Maths

Why sunflower seeds never leave gaps: the golden angle and the Fibonacci spirals

A disc of several hundred lime-to-orange seeds arranged in the interlocking spirals of a sunflower head
30seconds
The 30-second version

Sunflower seeds are not placed in spirals on purpose. Each new seed turns a fixed angle from the last, and only one angle, about 137.5 degrees, leaves no bare lanes.

Drag the angle yourself: any simple fraction of a turn piles seeds into straight arms, and even a fifth of a degree off the golden angle opens gaps. The famous Fibonacci spiral counts, like 34 and 55, are just that angle's near-returns showing up.

Deep dive · 4 min
Deep dive · 4 min

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