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Fibonacci Spiral

Math Experiment Details

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📖 About This Experiment

The Fibonacci spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every quarter turn it makes. This experiment visualizes how the Fibonacci sequence and the golden ratio (φ ≈ 1.618) appear throughout nature, from nautilus shells to sunflower seeds to spiral galaxies.

💡 Key Concepts

  • •Fibonacci Sequence: Each number is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, 13...)
  • •Golden Ratio (φ): The ratio of consecutive Fibonacci numbers approaches φ
  • •Golden Angle: ≈ 137.5° - optimizes seed packing in plants
  • •Logarithmic Spiral: Grows by constant factor per rotation
  • •Phyllotaxis: Arrangement of leaves on a plant stem

🔢 Key Formulas

Fibonacci Sequence
F(n) = F(n-1) + F(n-2)
Golden Ratio
φ = (1 + √5) / 2 ≈ 1.618034
Binet's Formula
F(n) = (φⁿ - (-φ)⁻ⁿ) / √5

🔬 Real-World Applications

  • 1.Botany: Seed arrangement in sunflowers, pinecones, and pineapples
  • 2.Marine Biology: Nautilus shells and other mollusks
  • 3.Astronomy: Spiral galaxy structure
  • 4.Art & Design: Composition and proportion in art and architecture
  • 5.Financial Markets: Technical analysis and retracement levels
🚀 Launch Fibonacci Spiral Experiment