symmetrinen

Symmetrinen is the Finnish term for symmetric. In mathematics and the sciences, symmetry describes a property of an object or system that remains unchanged under a set of transformations. An object is symmetric if there exists a transformation—such as a rotation, a reflection, or a translation—that maps the object onto itself.

Common forms include reflectional symmetry (mirror symmetry), rotational symmetry, and translational symmetry. The axis around which a figure is mirrored is called an axis of symmetry. A figure's rotational symmetry is of order n if it can be rotated by 360/n degrees and look the same.

Examples: A circle has infinite rotational symmetry and reflection symmetry; a square has rotational symmetry of order 4 and four lines of symmetry; a rectangle has rotational symmetry of order 2 and two lines of symmetry through midpoints.

Beyond geometry, symmetry appears in algebra and analysis: even functions satisfy f(-x) = f(x) and odd functions satisfy f(-x) = -f(x). In physics, symmetries correspond to conservation laws via Noether's theorem. In chemistry and crystallography, symmetry determines molecular point groups and space groups; in biology, bilateral symmetry and radial symmetry describe body plans. In art and design, symmetry is used to achieve balance and harmony.

Symmetry also plays a role in modern science as a guiding principle for formulating laws and models, and as a mathematical tool for simplifying problems through invariant quantities and conservation.