Ratio & Proportion · 2D
Phyllotaxis
The sunflower’s golden angle
Place each new seed a fixed angle around from the last. At 137.5°, the golden angle, they pack perfectly. Nudge it by a fraction of a degree and gaps appear.
- Golden angle
- 137.508°
- 360° ÷ φ²
- = 137.5°
Watch it drawn with compass and straightedge, hear the chord of its lines, and turn the Dimension dial to raise its form in space.
Facts
- The golden angle is 360° × (1 − 1/φ) ≈ 137.508°.
- Because φ is the "most irrational" number, seeds never line up into gaps.
- Count the spirals on a sunflower: usually 21 and 34, or 34 and 55: neighbouring Fibonacci numbers.
- Try the animation: near 137.5° the whole field suddenly locks into place.
History and meaning
Leaves, florets, pine cones and pineapples grow this way, which maximises light and packing. Helmut Vogel gave this simple model of the sunflower head in 1979.
Across the dimensions
- Shadow of Fibonacci SphereWrap the sunflower around a ball: the golden angle spreads points evenly over a sphere.
Learn it step by step
- Journey The Golden ThreadStep 3: The golden angle
