Fibonacci Phyllotaxis — Golden Angle Spiral

Plants pack seeds by placing each new seed at the golden angle (≈ 137.508°) from the last. This irrational angle minimizes overlap and produces Fibonacci-numbered spiral counts.

Golden Angle

φ = (1+√5)/2 = 1.61803…
Golden angle = 360°/φ² = 137.508°
In radians: 2π(2−φ) = 2.39996…
CW spirals: —
CCW spirals: —

Fibonacci Numbers

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
Ratio → φ: 55/34 ≈ 1.6176
Current angle offset: 0.000°
Visible seeds: —

The golden angle is the irrational angle that most evenly distributes points on a circle. Any rational angle (even close to golden) creates visible spoke gaps. Only the golden angle — an irrational number related to the hardest-to-approximate-by-fractions constant φ — fills space optimally. Spiral counts in sunflowers, pine cones, and pineapples are always consecutive Fibonacci numbers.