How does a fibonacci sequence work

The story began in Pisa, Italy in the year Leonardo Pisano Bigollo was a young man in his twenties, a member of an important trading family of Pisa. In his travels throughout the Middle East, he was captivated by the mathematical ideas that had come west from India through the Arabic countries.

When he returned to Pisa he published these ideas in a book on mathematics called Liber Abaci , which became a landmark in Europe. Leonardo, who has since come to be known as Fibonacci , became the most celebrated mathematician of the Middle Ages. His book was a discourse on mathematical methods in commerce, but is now remembered mainly for two contributions, one obviously important at the time and one seemingly insignificant.

The important one: he brought to the attention of Europe the Hindu system for writing numbers. European tradesmen and scholars were still clinging to the use of the old Roman numerals; modern mathematics would have been impossible without this change to the Hindu system, which we call now Arabic notation, since it came west through Arabic lands. But even more fascinating is the surprising appearance of Fibonacci numbers, and their relative ratios, in arenas far removed from the logical structure of mathematics: in Nature and in Art, in classical theories of beauty and proportion.

Consider an elementary example of geometric growth - asexual reproduction, like that of the amoeba. Each organism splits into two after an interval of maturation time characteristic of the species. This interval varies randomly but within a certain range according to external conditions, like temperature, availability of nutrients and so on. We can imagine a simplified model where, under perfect conditions, all amoebae split after the same time period of growth.

So, one amoebas becomes two, two become 4, then 8, 16, 32, and so on. We get a doubling sequence. Now in the Fibonacci rabbit situation, there is a lag factor; each pair requires some time to mature. The number of such baby pairs matches the total number of pairs in the previous generation. So we have a recursive formula where each generation is defined in terms of the previous two generations.

Using this approach, we can successively calculate fn for as many generations as we like. So this sequence of numbers 1,1,2,3,5,8,13,21, But what Fibonacci could not have foreseen was the myriad of applications that these numbers and this method would eventually have. His idea was more fertile than his rabbits. Just in terms of pure mathematics - number theory, geometry and so on - the scope of his idea was so great that an entire professional journal has been devoted to it - the Fibonacci Quarterly.

Now let's look at another reasonably natural situation where the same sequence "mysteriously" pops up. Go back years to 17th century France. Blaise Pascal is a young Frenchman, scholar who is torn between his enjoyment of geometry and mathematics and his love for religion and theology.

The Chevalier asks Pascal some questions about plays at dice and cards, and about the proper division of the stakes in an unfinished game. Pascal's response is to invent an entirely new branch of mathematics, the theory of probability. This theory has grown over the years into a vital 20th century tool for science and social science.

Pascal's work leans heavily on a collection of numbers now called Pascal's Triangle , and represented like this: This configuration has many interesting and important properties: Notice the left-right symmetry - it is its own mirror image. Notice that in each row, the second number counts the row. There are endless variations on this theme. Next, notice what happens when we add up the numbers in each row - we get our doubling sequence.

Now for visual convenience draw the triangle left-justified. If the price stalls near one of the Fibonacci levels and then starts to move back in the trending direction, a trader may take a trade in the trending direction.

Fibonacci levels are used as guides, possible areas where a trade could develop. The price should confirm prior to acting on the Fibonacci level. In advance, traders don't know which level will be significant, so they need to wait and see which level the price respects before taking a trade. Arcs, fans, extensions 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 support or resistance levels can be used to forecast where price may stop falling or rising in the future. Gann was a famous trader who developed several number-based approaches to trading. The indicators based on his work include the Gann Fan and the Gann Square. The Gann Fan, for example, uses degree angles, as Gann found these especially important.

Gann's work largely revolved around cycles and angles. The Fibonacci numbers, on the other hand, mostly have to do with ratios derived from the Fibonacci number sequence. Gann was a trader, so his methods were created for financial markets.

Fibonacci's methods were not created for trading, but were adapted to the markets by traders and analysts. The usage of the Fibonacci studies is subjective since the trader must use highs and lows of their choice. Which highs and lows are chosen will affect the results a trader gets. Another argument against Fibonacci number trading methods is that there are so many of these levels that the market is bound to bounce or change direction near one of them, making the indicator look significant in hindsight.

The problem is that it is difficult to know which number or level will be important in real-time or in the future. James Chen. Technical Analysis Basic Education.

Advanced Technical Analysis Concepts. Your Privacy Rights. To change or withdraw your consent choices for Investopedia. At any time, you can update your settings through the "EU Privacy" link at the bottom of any page.

These choices will be signaled globally to our partners and will not affect browsing data. We and our partners process data to: Actively scan device characteristics for identification. I Accept Show Purposes. Your Money. Personal Finance. Your Practice. Popular Courses. What are Fibonacci Numbers and Lines? Key Takeaways Fibonacci numbers and lines are created by ratios found in Fibonacci's sequence. You'll notice that most of your body parts follow the numbers one, two, three and five.

You have one nose, two eyes , three segments to each limb and five fingers on each hand. The proportions and measurements of the human body can also be divided up in terms of the golden ratio.

DNA molecules follow this sequence , measuring 34 angstroms long and 21 angstroms wide for each full cycle of the double helix. Why do so many natural patterns reflect the Fibonacci sequence? Scientists have pondered the question for centuries. In some cases, the correlation may just be coincidence. In other situations, the ratio exists because that particular growth pattern evolved as the most effective.

In plants, this may mean maximum exposure for light -hungry leaves or maximum seed arrangement. Where there is less agreement is whether the Fibonacci sequence is expressed in art and architecture.

Although some books say that the Great Pyramid and the Parthenon as well as some of Leonardo da Vinci's paintings were designed using the golden ratio, when this is tested, it's found to not be true [source: Markowsky ]. Sign up for our Newsletter! Mobile Newsletter banner close. Mobile Newsletter chat close. Mobile Newsletter chat dots. Mobile Newsletter chat avatar. Mobile Newsletter chat subscribe.

Physical Science. Math Concepts. The Fibonacci sequence floats over the Atlantic coastline under our home spiral galaxy, the Milky Way, to the South. The Golden Ratio in Nature " ". Take a good look at this Roman cauliflower. Its spiral follows the Fibonacci sequence. Tuomas A. The golden ratio is expressed in spiraling shells.