# Fibonacci

The Fibonacci sequence was invented by the Italian Leonardo Pisano Bigollo (1180-1250), who is known in mathematical history by several names: Leonardo of Pisa (Pisano means “from Pisa”) and Fibonacci (which means “son of Bonacci”). Fibonacci, the son of an Italian businessman from the city of Pisa, grew up in a trading colony in North **Africa** during the Middle Ages. Italians were some of the western world’s most proficient traders and merchants during the Middle Ages, and they needed **arithmetic** to keep track of their commercial transactions. Mathematical calculations were made using the Roman numeral system (I, II, III, IV, V, VI, etc.), but that system made it hard to do the addition, **subtraction**, **multiplication**, and **division** that merchants needed to keep track of their transactions.

If pupunta kayo ng Italy pwede ninyong isama sa tour ang statue ni Fibonacci. If you visit Piazza dei Miracoli in Pisa, you may enter the Camposanto Monumentale. Nasa corner at one end ng long cloister yung marble statue ni Leonardo Pisano. If familiar kayo sa leaning tower of Pisa nasa area din na yun halos.

The Fibonacci sequence is one of the most famous formulas in mathematics. **Leonardo Pisano** is better known by his nickname **Fibonacci.** He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. Fibonacci was born in Italy but was educated in North Africa where his father, Guilielmo, held a diplomatic post. His father’s job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia. Fibonacci was taught mathematics in Bugia and travelled widely with his father and recognised the enormous advantages of the mathematical systems used in the countries they visited.

### Fibonacci Sequence

Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

The next number is found by adding up the two numbers before it.

- The 2 is found by adding the two numbers before it (1+1)
- The 3 is found by adding the two numbers before it (1+2),
- And the 5 is (2+3),
- and so on!

The Fibonacci Sequence can be written as a “Rule”

First, the terms are numbered from 0 onwards like this:

n = |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
… |

x_{n} = |
0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | 233 | 377 | … |

So term number 6 is called x_{6} (which equals 8).

Example: the 8th term isthe 7th term plus the 6th term:x _{8} = x_{7} + x_{6} |

So we can write the rule:

The Rule is **x _{n} = x_{n-1} + x_{n-2}**

where:

**x**is term number “n”_{n}**x**is the previous term (n-1)_{n-1}**x**is the term before that (n-2)_{n-2}

### Example: term 9 is calculated like this:

x_{9}= x_{9-1} + x_{9-2} = x_{8} + x_{7} = 21 + 13 = 34

**The problem with rabbits**

One of the mathematical problems Fibonacci investigated in *Liber Abaci* was about how fast rabbits could breed in ideal circumstances. Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was… How many pairs will there be in one year?

- At the end of the first month, they mate, but there is still only 1 pair.
- At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits.
- At the end of the third month, the original female produces a second pair, making 3 pairs in all.
- At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produced her first pair also, making 5 pairs.

Now imagine that there are pairs of rabbits after months. The number of pairs in month will be (in this problem, rabbits never die) plus the number of new pairs born. But new pairs are only born to pairs at least 1 month old, so there will be new pairs. So we have

which is simply the rule for generating the Fibonacci numbers: add the last two to get the next. Following this through you’ll find that after 12 months (or 1 year), there will be 233 pairs of rabbits.

### Bees are better

The rabbit problem is obviously very contrived, but the Fibonacci sequence does occur in real populations. Honeybees provide an example. In a colony of honeybees there is one special female called the queen. The other females are worker bees who, unlike the queen bee, produce no eggs. The male bees do no work and are called drone bees.

Males are produced by the queen’s unfertilised eggs, so male bees only have a mother but no father. All the females are produced when the queen has mated with a male and so have two parents. Females usually end up as worker bees but some are fed with a special substance called royal jelly which makes them grow into queens ready to go off to start a new colony when the bees form a swarm and leave their home (a hive) in search of a place to build a new nest. So female bees have two parents, a male and a female whereas male bees have just one parent, a female.

Let’s look at the family tree of a male drone bee.

He has 1 parent, a female.

He has 2 grandparents, since his mother had two parents, a male and a female.

He has 3 great-grandparents: his grandmother had two parents but his grandfather had only one.

How many great-great-grandparents did he have?

Again we see the Fibonacci numbers :

Number of | parents | grandparents | great- grandparents |
great-great- grandparents |
great-great-great- grandparents |

of a MALE bee | 1 | 2 | 3 | 5 | 8 |

of a FEMALE bee | 2 | 3 | 5 | 8 | 13 |

### Golden Ratio

One such place is particularly fascinating: the golden ratio. So, what is this golden ratio? Well, it’s a number that’s equal to approximately 1.618. This number is now often known as “phi” and is expressed in writing using the symbol for the letter phi from the Greek alphabet. Phi isn’t equal to precisely 1.618 since, like its famous cousin pi, phi is an irrational number—which means that its decimal digits carry on forever without repeating a pattern.

If the length of *a+b* divided by the length of *a* is equal to the length of a divided by *b*, then the two quantities are said to be in golden ratio.

*(a* + *b)*/*a* = *a*/*b* = 1.6180339887…

The golden ratio appears every day in our lives, every time, everywhere.

**Our Bodies:** The ratio of the distance from the top of our head to our belly button to the distance of our belly button to the floor is in golden ratio.

**Flowers:** Take a closer look at a sunflower the next time you see one. It is said that these flowers grow in the Fibonacci Sequence number (I will explain this next). The reason is so that they get the maximum exposure to sun light.

**Architecture:** A lot of historical buildings were built using the golden ratio. The Parthenon and Great Mosque of Kairouan are some examples.

**Paintings:** The sacrament of the last supper by *Salvador Dali*, Mona Lisa and illustrations of polyhedral by *Leonardo da Vinci* were all said to exhibit the usage of the golden ratio.

### Fibonacci Retracement

The theory is that after a rate spike in either direction, the rate will often return or retrace. Part way back to the previous price level. Before resuming in the original direction. When the price of an asset pulls back, it typically has a mathematical relationship to the price wave that preceded it. If the price falls through one level it will likely proceed to the next level. Sometimes, a price may stall at one level, then proceed to the next, stall and proceed to the next and so on.

If you are a Technical Analyst, Fibonacci is probably your good friend. Most traders use Fibonacci Retracements, Fibonacci Arcs and Fibonacci Fans. In all 3 applications, the golden ratio is expressed in 3 percentages, 38.2%, 50% and 61.8%.Fibonacci retracements are areas on a chart that indicate areas of support and resistance. For Fibonacci Retracement, they are horizontal lines, for Fibonacci Arcs, they are curved lines and for Fibonacci Fans, they are diagonal lines. It is clear that 23.6%, 38.2%, and 61.8% stem from ratios found within the Fibonacci sequence. The 50% retracement is not based on a Fibonacci number. Instead, this number stems from Dow Theory’s assertion that the Averages often retrace half their prior move. Based on depth, we can consider a 23.6% retracement to be relatively shallow. Retracements in the 38.2%-50% range would be considered moderate. Even though deeper, the 61.8% retracement can be referred to as the golden retracement. It is, after all, based on the Golden Ratio.

### Paano e plot sa chart?

Una muna hanapin mo ang Trend. Uptrend ba or downtrend. Hanapin mo ang simula ng trend at ang dulo ng trend. Tandaan na subjective ang pagplot ng fibonacci retracement ibig sabihin depende sa trader kung alin para sa kanya ang simula ng trend. Pwede ka magsimula sa body ng candle or sa wick.

Hanap tayo ng uptrend.

Hanapin ang fib ret sa tools.

Palitan natin kulay para di masakit sa mata.

### Ano ba talaga ang Fibonacci Retracement lines?

Static na lines yan ibig sabihin fixed or di nagbabago. Ang idea is that kapag uptrend ang isang stock ay di ito dederecho pataas but may mga areas kung saan nagpapahinga ito or nagreretrace bago magcontinue pataas. Dun sa areas na yun bumibili mga traders or they often refer to it as “the price respected this or that fib ret level.” May kanya kanyang levels na binabantayan ang mga traders. Most popular is yung 61.8%. Once the 61.8% level has been broken, the trend may have reversed. This is when technicians will re-evaluate their trading strategy and plot a new set of Fibonacci lines. I learned fibonacci retracement not the same way most learn it. The person who taught me Fibo Ret made me do calculations at measure ang distance then plot the levels myself. Ngayon madali na lang kasi few clicks na lang ng button ok na but ang negative effect lang ng pagiging madali is wala mostly basic foundation kung saan galing ang levels at bakit may levels. Subjective ang pagplot ng fibo ret so nakadepende sa traders kung saan siya magsisimula. Basic principle lang is magsimula ka kung saan nagsimula ang trend. Kung saan man sa tingin mo yun eh di yun ang tama.

We are in a bear market at maraming nagpapanic dahil most ng markets sa mundo are going down yet nakakakita pa rin naman ng mga opportunities to make money. Here is a screenshot of my latest trades. I had a few but yan lang ang namanage ko eh screenshot since mabilisang buy at sell lang ako. Tight masyado stops ko.

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## 2 Comments

## mako solano

Thank you

## Avery

Pwede ba gamitin ang Fibo in conjunction with MAMA setup? In my experience, never pa ako gumamit ng Fibo sa kahit anong trades na ginawa ko.