaxies and hurricanes.
So how is it used?
What is the Fibonacci spiral?
It is an analysis tool that, using Fibonacci ratios, draws a spiral on the price chart of an asset and predicts support and resistance zones and time.
Fibonacci spirals connect price and time in such a way that each point of the spiral represents areas where corrections and trend changes occur. It is based on the application of a universal geometric law to the asset analyzed. The Fibonacci spiral is built by drawing concentric arcs whose radii correspond to the Fibonacci sequence.
To choose the center of the spiral, spirals should be drawn until we find that which best fits the market turning aspects in the past. Unlike the other Fibonacci study procedures, the precise procedures for drawing Fibonacci spirals used by experts is kept something of a secret. The broader initiative is to take extreme aspects of the market as the center and, from this point, the spiral based on the golden ratio will be drawn. Certain views during the spiral are thought of as strong views where prominent market events such as trend reversals, cost spikes, or strong support and resistance levels will take place. Fans of the Fibonacci spiral constantly speak of it as the most accurate method of forecasting market behavior based on time and critical cost levels and not just on the basis of costs.
There are various computer programs for calculating and drawing the Fibonacci spiral on a cost graph even though the precise calculations made are generally not made public.