GROUP: Martino Del Giudice (Italy); Iordache Giulia, Blaga Andrada, Necula Marina, Dandoczi Ruxandra, (Buchuresti, Romania); Kofopoulou Maria, Mavrapidi Mirsini (Mytilene, Greece), Posirca Alexandru, Hera Sebastian, Mir Robert from Rm. Vâlcea (Romania)

**NB: we've created this page all together**

DEFINITION

In general, the word "symmetry" refers to the presence of some repetitions in the geometric shape of an object.

Symmetry can be discussed from different perspectives:

- in geometry (we can consider reflection, rotational, translational, rotoreflection, helical and scale symmetry)

- in mathematics (when a mathematical operation, applied to an object, preserves some property of the object)

- in science (in this context, symmetry is related to some of the most profound results found in modern physics)

- in art (for example in architecture, paintings, symbols, vessels, music…)

EXAMPLES

**Symmetry in pottery**

**Symmetry in religious symbols**

**Symmetry in geometry**

**Reflection symmetry**

Reflection symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection.

In 1D, there is a point of symmetry. In 2D there is an axis of symmetry, in 3D a plane of symmetry. An object or figure which is indistinguishable from its transformed image is called mirror symmetric.

**Symmetry and nature**

**Symmetry in architecture**

Another human endeavor in which the visual result plays a vital part in the overall result is architecture. Both in ancient times, the ability of a large structure to impress or even intimidate its viewers has often been a major part of its purpose, and the use of symmetry is an inescapable aspect of how to accomplish such goals.

*Egyptian Pyramids, Koh Ker temple*

*Temple in Jerusalem*

*Beijing, Forbidden City*

*Cambodia, Choeung Ek*

*Cambodia, Angkor Wa*

*Pre-Columbian,Telamones Tula*

*Gothic architecture, Reims Kathedrale*

*Gothic architecture, Batalha Facade*

*America, President Thomas Jefferson's Monticello house*

*America,Capitol Building*

*India, Agra,Taj Mahal*

**Symmetry in aesthetics**

The relationship of symmetry to aesthetics is complex. Certain simple symmetries, and in particular bilateral symmetry, seem to be deeply ingrained in the inherent perception by humans of the likely health or fitness of other living creatures, as can be seen by the simple experiment of distorting one side of the image of an attractive face and asking viewers to rate the attractiveness of the resulting image. Consequently, such symmetries that mimic biology tend to have an innate appeal that in turn drives a powerful tendency to create artifacts with similar symmetry. One only needs to imagine the difficulty in trying to market a highly asymmetrical car or truck to general automotive buyers to understand the power of biologically inspired symmetries such as bilateral symmetry.

**Symmetry in other arts**

The concept of symmetry is applied to the design of objects of all shapes and sizes. Other examples include beadwork, furniture, sand paintings, knotwork, masks, musical instruments, and many other endeavors.

*Celtic Knotwork*

*Beadwork*

*Furniture*

*Sand paintings*

*Mask*

*Musical instruments*

**Symmetry in physics**

In physics, symmetry includes all features of a physical system that exhibit the property of symmetry that is, under certain transformations, aspects of these systems are "unchanged", according to a particular observation. A symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is "preserved" under some change.

A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group). Symmetries are frequently amenable to mathematical formulation such as group representations and can be exploited to simplify many problems.

**Symmetry in organic chemistry**

The symmetry of a molecule is determined by the existence of symmetry operations performed with respect to symmetry elements. A symmetry element is a line, a plane or a point in or through an object, about which a rotation or reflection leaves the object in an orientation indistinguishable from the original. A plane of symmetry is designated by the symbol σ (or sometimes s), and the reflection operation is the coincidence of atoms on one side of the plane with corresponding atoms on the other side, as though reflected in a mirror. A center or point of symmetry is labeled i, and the inversion operation demonstrates coincidence of each atom with an identical one on a line passing through and an equal distance from the inversion point (see chair cyclohexane). Finally, a rotational axis is designated Cn, where the degrees of rotation that restore the object is 360/n (C2= 180º rotation, C3= 120º rotation, C4= 90º rotation, C5= 72º rotation). C1 is called the identity operation E because it returns the original orientation.

An object having no symmetry elements other than E is called asymmetric. Such an object is necessarily chiral. Since a plane or point of symmetry involves a reflection operation, the presence of such an element makes an object achiral. One or more rotational axes of symmetry may exist in both chiral, dissymmetric, and achiral objects.

Three dimensional models illustrating these symmetry elements will be displayed on the right by clicking one of the following names. The forth and seventh of these are dissymmetric. The others are achiral.

**Symmetry in quasicrystals**

In quasicrystals (a quasicrystal is a structure that is ordered but not periodic) we find the fascinating mosaics of the Arabic world reproduced at the level of atoms: regular patterns that never repeat themselves. However, the configuration found in quasicrystals was considered impossible, and Dan Shechtman had to fight a fierce battle against established science. The Nobel Prize in Chemistry 2011 has fundamentally altered how chemists conceive of solid matter.