Fibonacci Spiral & Phyllotaxis

Why sunflowers, pinecones and galaxies use the golden angle

Show spirals:
φ =
Fibonacci #:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

Golden angle = 360°(2-φ) = 137.508°
φ = (1+√5)/2 ≈ 1.61803...

CW: 34, CCW: 55
Drag the angle slider away from 137.51° to see how pattern quality degrades — rational approximations create gaps. The golden angle is the "most irrational" number.