The Fibonacci Sequence is a special series of numbers by getting the sum of the two preceding numbers, starting with 0 and 1. This was named after an Italian Mathematician, Leonardo Pisano Bogollo or famously known as Fibonacci who discovered the unique pattern of numbers primarily with his observations during his travels with his father.
The first ten series of numbers in the Fibonacci Sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, and 34. As mentioned earlier, a number is obtained by adding up the two previous numbers.
1 is found by adding two numbers before it (1 + 0)
2 is found by adding two numbers before it (1 + 1)
3 is found by adding two numbers before it (2 + 1)
5 is found by adding two numbers before it (3 + 2)
so on and so forth!
The seventh term can be written as X7, which is equal to 13 (8 + 5)
xn = xn−1 + xn−2
To find the nth Fibonacci number without using the recursion formula, the Binet Formula is used:
The mathematics of the Fibonacci Sequence and the Golden Rule are interrelated. When two successive terms of Fibonacci numbers are compared, their ratio is called the Golden Ratio, denoted by the symbol 𝟇 (Phi), which has a value of 1.618. This ratio can also be observed in the Fibonacci sequence:
To understand how the golden ratio is obtained, look at the figures above. The longer side (a) over the shorter side (b) has the same ratio as the sum of both sides (a+b) over the longer side (a).
The given example above satisfies the golden ratio because both resulted in the same result, which is 1.618. The rectangle above shows us that a golden rectangle can be obtained by forming a square in a golden rectangle. The remaining rectangle from the formed perfect square is now the newly formed golden rectangle, and the process continues, forming a spiral Fibonacci spiral.
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