goldenangle

Goldenangle is the name given to the approximately 137.5-degree angle that frequently appears in the arrangement of leaves, seeds, and other botanical features around a stem or axis. It equals 360 × (1 − 1/φ), where φ is the golden ratio (~1.6180339887). Equivalently, it can be expressed as 360/φ^2 degrees, about 137.507764 degrees.

In phyllotaxis, placing successive organs at this angle relative to the previous one minimizes overlap and promotes even distribution. The resulting patterns often include parastichies that follow Fibonacci numbers. The angle thus helps explain the prevalence of spiral arrangements observed in sunflowers, pinecones, and many tropical inflorescences.

Using the goldenangle concept, researchers model optimal spacing in plants, and it is also used in computer graphics and design to distribute points around a circle with low clumping. Real biological systems may show approximations to the exact value due to growth variations and genetic factors.

See also golden ratio, phi, phyllotaxis, and Fibonacci numbers.