Hope you are all doing well. Today i am writing homework post for @imagrn which is about "fibonacci retracemmt".

Who was Fibonacci? What were your most important contributions in the field of mathematics?

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Leonardo Bonacci was a mathematic gem of middle ages born in Republic of Pisa around 1170 . His father named Guglielmo was a merchant indulged in full time trading activities and Fibonacci used to accompany his father and also assist him in trading related activities. We know that trading involves lot of calculations and it is through this process that he developed interest in mathematics. At that time merchants used Roman system of calculations to carry out there trading related activities. When Fibonacci got introduced to Hindu Arabic numerical system he found it easier then Roman system and thereby developed more interest in this system. Fibonacci wrote first book Named Libar Abacus in 1202 that acted as a sort of cornerstone in gaining recognition throughout the Europe. His mathematical skills started paying him when he was elected as advisor on accounting by Emperor Frederick II. Fibonacci didn't stop there, he wrote many books on mathematics. Worth mentioning books are

• Liber Abaci - A book on calculations . A book that gave him recognition throughout the world. In this book, Fibonacci gave detailed account of Hindu- Arabic system of calculations based on place value system and related it to the trading associated matters that he has witnessed while moving with his father like measurement of weight and volumes etc. Fibonacci sequence was also introduced in this book.

• Practica Geometriae - This book has revolutionized the mathematic geometery, as it was comprehensive book on surveying, the measurement and partition of areas and volumes. It was helpful for financial workers linked to measurement of land areas and volumes.

• Liber quadratorum - The Book of Squares. When Fibonacci was working with Frederick II, he was touched by seeing interest of Friedrick in mathematics. So he dedicated this book to Emperor Frederick II.

• Di minor guisa - it was about calculations in commercials fields.
  To honour Fibonacci many mathematical concepts have been
  named after him because these concept were based on his work. Let's mention few.

• Brahmagupta–Fibonacci
  Identity - related to sum and multiplication of squares of numbers.

• Fibonacci search technique - used in computer science

• Pisano period - related to Fibonacci sequence.

Each of these concepts is very interesting but let's not dive into more calculations now. We are yet to mention more contributions, but for the sake of this task, i think it is enough.

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Describe in depth the Golden Ratio. How is it obtained? Where is it located? Give examples of your application through history.

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From the basics of mathematics, we know that ratio involves relationship between two numbers. More precisely ratio indicates how many times one number contains another or how many times one number is greater or smaller than the other. So before understanding the concept of Golden ratio, we will have to understand the numbers on which Golden Ratio is based and these number are known as "Fibonacci sequence".


Fibonacci sequence was introduced by an Italian mathematician , Leonardo Fibonacci in his book Libra abaci as mentioned above. It Involves series of numbers having some definite relationship with each other. Fibonacci sequence contains following numbers

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on.

Above sequence of numbers are not randomly choosen
but they are obtained by adding two consecutive numbers starting from zero.
0+1 =1
1+0 = 1
1+1= 2
1+2+ 3
2+3= 5
3+5= 8
5+8=13
8+13= 21
13+21= 34
So on

Let's look at fibonacci ratio now.

Fibonacci ratios are important in trading as they represent different price levels that act as support and resistance levels. Before going into details of these ratios, let's calculate these ratios first.

Fibonacci series

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on

Let's take any number, say 89 as reference point and calculate Fibonacci ratio by dividing the precedding numbers with the selected number of the fibonacci series like

89/89 = 1 or 100%
55 /89 = 0.618 or 61.8%
34/ 89 = 0.382 or 38.2%
21/89 = 0.235 or 23.5%
So on

Of the above ratios, the key ratio is 61.8% that is obtained by dividing any number in the Fibonacci series with the number preceding it. This ratio is also known as golden ratio.

Now we will come to the concept of golden ratio separately. As seen above, Fibonacci sequence is obtained by adding two consecutive numbers. Let's see ratio of two consecutive numbers"
34/21= 1.6 and 21/34 = 0.6

21/13 = 1.6 and 13/21= 0.6

13/8 = 1.6 and 8/13= 0.6
8/5 = 1.6 and 5/8= 0.6
5/3 = 1.6 amd 3/5 = 0. 6

So this fixed proportion of 1.618 or 0.6 is known as golden ratio. This ratio is known to be followed by all the objects in the universe ranging from subatomic dimensions to the distance measured in lifht years. So the symmetry and comprehensiveness of the ratio has made traders to extrapolate the concept into the trading system or to the price of tokens. Utility in financial world shall be discussed later but let's focus on some historical facts as demanded by the task.

It is said that ratio of female to male bees in case of honey bees is somewhere around 1.618. You may think, how can 1.6 honey bees exist. Take it as 16/10 which is 16 female bees to 10 male bees. But valid argument is that , who could have counted it or if somebody even did we may still doubt its credibility, so we need further examples to clarify it.
In case of sunflowers, the organization of seeds is in spirals of various diameters. It is said that, the ratio between diameters of any two adjacent spirals is 1.618 approximately. It is possible to calculate but laborious. So let's move on to more practical examples.
Taking examples of our body. It is said that, ratio of length from head to toe to that of umblicus to toe is around 1.618. When i did this calculation on my body, i found that i am 6.1 feet tall and my lower body length from umbilicus to feet is 3.7 inch. When we divide 6.1/3.7 = 1.64 . Amazing!

Some studies concluded that people look beautiful while smiling, if the adjacent group of teeth is 1.61 times wider or 0.61 times wider when reversed like incisor are 1. 6 times wider than canines or canines are 0. 6 times wider than incisors.

It doesn't stop here, this ratio is seen to be existing between galaxies, historical artifacts, DNA molecules etc too.

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Describe how Fibonacci is used in Tradigviews. Show screenshots

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Fibonacci series is not something exclusive to trading system but is something that isb inherent to nature and according to fibonacci , these numbers / series / ratios are existing within everything in the universe. Same was extrapolated by traders to the trading system.

Fibonacci levels are important price levels used by traders for various trading parameters like finding out support and resistance levels , stoploss and take profit levels.

Working of fibonacci retracement.

We have fibonacci retracemearnt , arc, fans and time zones etc but for now, we will be discussing fibonacci retracement levels.

For drawing fibonacci levels correctly, we had to choose trending market ( up or down) and select two extreme points on price chart 100% and 0% ( say high and low or vice versa) and than price levels are drawn at intervals mentioned in Fibonacci ratio, that is, 23.6%, 38.2%, 50% and 61.8% . Please note that 50% is not part of fibonacci ratio as seen above but it is included for
trading purposes.

So it is presumed that after a price movement in either direction, the next pullback level will be formed at or near these levels before price reverse or continue. Let me give an example, suppose price of any token moves from 100$ to 200$ . If we have to draw fibonacci levels manually, how will we draw. We can draw in either direction according to fibonacci ratio.

Fibonacci on trading view

Let me show how to draw Fibonacci retracement on tradingview .

• Go to tradingview App. Launch the app and select the trading pair .

• Click on Gann tool
  and then select FIB retracement tool from the list of options available

• Go to the chart and select high and low points . Hold your pointer at the lowest point and push it to the the highest point . Fibonacci retrenchment levels will be drawn automatically and correspond to the Fibonacci ratios.

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Make an investment of at least $ 10 (show screenshots). Determine Fibonacci levels in the currency with which you made the investment, with a timeframe of 4 hours for a period of 48 hours. Identify possible support and resistance levels of the selected currency for a period of 24 hours (1 day) after the investment is made. Identify possible support and resistance levels of the selected currency for a period of 48 hours (2 days) after the investment is made. Show screenshots at 24 and 48 hours after the investment made with the Fibonacci levels.

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For this task I'll using my Wasirx account to perform trade. Analysts will be done on trading view. As task demands showing fib levels on 4h time frame. But entry and exit into a trade cannot be done on 4h time frame. We know that for entry smaller time frame has to be used. So I'll show my entry and exit points on 15 min timeframe and than I'll show fib levels on 4h time frame.

I made an investment of about 1110$ in IOTX and book profit at 1140$ and had net profit of about 30$ approximately.

In the above chart, i made entry at fib level of 0.618 and exit at fib level of 0.312.

Screenshot of completed transactions from my wazirx account.

Let's go onto 4h timeframe. Unfortunately it was a news stock with long consolidation. However on 4h timeframe we can see individual candles respecting these levels.

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What are Fibonacci extensions?

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Fibonacci extension is exact reverse of Fibonacci retracement. So to understand Fibonacci extension we should have basic understanding of Fibonacci retracement. Fibonacci retracement measures how deep a price pull back will go while as Fibonacci extension measuress how far an uptrend will go after a pull back has happened.

Let me give an example to explain this concept .

Suppose price of a token made a high of 20$ and high of $40 and than pullack to 30$ . We know that price movement in market happens in a zigzag manner , that is an impulsive wave followed by price correction and then again an impulsive wave and so on.

In the use case above, price movememt from 20$ to $40 would represent an impulsive move wireless drop of of price back to $30 represents a pullback. Here comes the role of Fivomacci extension which will help us in predicting how far the next impulsive move will go from 30$.

Fibonacci extension level are also formed on the basis of Fibonacci series. The most common levels are 61.8%, 100%, 161.8%, 200%, and 261.8%.. Here I would like to emphasize on one point and that is , 100% and 200% are not the part of Fibonacci series but they are commonly drawn by the traders because the lecels are believed to be the important from where price pullback or replacement takes place.

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Conclusion.

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Fibonacci series represents a series of numbers formed on the basis of definite mathematical relationship between the numbers and from the Fibonacci series, Fibonacci ratios are calculated. One of the ratio is known as Golden Ratio. going to the universal applicability of the Fibonacci series traders extrapolated to the trading system fever nokki retracement is used to major the length of pull back while as fever Nokia extension is used to measure length after perfume use after prize pool that have taken place

Thank you