The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55….. and so on forever. Each number is the sum of the proceeding two numbers.
Leonardo Fibonacci (1170 – c. 1250), an Italian mathematician, came up with the sequence when calculating the ideal expansion of pairs of rabbits over the course of one year. The success of rabbit experiment gave him the mathematical code to the working of nature.
The sequence was later on known as The Fibonacci Sequence. He introduced the series in his book named Liber abaci which mean ‘The book of Calculations’ , written in 1202.
However, the series was known by the Indian mathematicians many years before it was discovered by the Leonardo of Pisa or Leonardo Fibonacci.
Indian mathematician Virahanka (lived in the 6th century) studied syllables and came up with the same series. Leonardo Fibonacci studied Indian mathematics and Hindu–Arabic numeral system during his visit to the eastern world.
But before introducing it to the western world he experimentally observed the expansion pairs of rabbits. Authenticating what he introduced in his book Liber abaci.
Fibonacci sequence and the Golden ratio
If the ratio between any number and its preceding number in series is calculated then the ratio is nearly equal to the golden ratio. i.e, 1.618
If the ratio between any number and its succeeding number in series is calculated then the ratio is nearly equal to the inverse golden ratio. i.e, 0.618
Fibonacci sequence formula
Fibonacci sequence can be achieved using the recursive formula-
Fn = Fn-1 + Fn-2
where, n=1,2,3,4,5,6,7…..so on.
We can easily calculate the series using the above formula but it will take very much time to calculate for a greater value of n. To overcome this problem of heavy computation we can use another simple formula,
Fn = [ Phin – (phi)n ]/√5
where, Phi=(1+√5)/2 (Phi is the another name of golden ratio)
The beginning of magic
Now, the real magic of creation begins with the Fibonacci sequence and the golden number. Together they make up the pattern which gave birth to the whole creation (material world) and can be found everywhere in nature. This pattern is known as the golden spiral. Without any further delay let me show how Fibonacci rectangle is constructed using the golden ratio and how this rectangle gives birth to the beautiful and magical golden spiral.