The Fibonacci sequence has long caught people’s interest because of its unique mathematical characteristics. It is approximately 1.618 and is represented by the Greek letter phi. The “golden ratio” is a one-of-a-kind mathematical relationship. It’s a way for information to move quickly and efficiently. The spiral begins from her left wrist and travels to the background of the painting that follows the sequence.Everything in the universe is kept in order by a “golden ratio.” The Fibonacci sequence can be found throughout nature, from the tiniest to the biggest objects. One of the most famous examples was painted by Leonardo da Vinci, the Monalisa.

The golden ratio and the Fibonacci numbers guide design for websites, architecture, and user interfaces.

It appears in various fields of study, including cryptography and quantum mechanics.

It is used in stock prices and other financial data.

It is used in coding (distributed systems, computer algorithms ).

People claim this is ‘nature’s secret code’ for building the structures perfectly, just like the Great Pyramid of Giza.

The spiral can be seen in seashells and the shapes of snails.

In a pair of a male and a female rabbit, if no rabbits die or leave the place, it forms the Fibonacci sequence 1,1,2,3,5, and so on due to their reproduction. The pattern of seeds in the sunflower also follows this sequence.

It appears in plants with many seed heads, pinecones, fruits, and vegetables.

We find the Fibonacci Sequence in various fields, from nature to the human body. Here, the middle numbers of each row are the sum of the two numbers above it. It is a number triangle that starts with 1 at the top, and each row has 1 at its two ends. We can also derive the sequence in Pascal’s triangle from the Fibonacci Sequence. Thus, the Lucas numbers are found to get closer to the powers of the Golden Ratio. Here, the number sequence starting from 2 is formed by adding two preceding numbers, known as Lucas numbers. We get another number sequence from the Fibonacci Sequence that follows the same rule mathematically. = 233 – 1 = 232 Finding Lucas Numbers from the Fibonacci Sequence The sum of the first 12 terms = (12+2) th term – 2 nd term Where Fn is the nth Fibonacci number, and the sequence starts from F 0. Using the Golden Ratio, we can approximately calculate any Fibonacci numbers as It appears in many works of art and architecture.

In geometry, this ratio forms a Golden rectangle, a rectangle whose ratio of its length and breadth gives the Golden Ratio.

It follows a constant angle close to the Golden Ratio and is commonly known as the Golden Spiral. It is followed by the sum of the two previous squares, where each square fits into the next one, showing a spiral pattern expanding up to infinity. It starts with a small square, followed by a larger one adjacent to the first square. Geometrically, the sequence forms a spiral pattern.

To calculate the 50 th term, we need the sum of the 48 th and 49 th terms. Since the Fibonacci sequence is formed by adding the previous two Fibonacci numbers, it is recursive in nature. Thus, the Fibonacci sequence follows an even, odd, odd, even, odd, odd pattern.

Also, the sum of two odd numbers is always an even number, whereas the sum of an even and an odd number is an odd number.

Similarly, every fourth number after 3 is a multiple of 3, every fifth number after 5 is a multiple of 5, and so on.

Every third number in the series, starting at 2, is a multiple of 2.

The numbers in the sequence follow some interesting patterns: The following table lists each term and term value in the Fibonacci Sequence till the 10 th.

Extended fibonacci sequence nature