Sümmeetrilised

Sümmeetrilised is an Estonian term used to describe properties or objects that exhibit symmetry. In mathematics and related fields, symmetry denotes invariance under a set of transformations. A figure or object is considered sümmeetriline if there exists a transformation—such as a reflection, rotation, translation, or glide reflection—that maps it onto itself.

Common types of symmetry include reflective (mirror) symmetry, rotational symmetry, translational symmetry, and glide symmetry. An axis of symmetry is a line where reflection leaves the figure unchanged. The order of rotational symmetry is the number of times a figure maps onto itself during a full 360-degree rotation.

Examples: a circle has infinite axes of symmetry and infinite rotational symmetry; a regular n-gon has rotational symmetry of order n and typically n axes of symmetry; a rectangle has two axes of symmetry and 180-degree rotational symmetry; an isosceles triangle has a single axis of symmetry.

Symmetry has wide-ranging applications in science, engineering and art. In biology, bilateral symmetry is a common organizational principle. In crystallography and chemistry, symmetry influences molecular structure and properties. In physics, symmetry relates to conservation laws and fundamental interactions. In design and architecture, symmetrical layouts are often used for balance and harmony. In mathematics, symmetry is formalized through the concept of symmetry groups, which collect all symmetry operations that preserve an object. In two dimensions, tessellations and wallpaper groups describe repeating patterns, while in three dimensions, point groups and space groups classify spatial symmetries.

Sümmeetrilised thus encompasses a broad, interdisciplinary concept centered on invariance under transformations and its diverse manifestations.