1. What is the Fibonacci Series?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. It appears in many areas of mathematics and nature.

2. How Does the Calculator Work?

The calculator uses the Fibonacci formula:

Where:

• \( fib_n \) — Current Fibonacci number
• \( fib_{n-1} \) — Previous Fibonacci number
• \( fib_{n-2} \) — Fibonacci number before the previous one

Explanation: The sequence grows exponentially, with each term being the sum of the two immediately preceding terms.

3. Importance of Fibonacci Numbers

Details: Fibonacci numbers appear in biological settings, computer algorithms, financial markets, and have applications in mathematics and computer science.

4. Using the Calculator

Tips: Enter two consecutive Fibonacci numbers (as integers) to calculate the next number in the sequence.

5. Frequently Asked Questions (FAQ)

Q1: What are the first few Fibonacci numbers?
A: The sequence typically starts: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Q2: Can Fibonacci numbers be negative?
A: In the standard definition, no. Fibonacci numbers are defined for non-negative integers.

Q3: What is the golden ratio connection?
A: The ratio of consecutive Fibonacci numbers approaches the golden ratio (≈1.618) as n increases.

Q4: Are there real-world applications?
A: Yes, in computer algorithms, financial analysis, and modeling natural phenomena like plant growth patterns.

Q5: How does this relate to recursive programming?
A: The Fibonacci sequence is a classic example used to teach recursion in computer programming.