Simetrija

Simetrija is a property of an object or system that remains unchanged under a set of transformations. The term derives from the Greek symmetria, from syn- "together" and metron "measure," reflecting the idea of measuring sameness from opposite sides or directions. In mathematics and the sciences, symmetry refers to invariance under a group of transformations and is formalized through symmetry groups.

Geometric symmetry includes several common types. Mirror (or bilateral) symmetry occurs when an object has a reflection line or plane. Rotational symmetry means the object matches itself after rotation by a nonzero angle. Translational symmetry occurs when a pattern remains the same after shifting along a direction. Dihedral symmetry combines rotations and reflections, and radial symmetry centers on a point, with all parts arranged around it. Many objects exhibit continuous or infinite symmetry, where an entire set of transformations leaves the object unchanged.

Symmetry influences both structure and behavior. In crystallography, space groups describe the symmetries of a lattice and govern material properties. In molecular chemistry and spectroscopy, point groups determine selection rules and spectral patterns. In physics, invariances under transformations underpin conservation laws via Noether’s theorem.

Beyond science, symmetry is a central concept in art, architecture, and design, contributing to balance, harmony, and aesthetics. In biology, bilateral symmetry is common in animals, while radial symmetry is typical of flowers and some marine organisms. In computation and graphics, detecting and exploiting symmetry can simplify algorithms and improve efficiency.

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