The Beauty in Nature and The Poetry in Fibonacci’s Mathematics
We have had to wait a good deal longer than usual this year for the Spring’s to burst forth with its signature display of natural beauty. We all have the privilege of deciding what amounts to beauty in nature. What we can share is the experience of Spring bursting forth in the Chilterns countryside. Beauty in nature is, as in love, ‘in the eye of the beholder’. For some it will be the blossoming of bluebells, it might be the nesting of birds or the greening of beech trees. And for others it is the sense of the whole world coming alive once again after the dead of winter; rejuvenation and rebirth, reawakening of the senses. Poetry has oft been used to capture the beauty of nature as in this poem about Spring:
The air is cool, the breeze is light.
The clouds in the sky are fluffy and white.
The flowers open to show their bright faces,
as the garden snail alongside paces.
The trees unfold their bright green leaves.
The spider a silken web she weaves.
The birds sing their notes high and clear.
Cheer up! Cheer up! Spring is here!
– Teresa Underwood
Don’t get me wrong I’ve not gone all romantic about Spring! It’s just my way of setting things up so I can introduce another way you could start to look at the beauty of the Chilterns or any landscape for that matter. Spring brings to the fore recurring patterns that are commonplace throughout the natural world and are based on a formula which is to be found in the structure of plants or animals, in the activities and constructions of the latter, as well as in natural phenomena. In effect what is at play here is the poetry of mathematics contributing to the beauty of nature. Specifically there is a pattern of numbers known as the Fibonacci Sequence. This is a series of numbers which starts 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… and so on – where each successive number being the sum of the previous two numbers. This sequence was first discovered by Indian mathematicians in the 6th century; however it was an Italian mathematician, Leonardo de Pisa, aka Fibonacci who, in the 11th century, first applied this sequence to events in the natural world. He predicted that the sequence which, only later became named after him, would be found throughout nature and in natural phenomena such as in the structure of waves.
My cast of characters is drawn from those referred to in the poem above. We are all familiar with the sticky leaf buds of the horse chestnut. The assemblage of buds on the branch is not random but is based on the fibonacci sequence. Subsequently, as the trees unfold their bright green leaves an order becomes apparent in their organisation. The distance between the buds increases the further they are from the tip of the stem and their relative position is also orientated along a spiral drawn according to the fibonacci sequence. As a tree grows from a single stem this simple layout contributes towards the overall configuration of all the branches in the mature tree. Of course no tree remains in such a pristine state but is affected by pest attack and disease but the general symmetry obvious in mature broad-leaved and coniferous trees which have avoided major damage is dictated at the outset by this sequence.
Flowers open to show their bright faces and in plants such as daisies and dandelions these flowers are in reality composite structures called inflorescences, comprising large number of tightly-packed florets which make up one large super-flower. The orientation of these florets follows the line of several spirals arcing out from the centre of the inflorescence which describe a pattern again based on this special numerical sequence. Perhaps the best display of this is in the seed head of a sunflower. Other examples can be found in fruit such as the pineapple, the cones of cycads and cypress firs and when taking a cross-section through a red cabbage.
Moving onto the animal kingdom a most pervasive of examples is the garden snail. Alongside (your prized herbaceous border) paces this rampant mollusc carrying on its back a conspicuous spiral shell with annualised growth rings though varying from season to season, for reasons of climate, has been perfectly formed in accord with the mathematical formula. A slow motion billboard advertising it belongs to the fibonacci brand. Another example in the animal world is the spiral horns of sheep, goats and some deer.
An example where the fibonicci sequence comes into play is the construction when the garden spider a silken web she weaves. The web comprises several spirals built on radiating spokes. The mystery is how the fibonacci spiral based on this mathematical sequence produces, without failure, such a perfectly proportioned web structure. The plan for the web is embedded within the ganglia of the spider. As set out in Darwin’s theory of natural selection which drives the process of evolution there is a continuous drive to refine processes to achieve the most efficient use of scarce materials.
To put another way, there’s simplicity, complexity and, above all, beauty in nature. So when around and about our Chiltern Hills do enjoy its beauty, whatever is your chosen way.
More Nature Notes