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Fibonacci was a cool Italian mathematician.
Being an expert with numbers, he added numbers to other numbers, and found the famous Fibonacci string:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc...

0+1 = 1
1+1 = 2
2+1 = 3
3+2 = 5
5+3 = 8 ... you get it. Grandiose expert.

Those numbers are used in geometry of nature, as in broccolis, pineapples, and even sunflowers, as one can obviously see:

A sunflower Fibonacci on a sunflower

Those numbers are also encountered in financial markets.

Fibonacci retracement levels are derived from the previous sequence:
0.236, 0.382, 0.618, 0.786. Most tools add the 0.5 level.

Fibonacci retracements

Fib. retracements are used to identify possible zones of resistance and support.

"swing low": the lowest point of a move
"swing high": the highest point of a move

Selecting the fibonacci retracement tool on tradingview

Let's say we see a small leg down in a general bull market.
For some reasons you think bulls will continue their course, and want to enter the market at the cheapest price possible.
Identify the swing low and high of the move:

Defining swing low and swing high

Select the Fib retracement tool.
Place the first point on swing low.
Place the second point on swing high.

It gives you a ration of possible support levels:

Fibonacci retracements as supports

Here the 0.618 ratio gave you a nice entry!

As with every supports and resistances, see the indications as possible areas of reversal, rather than bulletproof limits.

You can use retracements to get a general idea of where the market could slow down or turn around.
Here is an example on BTS/BTC:

Example of resistances and supports found with fibonacci retracements on a BTS/BTC chart

In bear markets

First select the swing high.
Then the swing low.

Using fibonacci retracements in bear markets

Why does it work

Maybe a lot of traders look at the same levels, and therefore engage at the same time.
Or maybe the human psyche is akin to sunflowers.

I advise you to not fall in the trap of making tons of hypotheses about why a move happened or not: theories will stay theories.
Your goal is to make money.

You don't need to know how a calculator works to use it.

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  Moving averagesChart patterns