Relational equation between Fibonacci series with Pi

There is an interesting connection between the Fibonacci sequence and π (pi), though it is not immediately obvious. One way to establish a relationship between them is through continued fractions and asymptotic behavior.

A Relational Equation:

One well-known relation involves Binet’s Formula for Fibonacci numbers:

where ϕ
(the golden ratio) is:

Now, π can be related to the Fibonacci numbers using the Wallis product and continued fractions. A well-known formula that connects Fibonacci numbers and π is:

This converges to π, demonstrating a deep connection between Fibonacci numbers and π