Symmetry : yrtemmyS

Symmetry in its essence is the harmony of the different parts of an object; symmetry can mean also good proportions between its constituent parts. Symmetry denotes that sort of agreement or concordance of several parts by which they integrate into a whole. Symmetry as well as asymmetry characterizes many phenomena in our natural and man-made environment even our ideas about the world aims for symmetry too. Symmetry is in no doubt attractive to the human eye for it strikes a sense of balance, equilibrium and harmony.

Symmetry has always been a part of our lives. In its everyday use symmetry is associated with its different manifestations, like reflection or mirror-symmetry, rotation/rotational symmetry, and repetition/translational symmetry. A few further geometrical appearances of symmetry are glide symmetry, similitude, perspective and topological symmetry. All they are associated with the observation, that one performed a certain geometric transformation on an object and during that transformation one or more geometric properties of that object did not change or they were conserved. Those properties that have not changed prove to be invariant. Those invariances are referred to as “symmetry” in our everyday lives.

Symmetry shows its manifestations in a vast expanse of area. The reflection of a mountain in a lake, a starfish underwater, flowers of many types, a honeycomb, a snowflakes, the symmetry of our face, the facade of a cathedral, etc. All of these possess symmetry in the natural world and aesthetics. Symmetry does not always need to be spatial or visual: a musical composition, a play with its balanced structure of beginning, middle and end, etc. Symmetry is also an obvious feature of good, practical and effective design: a chair or table standing squarely, a clock face is symmetric, tea-cups and dinner plates have their own symmetries too.

Symmetry is a wonderful theoretical concept for science providing structure, organization (as oppose to asymmetry) and simplification for a host of complex phenomena across many disciplines. It is also worth noting the interrelationship between symmetry and asymmetry in a way that it tries to compensate for the other one. However without an understanding of the mathematical structures of symmetry we would not be able to comprehend asymmetry. Symmetry and asymmetry are therefore an essential dialectic for science, arts and society.