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The natural world abounds in beautiful patterns, each evolved to enhance survival of a species – the extravagant, iridescent peacock’s tail, which serves to attract a mate, while intricate orchid flowers entice pollinators and tigers’ stripes provide camouflage.
But not all nature’s patterns are quite as showy; it is the mathematical symmetries that I find most intriguing.
Italian mathematician Leonardo Fibonacci lived in 12th century Algeria when Indian numerals were introduced to the West via the Middle East. In his book, Liber Abaci (published in 1202), he describes a numerical sequence, now called the Fibonacci sequence, in which each number is the sum of the previous two digits: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ad infinitum. He formulated this recurrence in relation to rabbit breeding, but it turns out to be exceedingly wide-spread in nature, from tree branching to mollusc shell growth to bee reproduction.
Plant leaves are like solar panels, absorbing sunlight to power energy-providing photosynthesis. Thus, leaves appear in a spiral around the stem, each positioned to optimise sunlight capture. The ratio of leaves to turns is always a ration of Fibonacci numbers; 3 leaves to 1 turn for hazel, 8/3 for pear and 13/5 for almond trees. The angle between consecutive leaves is always close to 137.5o, called ‘the golden angle’ – perfect for maximising energy production.
The number of petals in most flowers also follows the Fibonacci sequence: lilies have 3, buttercups 5, delphinium 8, common marigolds 13, asters 21. But even more striking are the complex spirals of seed-heads of sunflowers, fir cones and pineapples. In each case new seeds forming in the centre of the flower push older seeds out into mesmerising patterns of interlocking, clockwise and anticlockwise spirals.
The numbers of spirals in both directions are consecutive Fibonacci numbers with 5 and 8 or 8 and 13 in pineapples, 8 and 13 in fir cones, and numbers as high as 144 and 233 recorded in sunflower heads.
Why? Because these configurations pack in the most seeds.