symetria

Symetria is the Polish term for symmetry, describing a property where an object or system remains unchanged under a set of transformations or exhibits balanced proportions. In everyday language, symmetry conveys pleasing balance; in formal contexts it denotes precise invariance under operations such as reflection, rotation, or scaling.

The word derives from the Greek symmetria, meaning concordant in measure.

In mathematics, symmetry means an object is invariant under a group of transformations, and the set of all such transformations forms its symmetry group. Geometric symmetry is central to geometry and group theory, with objects classified by their symmetry groups and invariance properties.

Common types include reflection (mirror) symmetry, rotational symmetry, translational symmetry, and self-similarity or scaling symmetry. Examples: a square has reflection and rotational symmetry; a circle has infinite rotational symmetry; a snowflake exhibits rotational symmetry; fractal patterns show self-similarity across scales.

Symmetry is important in science and art: in physics, many laws follow from symmetry principles; in chemistry and crystallography, molecular and crystal symmetries determine spectra and properties; in art and architecture, symmetry is a fundamental principle of design. Approximate symmetry is widespread in nature, where perfect symmetry is often broken by small perturbations.

See also: symmetry breaking, invariance.