kiertosymmetriat

Kiertosymmetria, also known as rotational symmetry, is a fundamental concept in geometry and symmetry studies. It refers to the property of an object or pattern that remains unchanged when rotated by a certain angle around a fixed point, known as the center of rotation. This type of symmetry is prevalent in various natural and man-made structures, including crystals, snowflakes, and architectural designs.

The order of rotational symmetry, denoted by n, indicates the number of distinct positions an object can occupy before appearing identical to its original orientation. For example, a square has fourfold rotational symmetry (n=4), meaning it can be rotated by 90, 180, 270, or 360 degrees to appear the same. Similarly, an equilateral triangle has threefold rotational symmetry (n=3).

In mathematical terms, an object exhibits kiertosymmetria if there exists a rotation by an angle θ (where 0 < θ < 360 degrees) that maps the object onto itself. The smallest such angle θ is known as the angle of rotation, and the corresponding symmetry is called the principal axis of rotation.

Rotational symmetry is closely related to other types of symmetry, such as reflectional (or mirror) symmetry and translational symmetry. It plays a crucial role in various fields, including crystallography, art, and computer graphics, where it is used to analyze patterns, design structures, and create visually appealing compositions. Understanding kiertosymmetria is essential for appreciating the beauty and complexity of symmetrical objects and patterns in our surroundings.