Fibonacci Calculator
Explore the Golden Sequence of Nature
Discover the beauty of the Fibonacci sequence. Generate sequences, find specific terms, calculate the golden ratio, and explore the mathematics that appears throughout nature.
Mathematicians' favorite
Golden ratio: 1.618
Nature's pattern
Fibonacci Calculator
Explore the Fibonacci sequence, golden ratio, and related mathematical sequences
Generate first N Fibonacci numbers
Generate first N Fibonacci numbers (max 1000)
The Magic of Fibonacci
Discover why this sequence has fascinated mathematicians for centuries.
What is Fibonacci?
The Fibonacci sequence starts with 0 and 1, then each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21...
The Golden Ratio
As the sequence progresses, the ratio between consecutive terms approaches phi, approximately 1.618033988749895, known as the golden ratio.
In Nature
The Fibonacci sequence appears in flower petals, pinecones, sunflower seeds, and even hurricanes, demonstrating nature's mathematical beauty.
Fibonacci Spiral
When you draw quarter-circle arcs connecting opposite corners of squares in the Fibonacci pattern, you create the famous Fibonacci spiral.
Lucas Numbers
A related sequence starting with 2 and 1 instead of 0 and 1. Lucas numbers share many properties with Fibonacci numbers.
In Biology
DNA molecules measure 34 angstroms long by 21 wide for each full cycle of the double helix. Both are Fibonacci numbers!
Fibonacci in the World
Nature
- Sunflower seed patterns
- Pinecone spirals
- Flower petal counts
- Nautilus shell curves
- Tree branching patterns
Art & Design
- Golden rectangle composition
- Classical architecture
- Logo design
- Typography proportions
- Photography rule of thirds
Science & Tech
- Algorithm complexity
- Data structure analysis
- Stock market analysis
- Cryptography
- Computer graphics
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