Why exactly 137.5°? The secret of the angle seeds grow at
Change the angle with a slider, and see that there's exactly one angle at which seeds pack in tightly with no overlap. That angle is called the "golden angle."
The golden angle (137.5°) is what you get by dividing one full turn (360°) by the golden ratio (about 1.618). Every time a plant grows a new seed or leaf, it turns by this exact angle before settling into place, and the reason is simple — 137.5° is the angle that comes "closest to irrational," never dividing evenly into any whole fraction of a turn (1/2 turn, 1/3 turn, 2/5 turn...), so the seeds never stack up overlapping in the same direction, letting them share sunlight and space as efficiently as possible. If you actually count a real sunflower's seeds, the number of clockwise and counterclockwise spirals always comes out as neighboring Fibonacci numbers, like 34 and 55 — and that's no coincidence either; it's a direct mathematical result of the spiral arrangement the golden angle produces.
137.5°
200
Golden angle = 360° ÷ φ²
about 137.5°
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Sunflower seeds
Each seed grows turned 137.5° from the last, which creates spiral arms in both the clockwise and counterclockwise directions. Count them and you'll usually get neighboring Fibonacci numbers, like 34 and 55.
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Pinecones
The scales are arranged by this same principle, so counting along the spiral directions reveals spirals in Fibonacci numbers too, like 8 and 13.
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Nautilus shell
The shell grows larger by a constant ratio (the golden ratio, about 1.618×) with each new chamber, coiling into a smooth spiral shape.