Fibonacci Sequence
Online calculator for computing the Fibonacci sequence and displaying it in a table
Fibonacci Sequence Calculator
Fibonacci Table Generator
Creates a table with Fibonacci numbers starting from a selected index with a specific number of values.
Fibonacci Table
Enter parameters and click "Calculate"
to generate the Fibonacci table.
The table shows index and corresponding Fibonacci numbers.
Fibonacci Function Formulas
Binet's Formula
This formula allows the direct calculation of the nth Fibonacci number.
Fibonacci Number Sequence
The Fibonacci sequence is an infinite sequence of numbers that begins with 0 and 1. The sum of two consecutive numbers gives the immediately following number:
Usage Examples
Table Examples
- Start: 0, Count: 10
First 10 Fibonacci numbers - Start: 10, Count: 5
F₁₀ to F₁₄ - Start: 20, Count: 10
Large Fibonacci numbers
Practical Application
Ideal for teachers, students, and anyone who needs Fibonacci numbers in table format.
Golden Ratio
The ratio of consecutive Fibonacci numbers approaches φ ≈ 1.618.
Description of the Fibonacci Table
Functionality
On this page, a sequence of Fibonacci numbers is calculated using the Fibonacci function Fₙ. The result is displayed in a clear table. You can freely choose the starting index and the number of elements to be calculated.
Operation
- Enter the desired start index (starting with 0)
- Choose the number of rows for the table
- Click on "Calculate"
- The table will be automatically generated and displayed
Table Format
The table shows the index in the first column and the corresponding Fibonacci number in the second column. This allows for clear assignment between position and value in the Fibonacci sequence.
Practical Examples
Educational Sector
- Mathematics education: Explain number sequences
- Computer science: Demonstrate recursive algorithms
- Research: Analyze large Fibonacci numbers
- Homework: Quick reference table
Scientific Application
- Explore biological patterns in nature
- Architecture: Apply the golden ratio
- Financial analysis: Fibonacci retracements
- Cryptography: Random number generation
Interesting Properties
- Every 3rd Fibonacci number is divisible by 2
- Every 4th Fibonacci number is divisible by 3
- Every 5th Fibonacci number is divisible by 5
- The ratio F(n+1)/F(n) converges to φ
Calculation Notes
The calculator uses the efficient Binet formula for calculation. For very large indices, rounding errors may occur. The table scrolls automatically with many entries.
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