GOLDEN RATIO & FIBONACCI

▸ Loading the constant φ = 1.6180339887…
▸ Building the sequence 1, 1, 2, 3, 5, 8, 13, 21…
▸ Calibrating the golden angle 137.507°
▸ Tiling squares & sowing sunflower seeds
▸ Drawing the logarithmic spiral…
▸ Ready — Online. ✅
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⌂ Mathematics

Simulation room Golden ratio & Fibonacci

Golden Ratio
Online
φ = 1.618… · golden angle 137.5°
Convergence to φ
🐚 Golden spiral
ratio Fₙ₊₁/Fₙ → φ
φ (golden)
Ratio Fₙ₊₁/Fₙ
Index n
Seeding angle
Element count
Deviation from φ
Tip
Each Fibonacci number is the sum of the two before; their ratio chases φ. Sow seeds spaced by the golden angle and they pack the tightest — that is why sunflowers, shells and pine cones all bear the mark of φ.
Pick a mode on the right to see each phenomenon · drag the Angle slider in Sunflower mode
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Fibonacci ratio converging to φ with n ratio Fₙ₊₁/Fₙφ = 1.618