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Fibonacci Sequence: Definition, How it Works, and How to Use It

File Photo: Fibonacci Sequence: Definition, How it Works, and How to Use It
File Photo: Fibonacci Sequence: Definition, How it Works, and How to Use It File Photo: Fibonacci Sequence: Definition, How it Works, and How to Use It

Definition of Fibonacci Sequence

Leonardo Fibonacci, an Italian mathematician who lived in the 13th century, developed the Fibonacci sequence. The numerical series begins with the values zero and one and shows an unending progression upward, with each succeeding number being the addition of the sums of the two numbers that came before it in the series.

Specific traders are under the impression that the use of Fibonacci numbers and ratios in financial research may be made more accessible by the utilization of technical analysis. This is a common misconception.


The Fibonacci sequence lacks a closed-form formula. Nonetheless, its numbers exhibit distinct relationships, and the sum of the two preceding numbers determines the value of each number, for example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, and 377.

Fibonacci Sequence Rule

xn = xn−1 + xn−2


xn is the term “n.”

xn−1 is the previous term (n−1)

xn−2 is the term before that (n−2)

For decades, scholars in the fields of mathematics, physics, and natural sciences have employed the Fibonacci sequence as a tool for determining the value of the golden ratio, which is around 1.618. The ratio between consecutive Fibonacci numbers approximates the values of 1.618 or 0.618.

Honeybees and other natural things exhibit dimensional properties that conform to the golden ratio, approximately equal to 1.618. To get a ratio of around 1.618, it is necessary to partition the female bees from the male bees within a hive. Prominent architectural icons, such as the Parthenon in Athens and the Great Pyramid at Giza, exhibit rectangular forms that conform to the golden ratio.

Use of Fibonacci Sequence

The use of the Fibonacci sequence in the banking industry involves the utilization of retracements, arcs, fans, and time zones.

Using swing high and swing low chart markers is a fundamental need in standard Fibonacci retracements. The Fibonacci sequence and its associated lines are constructed by selecting two arbitrary points and drawing lines at specific percentage intervals. The threshold for a stock to rise from $15 to $20, based on a percentage increase of 23.6%, is $18.82. This value is obtained by subtracting the product of $5 and 0.236 from $20. Calculating the threshold of 50% results in $17.50, which is equal to $15 less the product of $5 and 0.5.

The majority of Fibonacci technical analysis methodologies utilize retracements. Fibonacci retracements that are associated with trends might potentially indicate the extent of a retreat. Under these conditions, traders closely monitor Fibonacci ratios ranging from 23.6% to 78.6%. When the price aligns with a Fibonacci level, an investor can engage in trend trading.

Arcs, fans, and time zones exhibit similar usage on charts while serving distinct purposes. Based on the mathematical concept of Fibonacci numbers and historical price movements, both indicators provide potential indications of support or resistance levels. The identification and analysis of support and resistance levels contribute to the anticipation of price fluctuations.

Definition of Fibonacci Spiral

The bounds of successive Fibonacci squares form the Fibonacci spiral. Golden spirals follow twists at a constant angle near the golden ratio. Pinecone spirals and flower petals are Fibonacci numbers. Plants exhibiting spiral growth patterns possess leaves that emerge at specific angles. At the same time, the arrangement of sunflower seeds inside their floral structure adheres to a spiral pattern derived from the golden ratio.

Where is Fibonacci evident?

The majority of angiosperms demonstrate petal numbers that adhere to this sequence. The floral structures of maize marigolds, cineraria, and daisies consist of 13 petals, whereas asters and chicory have a petal count of 21.

Fibonacci Sequence Effects on Trading

People can recognize patterns, and traders use the Fibonacci sequence to align chart patterns. Fibonacci numbers may not directly affect market dynamics, but participant expectations may. Fibonacci analysis by investors when buying or selling might create a self-fulfilling prophecy, affecting market trends.

Remaining Statement

Every number in the Fibonacci sequence is the sum of the two numbers before it. The “golden ratio,” derived from the Fibonacci sequence, appears in many natural occurrences. Technical analysis techniques like retracements, arcs, fans, and time zones let investors apply the Fibonacci sequence to finance and trading.


  • The Fibonacci sequence is defined such that each number in the series is the sum of the two previous integers.
  • The calculation of the golden ratio, which is about 1.618, may be derived by utilizing the Fibonacci sequence.
  • Numerous dimensions in the natural world adhere to the mathematical principle known as the golden ratio, which is approximately equal to 1.618.
  • The utilization of the Fibonacci sequence in the banking sector involves the application of retracements, arcs, fans, and time zones.



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