Charting
Discovering The World Of Fibonacci
Fibonacci Tools
Here’s a look at the numbers behind the Fibonacci sequence and how it can be applied to your charts.
The sequence of the Fibonacci numbers is considered to have been discovered by Leonardo of Pisa, better known as “Fibonacci,” a 13th-century Italian mathematician. (“Fibonacci” is an abbreviation of filius Bonacci; filius is Latin for “son of.”) In the early 1200s, after traveling through parts of the Middle East and studying with Arab mathematicians, Fibonacci published his book Liber Abaci, or “Book of Calculation,” which introduced to the West something that is one of the greatest discoveries of all time: the decimal numeration system, including the position of zero as the first number in the number sequence. This system, known as the Hindu-Arabic numeral system, includes zero, 1, 2, 3, 4, 5, 6, 7, 8, and 9 and is commonly used today instead of Roman numerals.
Fibonacci became one of the best-known mathematicians of his time. He wrote three essential, ground-breaking books on mathematics: Liber Abaci, published in 1202 and updated in 1228; Practica Geometriae (“Practical Geometry,” a compendium on geometry and trigonometry), published in 1220; and Liber Quadratorum (“The Book of Squares”)
The fibonacci sequence
In Liber Abaci, Leonardo presented the following task: “How many couples of rabbits, placed into a rabbit corral, can be produced for a year by a rabbit couple, if each couple produces one more couple every month since the second month?” This resulted in the Fibonacci sequence of numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
The mathematic sequence begins with 1 and the next number forms the sum of the two previous ones:
1 + 1 = 2; 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8…
Why is the sequence so important? The sequence strives for a constant ratio slowly, but this ratio is irrational — that is, a number with an endless and unpredictable sequence of decimal numbers in the fractional part. It is impossible to express it precisely. If any number of the Fibonacci sequence is divided by the previous one (for example, 13:8), the result is a value fluctuating around an irrational value (1.61803398875…). But it would be impossible to determine the exact ratio to the last decimal number, and hence, it is represented as 1.618.
This ratio has been referred to by other names, ranging from “divine proportion” in ancient times to the “golden section,” the “golden average,” or the “ratio of rotating squares” (or logarithmic spiral). The mathematician Johannes Kepler called the ratio “one of the treasures of geometry.” In mathematics, the Greek letter ϕ (phi) is adopted as the symbol of the ratio:
ϕ equals 1.618
It has also been referred to as the “golden coefficient.”
The Fibonacci sequence as well as its numbers can have numerous combinations. This is not just a game with numbers, but the most important mathematical expression of natural phenomena. The best-known and interesting applications of the mathematical sequence are the pyramids of Egypt and Mexico, and the plants found in nature!
Fibonacci ratio in geometry
Mathematical properties of these ratios are not of great practical interest to us. Although this is not intended to be a lecture in geometry, it could be worth your while to pay some attention to the main examples that have some importance to trading.
Figure 1: the golden section. The ratio of the total length (AC) to the large segment (AB) is equal to the ratio of the large segment (AB) to the small segment (BC).
Golden section: Any segment may be divided in such a way that the ratio between its smaller and bigger parts will be equal to the ratio between the bigger part and the whole segment (Figure 1). This ratio is always equal to 0.618.
