What is the Golden Ratio?
The Golden Ratio (φ) is a special number (≈ 1.618) that appears throughout nature.
When two quantities have this ratio, they're considered aesthetically pleasing and harmonious.
Formula: a/b = (a+b)/a = φ
Golden Rectangle
Long side (height)
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Golden Rectangle
Golden Rectangle:
A rectangle where the ratio of the longer side to the shorter side equals φ (1.618).
If you remove a square from it, you get a smaller golden rectangle. This creates the famous Fibonacci spiral!
Fibonacci Sequence Generator
Fibonacci Sequence
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Consecutive Ratios (approaching φ)
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Fibonacci & Golden Ratio:
As you progress through the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13...),
the ratio between consecutive numbers gets closer and closer to φ.
This pattern appears in sunflowers, pinecones, and seashells!