The Fibonacci sequence describes the pattern in which the petals of flowers grow, the number of spirals of seeds that evergreen cones have, and the pattern in which flowers fit the most seeds possible into their centers. So what do these numbers mean to us as amateur mathematicians and naturalists? They help us to understand the deeper non-aesthetic meaning behind the patterns that we observe in nature. If you divide any two consecutive numbers in the sequence – 55 and 34, for example – the quotient will be phi. The ratio was originally discovered in order to describe the relationship between the longest and shortest sides of a rectangle thought to be the most beautiful to the human eye, but it is very closely related to the Fibonacci Sequence. Meanwhile, the Golden Ratio is a number called phi, which is equivalent to roughly 1.618. It is a series of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.) in which each number in the pattern is equal to the two numbers before it – for example, 1+1=2, 2+1=3, and 2+3=5. The Fibonacci Sequence and the Golden Ratio describe, in mathematical terms, the reasons for nature’s plethora of spiral patterns. Beneath the aesthetically pleasing shapes of petals, seeds, and branches are two fascinating mathematical concepts that explain nature’s tendency to expand in spirals. The spirals that appear all around us are no accident of nature – while they’re beautiful to look at, their purpose is much more important than vanity alone. Evergreen cones, heads of broccoli and cauliflower, and tree branches all display noticeable iterations of this spiraling pattern, too. Snail shells, too, show growth rings that become gradually larger as they spiral away from the shell’s center. Sunflowers, for example, seem to spiral their seeds from their centers in some sort of mathematical pattern. Nature is filled with patterns – spirals, in particular, are especially noticeable in species of plants and animals. So next time you’re admiring a bouquet of flowers, take a closer look and you might just see the miracle of science as well as the beauty of nature.The Fibonacci sequence describes the pattern in which flowers fit the most seeds possible into their centers. 55, 89 Petals: michelmas daisies, the asteraceae family.21 Petals: aster, black-eyed susan, chicory.13 Petals: ragwort, corn marigold, cineraria.5 Petals: buttercup, wild rose, larkspur, columbine. In fact, the Fibonacci effect can be applied to many species of flowers in relation to their number of petals. Known as the ‘golden spiral’ the arrangement allows for the most compact containment of the petals (just think of the size of a rose bud in comparison to its fully opened bloom). That signature spiral isn’t just pretty to look at – like the sunflower head, its form has an essential function. A rose by any other pattern…įibonacci numbers also reveal themselves in the spiral of a rose bloom. As the individual seeds grow, the centre of the seed head is able to add new seeds, pushing those at the periphery outwards so the growth can continue indefinitely. In the case of sunflowers, Fibonacci numbers allow for the maximum number of seeds on a seed head, so the flower uses its space to optimal effect. The Fibonacci sequence is also closely related to the Golden Ratio – a number that has cropped up time and time again in human culture for thousands of years. In the 19th century it emerged that the sequence commonly occurred among the structures of the natural world, from the spirals of a pinecone to the seeds on a sunflower. It starts 1 1 2 3 5 8 13 21 and goes on forever. Named after a 13th century Italian Mathematician, Leonardo of Pisa who was known as Fibonacci, each number in the sequence is created by adding the previous two together.
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