Fibonacci was an 12th Century Italian Mathematician that introduced digital notation to Europe. Digital Notation was being used India and the Middle East several centuries before Europe. Fibonacci developed the Fibonacci sequence as a solution to the natural growth progression of rabbits puzzle.
Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: 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; rabbits never die and a mating pair 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? (ref Wikipedia)
Fibonacci retracement and Trading
In trading Fibonacci utilizes the Golden Ratio as a key reversal area.
The Golden ratio above also translates as
Simply in a straight line a +b is the same as a is to b. This can be transferred into the markets making the Golden ratio significant in trading.
Reversals tend to occur at the 0.618 and 1.618 of a price trend. So a trend is likely to pull back 38.2% of a 100% and continue to at least 61.8% of the previous leg down or up. Fibonacci retracement
Not an exact science but as we can see from this measurement holds true on this 15M chart of cable.
See this 1H chart as well. I could go on…
You get the point the Golden ratio works.