XIII A: Role of Mathematics behind amazing symmetry in nature

XIII A: Role of mathematics behind amazing symmetry in nature

 [Contd. A Journey to the Wonderland of Math.by Ajay Kumar Chaudhuri ]

       " The chief forms of beauty are order and symmetry and definiteness,which mathematical scicences demonstrate in a special degree."------Aristotle.

 Nature has been a perennial source of inspiration for many of us. Artists, architects, designers imitate the design patterns of nature. Poets describe its beauty and scientists try to unravel the mysteries of nature. A deep look into nature unlocks imagination and inspires creativity.

Nature paints the most wonderful pictures those can take our breath away and engulf us in their majestic beauty.

One cannot marvel at the designs of nature. The spirals of seashells, swirl of rose petals and the arrangement of sunflower seeds, air vortex created by the flapping of wings of insects, the galaxy spirals and even the eye of a hurricane follow a geometrical pattern which is represented by the Fibonacci Series.

When we look deep into the natural world around us, we observe some amazing regularities in them which is termed as “pattern”.  At a first glance, it may appear overwhelming in its diversity and complexity but there are regularities running through it, from the hexagons of a honeycomb to spirals of sea shell and branching veins of a leaf, revealing the order at the very foundation of the seemingly chaotic natural world. Patterns in nature explore not only math and science but also the beauty and artistry behind nature’s awe -inspiring designs.

We create many patterns in our technology, architecture and art, but natural patterns are formed spontaneous from the sources that act in the physical world. Very often the same types of patterns and form, say for example, spirals, stripes, spots, dunes,meanders fractals etc. recur in places that seem to have nothing in common, such as marking of zebra mimic the ripples in windblown sand. That’s because, the patterns in nature can often be described using the same mathematical and physical principles. There is a surprising underlying unity in the Kaleidoscope of the natural world.

By exploring similarities such as those between a snail shell and whirling stars of a galaxy, or the branches of a tree and those of a river network, we can discover spectacular visual wonder, beauty and richness of natural pattern formation.

Through our long observations and experience, we are convinced to believe that the nature in which we live and an inseparable part, does nothing without any purpose. So the obvious question arises: What is the purpose behind these patterns in natural world?

Early Greek philosophers like Plato, Pythagoras, Empedocles attempted to explain order in nature. The modern understanding of the visible patterns developed with the passing of time.

Mathematics, physics and chemistry can explain patterns in nature at different levels. Patterns in living things are explained by the biological process of natural selection and sexual selection.

Living things like orchids, humming birds, and the peacock’s tail have abstract designs with a beauty of form, pattern and colour that artists struggle to match. . Mathematics seeks to discover and explain abstract patterns or regularities of all kinds.

The laws of physics apply the abstractions of mathematics to the real world, often as it were perfect. Exact mathematical perfection can only approximate real objects, visible patterns in nature are governed by physical laws . In biology, natural selection can cause the development of patterns in living things for several reasons, including camouflage, sexual selections and different kinds of signaling, including mimicry and cleaning symbiosis. In plants, the shapes, colours and pattern of flowers like the lily have evolved to optimise insect pollination where as other plants may be pollinated by wind, birds or bats. Honey bees, butterflies and many other pollinating insects are attracted to flowers by a radial pattern of colours and stripes, some of which are visible only in ultraviolet light. Interestingly, some creatures like birds, snakes, bees and many insects could perceive ultraviolet and infrared lights but the humans couldn’t. The pollinating creatures and insects attracted by colours and stripes on flowers that serve as a nectar guide that can be seen at a distance by scent and by rewards of sugar-rich nectar and edible pollen

So far, we have come across many examples and convincing role of mathematics in nature and now can emphatically say that mathematics is all around us. As we discover more and more about our environment and our surroundings we see that nature can be described mathematically. The beauty of a flower, the majesty of a tree, even the rocks upon which we walk can exhibit nature’s sense of symmetry. But what is symmetry?

Symmetry of an object whatsoever or of a geometrical figure is:

When one shape becomes exactly like another if you flip, slide or turn it. The symmetry is a very important form of patterns ---- most common, most frequently occurring and the secret behind beauties of both living and non-living natural things.

Symmetry exists all around us. If we look around a bit carefully, we will find plenty of examples of symmetrical things : our body, the buildings on the street, pets like cats and dogs, butterflies, birds and many many others. The examples of symmetries observable in nature around us are inexhaustive. Symmetry is a perfect, harmonious structure of an object. In fact, symmetry is a magical and fascinating reflection in terms of biology, geometry, art and even architecture.

For centuries, symmetry has remained a fascinating subject for the philosophers, astronomers, mathematicians, artists, architects and physicists. The ancient Greeks were downright obsessed with it. Even today we struggle to apply it in everything from planning our furniture layout to styling our hair.

No one is sure why it is such ever present property or why mathematics behind it seems to permeate everything around us. Be careful, for once you aware of it, you likely have an uncontrollable urge to look for symmetry in everything you see!

Among the types of symmetries in the natural world, two main types are: reflective and rotational. Reflective or line symmetry means that one half of an image is the mirror image of the other half.
Look at the right and left half of our human body [Pic.No14a]. Stare at the body of animals like tigers,cats,dogs,elephants [Pic.No14b]. Gaze at the wings of a butterfly or a bird [Pic.No14c] .All of these possess line symmetry as well as bilateral symmetry. 

Pic.No 14a.

                                         Reflective (or line) symmetry in human face.

          

                    Pic.No14b.

    
                                                        Line symmetry in Elephant.      

pic.No14c.

Bilateral symmetry in bird`s wings. 

The rotational symmetry means that the object or image can be turned through a certain number of degrees, around a central point and match some number of times. The number of positions in which the object looks exactly the same is called order of this symmetry. So, if we look at the starfish, [Pic. No.-14d] sea shells, [Pic. No.-14e] some flowers, sections of fruits etc. we may get a first-hand idea of rotational symmetry.

                   Pic. No.14d.

      

                                          Radial as well as Rotational symmetry in Starfish.

Pic. No. 14e

Rotational as well as Spiral symmetry in Nautilus shell.

                                                                    

In biology, apart from those two symmetries, namely reflective and rotational, a third type of symmetry called Point Symmetry is found in living organisms. Point symmetry is kind of reflective symmetry which means any straight cut through the centre point divides the organism into mirroring halves. Some floating animals with radiating parts, and some microscopic protozoa fit into this category, animals with this layout are all very small.

Radial symmetry, a kind of rotational symmetry, (as is found in a cone or disk shape which is symmetrical about a central axis) also found in starfish, sea anemones, jellyfish and some flowers have radial symmetry.

Human being is naturally attracted to symmetry. Very often we consider a face beautiful when the features are symmetrically arranged. We are even attracted by proportions (perhaps you have not forgotten the amazing role of golden ratio, phi in aesthetic and beauties). In this aspect we are not alone. Many animals choose mates on the basis of symmetry. Biologists believe the absence of a symmetry is an indicator of sickliness, since only a healthy organism can maintain a symmetrical plan throughout its development in the face of environmental stresses, such as illness or lack of   food. A symmetrical animal is usually a healthy animal. The same is true for humans.

Symmetrical forms can be found in the inanimate world and in a broader sense, in this universe as well. The planets, more or less, exhibit radial symmetry. Snowflakes also provide a wonderful example of hexagonal symmetry. The fact is that all Snowflakes have this sort of symmetry due to way water molecules arrange themselves when ice formed. It is therefore a reminder that symmetry is part of the structure of the world around us.

In the Pic. No. 14, some beautiful examples of different types of symmetries are exhibited.

Another important, fascinating and most common pattern is Spiral shape which I have already touched citing some examples. In fact, the visual motif of the spiral is one of the oldest and most enigmatic sacred images known. It is one of the earliest examples of human creative expression appearing on nearly every society in the ancient world. The spiral has universal appeal and has a mysterious resonance with the human spirit. It is complex yet simple, intriguing and beautiful. The spiral pattern is found extensively in nature around us-- encoded into plants [Pic. No. 14f], animals, humans, the earth, galaxies [Pic. No. 14g] etc. Mathematics can explain the complex algorithms, sequences and equations that make up a spiral pattern, but it cannot explain the lure and fascination of the spiral to the human heart. Here another type of symmetry, called Triangular symmetry as is beautifully depicted in the[ Pic. No.14h.]
     Pic.No 14f.

                                                      Spiral symmetry in plants.                                                               

      Pic.No14g.                                           

                                        

    
                                                      NGC4414--a typical spiral galaxy.

     Pic.No14h.           Triangular symmetry in a flower.

                                                                                                                      

Reference Internet: All the images (except otherwise mentioned ) of this article are downloaded from Public Domain. 

   
Pic.No 14(e) Nautilus shell (Attribution: Wikimedia Cosmos :https://en.wikipedia.org/wiki/Nautilus
    e. j)
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