tesselaatio

Tessellation is a geometric arrangement of shapes that fit together without gaps or overlaps to cover a plane. The term originates from the Latin word "tessella," meaning "small square," reflecting its historical use in mosaic art. Tessellations can be created using various shapes, including triangles, squares, hexagons, and more complex polygons. They are classified into three main types based on their symmetry: translation, rotation, and reflection tessellations.

Translation tessellations involve shapes that are repeated by sliding them along a straight line without rotating them. Examples include tiling a floor with identical square tiles. Rotation tessellations require shapes to be rotated by a certain angle before they can be repeated. A classic example is the use of equilateral triangles. Reflection tessellations involve shapes that are mirrored across a line before being repeated. These can be seen in patterns like those created by kaleidoscopes.

Tessellations have applications in various fields, including art, architecture, and mathematics. In art, they are used to create intricate and visually appealing patterns. In architecture, they can be seen in the design of tiling patterns and the layout of buildings. In mathematics, tessellations are studied for their properties and symmetries, contributing to the understanding of geometric principles.

The study of tessellations has a rich history, with examples found in ancient cultures such as the Romans and the Islamic world. Today, tessellations continue to inspire artists, mathematicians, and designers, showcasing the beauty and complexity of geometric patterns.