The Fibonacci Sequence

The Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones: 0 +1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5... The first 20 terms of Fibonacci series are :- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181.

The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five, the chicory`s 21, the daisy`s 34, and so on.

Fibonacci numbers can be illustrated as a spiral with squares representing the widths of the numbers in the sequence. The squares fit nicely together, forming the spiral. In this example, 1 plus 1 equals 2, 1 plus 2 equals 3, 2 plus 3 equals 5, 3 plus 5 equals 8, 5 plus 8 equals 13, etc.

Descri ption automatically generated">Fibonacci numbers appear in many contexts in our lives and surroundings, for example, the number of the petals in a flower, the seed heads of a flower, paintings and a lot more. In fact, the beauty of a human face is based on Golden Ratio, a constant which can be calculated from the numbers in the Fibonacci sequence.

The Golden Ratio is a constant and is represented by the symbol phi, 𝜙. If we have 2 numbers, A and B, with B > A,they are said to be in golden ratio, if, 𝜙

^(A+B) / _B = ^𝐵 / _𝐴 ≡𝜙

Phi has the value 1.618 and we can see this value emerge from the Fibonacci sequence by dividing successive numbers in the sequence:

3/2 =1.5, 5/3 = 1.67, 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.615, 34/21 = 1.619, 55/34 = 1.618

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