Phyllotaxis is the arrangement of leaves, seeds, or florets on a plant. Each new leaf or seed is placed at the golden angle from the previous one. This gives each element the maximum exposure to sunlight and rain, and packs seeds as tightly as possible without overlap. The spirals you see in sunflowers, pine cones, and pineapples always number consecutive Fibonacci numbers, a direct consequence of the golden angle.
Da Vinci observed and drew spiral leaf arrangements in plants and noted their beauty and regularity. However, the mathematical explanation via the golden angle came much later. The term phyllotaxis was coined in 1754, and the connection to the golden ratio was established in the 19th century by researchers including the Bravais brothers.
The golden angle ≈ 137.508 degrees divides a full rotation (360°) in the golden ratio: the larger part is 360/phi ≈ 222.5° and the smaller is 360/phi^2 ≈ 137.5°. Plants arrange leaves and seeds at the golden angle to maximise exposure and packing. The resulting spirals always show consecutive Fibonacci counts: sunflowers typically have 34 and 55 spirals, or 55 and 89. This efficient packing is a direct consequence of the golden angle's extreme irrationality.