In nature, symmetry is never mathematically perfect. However, clear differences from normal usually catch the eye. To some extent, the structure of plants and animals can be considered symmetrical. Symmetricity can also be found in the human body. However, the symmetry of appearance does not necessarily have anything to do with internal anatomy. In everyday speech, symmetry often refers to some kind of proportionality and beauty. In most cases symmetry gives most people positive associations. Studies show that the more symmetrical a face is, the more beautiful it is perceived to be.

Symmetry is often taken for granted. Therefore, asymmetry is often a startling feature that immediately attracts attention. In particular, structures and objects made by humans are usually assumed to be symmetrical. Have you ever come to think about how much symmetry there is in cars or airplanes, for example?

In mathematics, several types of symmetry are distinguished that leave the pattern as a whole unchanged. Symmetry preserves the size, shape, distances, and angles of the part. A piece is said to be symmetrical if it has any of the three basic symmetries. These are rotation, translation, and reflection. Translation always has a direction and a distance. Reflection, on the other hand, refers to the production of a mirror image of an object. In rotation, the object is rotated by a certain angle around a center of the rotation. For example, a square can be rotated [[$ 90° $]]​ so that it coincides with its former position. The square has a four-fold axis of symmetry.

An irregular pattern cannot be rotated so that it coincides with itself. The most symmetrical shape possible is a sphere that can be rotated to any extent without it not being symmetrical. The sphere has many special mathematical and physical properties. Indeed, the Pythagoreans considered the circle and the sphere to be the most perfect possible shapes due to their rotational symmetry.

Symmetry has such a fundamental conceptual position in many theories that the lack of symmetry is always perceived as particularly problematic. Symmetry is studied in a field of mathematics called group theory, which plays an important role in quantum mechanics.