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Fibonacci Calculator
Generate sequences, find nth terms, and check Fibonacci numbers
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About Fibonacci Calculator
Explore the Fibonacci sequence: generate the first N terms, find any specific term, check if a number belongs to the sequence, or sum a range. Shows the golden ratio approximation.
How It Works
In sequence mode, generates Fibonacci numbers iteratively (max 100 terms). The check mode uses the mathematical property that N is Fibonacci if and only if 5N²+4 or 5N²-4 is a perfect square. Shows φ (phi) approximation.
Step by Step
- 1 Select a mode: sequence, nth term, check, or sum
- 2 Enter a number (N for sequence/term, or a value to check)
- 3 Click Calculate to see the results and golden ratio
Tips
- The golden ratio φ ≈ 1.618034 — the ratio of consecutive Fibonacci numbers converges to this value
- Fibonacci numbers appear in nature: sunflower spirals, pinecone patterns, nautilus shells
- The sum of the first N Fibonacci numbers equals F(N+2) - 1
- Maximum sequence length is 100 terms to avoid browser performance issues
Frequently Asked Questions
What is the golden ratio?
The golden ratio (φ ≈ 1.618034) is the limit of F(n+1)/F(n) as n approaches infinity. It appears throughout mathematics, art, and nature.
How can I check if a number is in the Fibonacci sequence?
A number N is a Fibonacci number if and only if 5N²+4 or 5N²-4 is a perfect square. This mathematical property avoids generating the entire sequence.