# Golden Section

14 15 orDer behinD DiversiTy she loves me, she loves me not Despite its seemingly endless variety and diversity, nature employs only three basic ways to arrange leaves along a stem disticious, like corn, decussate or whorled, such as mint, and the most common, spiral phyllotaxis for about 80 of the 250,000 different species of higher plants, where the divergence rotation angle between leaves has only a few values, these being close Fibonacci approximations to the golden angle, 137.5o. This pattern aids photosynthesis, each leaf receiving maximum sunlight and rain, efficiently spirals moisture to roots, and gives best exposure for insect pollination. Opposing spirals of seeds in a sunflower generally appear as adjacent Fibonacci numbers, typically, 5534 1.6176 or 8955 1.6181. Scales of pinecones are typically 53 1.6666, or 85 1.6. Artichokes likewise display 8 spirals one way, 5 the other. Pineapples have three spirals, often 8, 13 and 21 each below, where 21138 approximates 1 1, with 2113 1.6153, 138 1.625, and 218 2.625, aspiring towards 2, or 1. Similarly, the pussy willow branch spirals 5 times with 13 buds appearing. Next time you are out in the park, woods, countryside, or along a trail, take a moment to examine the petals on a daisy, count the spirals on a pinecone, or note the buds on a pussy willow. 8 gradual 5 gradual 13 medium 8 steep 21 steep Simple phyllotaxis deriving from Fibonacci numbers in each case ab, a leaves are produced in b turns, meaning that the leaf divergence angle is ba360o. As a and b increase, the divergence angles approach 137.5o and 222.5o. A frond of brown alga left, with a schematic centre showing the number of bifurcations exhibiting Fibonacci numbers. Sneezewort right also displays Fibonacci numbers in the count of its stems and leaves as it grows. The three phyllotactic patterns, disticious, whorled, and spiral after Ball, flanked by two Fibonacci spiral examples. The plant on the left displays 8 leaves in 5 turns, the pussy willow on the right produces 13 buds in exactly 5 turns. stems leaves