**Fibonacci – The Magical Series of Numbers**

Fibonacci is something which is widely used by mathematicians, traders and many other people throughout the world because of its wide range of applications and utility. If one calls it a magical series of numbers then that would definitely not be an exaggeration because it has provided ground to so many mathematical breakthroughs.

Italian mathematician, Leonardo Fibonacci, came up with this series of numbers which were later named after him. He was no ordinary person but a number genius who was renowned for being an ultra-mathematician during his time. It was his moment when he discovered that a simple series of numbers can actually provide you with ratios which can further be helpful to make very important predictions and discoveries.

**Initially the Fibonacci numbers were considered to be:**

1,1,2,3,5,8,13,21,34,55,89,144,……

**But in the modern times, the sequence has been extended by adding an additional term in the start and now the series has become**

0,1,1,2,3,5,8,13,21,34,55,89,144,……..

If you look at the numbers closely, you will see that each subsequent number is a sum of the previous two numbers. 0+1 is equal to 1, 1+1 is equal to 2 and the series continues like this. The series has so much important that currently it is being used in computer applications and algorithms which are further used for crucial tasks.

Taking the magic further, when we take the ratios of two consecutive numbers then the answer which we get is very close to the “golden ratio”. After the first few numbers in the sequence, the answer to the rest might vary slightly but is very close to the value of 0.618, for example, when 34 is divided by 55 we get 0.618. When 2 is divided by 3 we get 0.667.

These ratios are taken advantage of by the mathematicians who use these ratios in simple formulas in order to predict any particular number in the sequence. The answers which are obtained with the help of these formulas are very near to the original numbers, thus, making these formulas very reliable. They can effectively be used to predict any number in the series no matter how farthest it exists.

Even when two alternate numbers are divided the ratio comes out to be 0.382, for example, when 34 is divided by 89 the answer is 0.382. When 55 is divided by 144 we again get the same answer which is 0.382. These ratios are known as the “golden mean” which provide a platform for making huge advancements in the field of mathematics.

These ratios are known as Fibonacci retracement levels which can be used to recognize the Fibonacci extensions. These extensions are a very easy way for all the traders to determine their ratio of profit. They can predict the resistances and spaces in the market which makes them very useful for any businessman or trader.

In order to gain familiarity with Fibonacci extensions, it is very important to identify the swing high and swing low points. The swing high is a candlestick which has two lower highs on its both sides whereas a swing low is the one which has two higher lows at both the ends.

Traders use these levels to identify the profits which serve as a more reliable tool as compared to any market situation or personal intuition.

**Although computers and calculators will do all the work but it is very important to gain basic knowledge about the wonders of Fibonacci sequence and how it works for traders.**