Rotatiesymmetrieën

Rotatiesymmetrieën, or rotational symmetries, are a fundamental concept in geometry and symmetry studies. They describe the properties of shapes that remain unchanged when rotated about a central point, known as the center of rotation. The degree of rotation that leaves the shape unchanged is called the order of rotational symmetry. For example, a square has fourfold rotational symmetry because it looks the same after every 90-degree rotation around its center.

In mathematical terms, a shape has n-fold rotational symmetry if it can be rotated by 360/n degrees and still appear the same. This concept is crucial in various fields, including crystallography, where it helps in understanding the structure of crystals, and in art and design, where it is used to create visually appealing patterns and motifs.

Rotational symmetry is also closely related to other types of symmetries, such as reflectional symmetry and translational symmetry. A shape with both rotational and reflectional symmetry is said to be centrally symmetric, while a shape with both rotational and translational symmetry is said to be periodic.

The study of rotatiesymmetrieën provides insights into the underlying mathematical structures of various natural and man-made objects, contributing to a deeper understanding of symmetry in the world around us.