class of properties,
which is present in
all scientific disciplines
all kinds of the arts
The term symmetry is of ancient Greek origin. Its meaning is in close association with the related terms of
. Symmetry and the lack of symmetry characterise the
phenomena in our natural and artificial environment, as well as our ideas about the world.
Traditional meaning of symmetry
The meaning of this term went through a fabulous transformation during its use for dozens of centuries.
The proper translation of the Greek term symmetria
- (from the prefix syn
[common] and the noun metros
- is 'common measure'. The Greeks interpreted this word, as the harmony
of the different parts of an object, the good proportions
its constituent parts. Later this meaning was transferred to e.g., the rhythm
of poems, of music, the cosmos
('well-ordered system of the universe as contrast of chaos').
Therefore the Latin and the modern European languages
used its translations like harmony, proportion
until the Renaissance.
In wider sense, balance, equilibrium
belonged also to this family of synonyms.
Some way symmetry was always related to beauty
(These relative meanings determined its application in the arts
, the sciences
, and the ethics
Symmetry was not only related to such positive values, it became even a symbol of seeking for perfection.
Common meaning of symmetry
In its everyday use symmetry
is associated with its
most frequent manifestations, like reflection
or, in other words,
(rotational symmetry), and repetition
(translational symmetry). A few further geometrical appearances of symmetry
belong also to this class of interpretations, like glide reflection,
similitude, affine projection, perspective, topological symmetry
All they are associated with the observation, that one performed
a certain geometric operation
(a transformation) on an object;
and during that transformation one (or more) geometric properti(es)
of that geometric object
did not change (were conserved).
That/those property/ies proved to be invariant under the given transformation
They are called 'symmetry
' in everyday life.
Generalised, contemporary meaning of symmetry
In generalised meaning one can speak about symmetry if
- under any
(not certainly geometric) kind of transformation
- at least one
(not certainly geometric) property
- of the
(not certainly geometric) object
is left invariant
Thus we made a generalisation in 3 respects: to
- any transformation
- any object
, and its
- any property
This generalised meaning of symmetry
made possible to apply symmetry
to materialised objects in the physical and the organic nature, to products
of our mind, etc. Over geometric (morphological) symmetries, we can discuss
(e.g., in the human brain),
(of physical phenomena);
properties, like colour, tone, shadiness, weight
, etc. (of artistic objects).
: The lack of symmetry
: The observed object is symmetric in its main features,
but this symmetry is slightly distorted
(e.g., an arabesque ornament)
: The observed object is symmetric in one of its properties,
but one of its other properties changes to its opposite
(e.g., a chess-board)
(G. Darvas © )
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