Fibonacci Sequence: Definition, How it Works, and How to Use It (2024)

What Is the Fibonacci Sequence?

The Fibonacci sequence was developed by the Italian mathematician, Leonardo Fibonacci, in the 13th century. The sequence of numbers, starting with zero and one, is a steadily increasing series where each number is equal to the sum of the preceding two numbers.

Some traders believe that the Fibonacci numbers and ratios created by the sequence play an important role in finance that traders can apply using technical analysis.

Key Takeaways

  • The Fibonacci sequence is a set of steadily increasing numbers where each number is equal to the sum of the preceding two numbers.
  • The golden ratio of 1.618 is derived from the Fibonacci sequence.
  • Many things in nature have dimensional properties that adhere to the golden ratio of 1.618.
  • The Fibonacci sequence can be applied to finance by using four techniques including retracements, arcs, fans, and time zones.

Understanding the Fibonacci Sequence

The numbers in the Fibonacci Sequence don't equate to a specific formula, however, the numbers tend to have certain relationships with each other. Each number is equal to the sum of the preceding two numbers. For example,0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.

Thegolden ratioof 1.618, important to mathematicians, scientists, and naturalists for centuries is derived from the Fibonacci sequence. The quotient between each successive pair of Fibonacci numbers in the sequence approximates 1.618, or its inverse 0.618.

Golden Ratio

The golden ratio is derived by dividing each number of the Fibonacci series by its immediate predecessor. Where F(n) is the nth Fibonacci number, the quotient F(n)/ F(n-1) will approach the limit 1.618, known as the golden ratio.

Many things in nature have dimensional properties that adhere to the ratio of 1.618, like the honeybee. If you divide the female bees by the male bees in any given hive, you will get a number near 1.618. The golden ratio also appears in the arts and rectangles whose dimensions are based on the golden ratio appear at the Parthenon in Athens and the Great Pyramid in Giza.

How to Use the Fibonacci Sequence

The Fibonacci sequence can be applied to finance by using four techniques including retracements, arcs, fans, and time zones.

Fibonacci retracements require two price points chosen on a chart, usually a swing high and a swing low. Once two points are chosen, the Fibonacci numbers and lines are drawn at percentages of that move. If a stock rises from $15 to $20, then the 23.6% level is $18.82, or $20 - ($5 x 0.236) = $18.82. The 50% level is $17.50, or $15 - ($5 x 0.5) = $17.50.

Fibonacci Sequence: Definition, How it Works, and How to Use It (1)

Fibonacci retracements are the most common form of technical analysis based on the Fibonacci sequence. During a trend, Fibonacci retracements can be used to determine how deep a pullback may be. Traders tend to watch the Fibonacci ratios between 23.6% and 78.6% during these times. If the price stalls near one of the Fibonacci levels and then start to move back in the trending direction, an investor may trade in the trending direction.

Arcs, fans, and time zones are similar concepts but are applied to charts in different ways. Each one shows potential areas of support or resistance, based on Fibonacci numbers applied to prior price moves. These supportive or resistance levels can be used to forecast where prices may fall or rise in the future.

What Is the Fibonacci Spiral?

The limits of the squares of successive Fibonacci numbers create a spiral known as the Fibonacci spiral. It follows turns by a constant angle close to the golden ratio and is commonly called the golden spiral. The numbers of spirals in pinecones are Fibonacci numbers, as is the number of petals in each layer of certain flowers. In spiral-shaped plants, each leaf grows at an angle compared to its predecessor, and sunflower seeds are packed in a spiral formation in the center of their flower in a geometry governed by the golden ratio.

Where Is the Fibonacci Sequence Evident?

In almost all flowering plants, the number of petals on the flower is a Fibonacci number. It is extremely rare for the number of petals not to be so and examples of this phenomenon include corn marigold, cineraria, and daisies with 13 petals and asters and chicory with 21 petals.

How Can the Fibonacci Sequence Affect Trading Behavior?

Humans tend to identify patterns and traders easily equate patterns in charts through the Fibonacci sequence. It's unproven that Fibonacci numbers relate to fundamental market forces, however, markets by design react to the beliefs of their players. Consequently, if investors buy or sell because of Fibonacci analysis, they tend to create a self-fulfilling prophecy that affects the market trends.

The Bottom Line

The Fibonacci sequence is a set of steadily increasing numbers where each number is equal to the sum of the preceding two numbers. Many things in nature have dimensional properties that adhere to the golden ratio of 1.618, a quotient derived from the Fibonacci sequence. When applied to finance and trading, investors apply the Fibonacci sequence through four techniques including retracements, arcs, fans, and time zones.

Fibonacci Sequence: Definition, How it Works, and How to Use It (2024)

FAQs

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

The Fibonacci sequence is a type series where each number is the sum of the two that precede it. It starts from 0 and 1 usually. The Fibonacci sequence is given by 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on.

What is the Fibonacci sequence and how does it work? ›

The Fibonacci sequence is the series of numbers where each number is the sum of the two preceding numbers. For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …

How do you use the Fibonacci? ›

How to use Fibonacci retracements in trading. Fibonacci retracement lines can be created when you divide the vertical distance between the high and low points by the key Fibonacci ratios. Horizontal lines are drawn on the trading chart​​ at the 23.6%, 38.2% and 61.8% retracement levels.

How does Fibonacci algorithm work? ›

The Fibonacci Algorithm is a numerical series where each number is the sum of the two preceding ones, starting from 0 and 1. It's a simple and significant concept in computer science with base cases F(0) = 0, F(1) = 1, and recursive case F(n) = F(n-1) + F(n-2).

What makes the Fibonacci sequence so special? ›

The pattern hides a powerful secret: If you divide each number in the sequence by its predecessor (except for 1 divided by 0), then as you move toward higher numbers, the result converges on the constant phi, or approximately 1.61803, otherwise known as the golden ratio.

What does Fibonacci tell you? ›

Fibonacci retracement levels are horizontal lines that indicate the possible locations of support and resistance levels. Each level is associated with one of the above ratios or percentages. It shows how much of a prior move the price has retraced. The direction of the previous trend is likely to continue.

How is the Fibonacci sequence used today? ›

Fibonacci retracements are the most common form of technical analysis based on the Fibonacci sequence. During a trend, Fibonacci retracements can be used to determine how deep a pullback may be. Traders tend to watch the Fibonacci ratios between 23.6% and 78.6% during these times.

How does the Fibonacci sequence work in nature? ›

In trees, the Fibonacci begins in the growth of the trunk and then spirals outward as the tree gets larger and taller. We also see the golden ratio in their branches as they start off with one trunk which splits into 2, then one of the new branches stems into 2, and this pattern continues.

What is the golden rule of the Fibonacci numbers? ›

The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter phi, it is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last.

How is the Fibonacci sequence used in the human body? ›

The bones of your finger (including the bone from your knuckle to your wrist) follow the Fibonacci sequence. We have 8 fingers in total, 5 digits on each hand, 3 bones in each finger, 2 bones in 1 thumb, and 1 thumb on each hand. Many flowers also exhibit the Fibonacci sequence.

Where does Fibonacci appear in real life? ›

This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space. But the Fibonacci sequence doesn't just stop at nature. In graphic design, we refer to it as the Golden Ratio.

What is the golden ratio in life? ›

Going back to the Fibonacci numbers — the numbers that make up the golden ratio. When applied to the life events model, 61.8% (. 618) represents the amount of time that should be spent on the present. This means focusing on your present situation and actions.

What is the easiest way to solve the Fibonacci sequence? ›

Remember, to find any given number in the Fibonacci sequence, you simply add the two previous numbers in the sequence. To create the sequence, you should think of 0 coming before 1 (the first term), so 1 + 0 = 1.

Why does Fibonacci work? ›

The values in the Fibonacci scale work well because they roughly correspond to Weber's Law. After the two (which is 100% bigger than one), each number is about 60% larger than the preceding value.

How does the Fibonacci equation work? ›

The Fibonacci sequence formula deals with the Fibonacci sequence, finding its missing terms. The Fibonacci formula is given as, Fn = Fn-1 + Fn-2, where n > 1. It is used to generate a term of the sequence by adding its previous two terms.

What is the basic concept of the Fibonacci series? ›

The sequence follows the rule that each number is equal to the sum of the preceding two numbers. The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ... Each number, starting with the third, adheres to the prescribed formula.

What is Fibonacci strategy? ›

The Fibonacci trading strategy uses the "golden ratio" to determine entry and exit points for trades of all time frames. This type of trading is highly contested as it is based on ratios that don't necessarily correlate to the individual trade.

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