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