Chapter 10, Part I. Mysterious Fibonacci. Page 2 of 6

Commander in Pips: His father’s name was Bonacci, so Leonardo was “Figlio Bonacci” which means “son of Bonacci” and then it was contracted to FiBonacci. He was a genius mathematician and discovered the next consequence of numbers, when he had trying to solve the task “How many rabbits would be produced in one year’s time, beginning with two rabbits”. The answer is what we know today as the Fibonacci summation series:

1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 610; 987; 1597; 2584; 4181; 6765; 10946 etc.​

The major feature of this consequence is that each number equals to the sum of two previous ones:

2=1+1;

3=2+1;

5=2+3;

……..

377=233+144

10946=6765+4181

………​

And you can prolong this consequence to infinity. But we dare not interesting much in these numbers themselves, but in some ratios that could be obtained from any pair of these numbers. Particularly these ratios are extremely useful in trading and strongly applied by many market participants:

1. If you divide any number (after the initial 5 numbers) into the next standing one you will get 0.618. For instance – 233/377 = 0.618, or 6,765/10,946 = 0.618

2. If you divide any number (after initial 5 numbers) into the previous standing one you will get 1.618. For instance – 377/233 = 1.618, or 144/89 = 1.618

3. If you divide any number (after initial 5 numbers) to next nearest one you will get 0.382. For instance – 144/377 = 0.382. or 4,181/10,946 = 0.382. Also this ratio could be obtained as 1-0.618 = 0.382

From these three major numbers 0.382, 0.618 and 1.618 we will get some derivative numbers that are highly applied in trading:

1. 0.786 – square root from 0.618;

2. 1.000;

3. 1.272 – square root from 1.618;

4. 0.500;

5. 0.886 – square root from 0.786;

6. 2.000;

7. 2.618.​

So, here is a full series of ratios that you should learn and remember better, than your parents’ names:

0.382; 0.5; 0.618; 0.786; 0.886; 1.0; 1.272; 1.618; 2.0; 2.618​

We’ve skipped some minor levels, such as 0.236 and 0.707, because they are not so significant. If you want – you may use them also.