Place a seed on a disk. Rotate by some angle θ. Place another seed. Rotate by θ again. Repeat. For most angles θ, seeds cluster in spokes and leave empty wedges. But if θ is the golden angle ≈ 137.5°, seeds pack perfectly: no two seeds ever align and no gap ever forms, no matter how many you add.
The golden angle is 360° × (2−φ) where φ ≈ 1.618 is the golden ratio. It works because φ is the "most irrational" number: hardest to approximate by any fraction. Any rational fraction p/q produces exactly q spokes. The golden ratio, never well-approximated by rationals, spreads seeds evenly forever.
Evolution has discovered this optimal packing in sunflowers, pine cones, pineapples, artichokes, and cacti. The spirals you count in a sunflower head are always consecutive Fibonacci numbers (34 and 55, or 55 and 89) a direct consequence of the golden angle.