Tilaseurannan

Tilaseurannan, also known as tiling or tessellation, is a mathematical concept involving the arrangement of shapes, called tiles, to cover a plane without gaps or overlaps. The tiles used in tiling are typically regular polygons, such as squares, equilateral triangles, or hexagons, but can also be irregular shapes. The study of tiling has applications in various fields, including art, architecture, and computer graphics.

The simplest form of tiling is the square tiling, where squares are arranged in a grid pattern. Other common tilings include the triangular tiling, where equilateral triangles are used, and the hexagonal tiling, where hexagons are arranged in a honeycomb pattern. These tilings are known as regular tilings because they use only one type of tile and the tiles fit together perfectly.

Tilings can also be classified as semi-regular or irregular. Semi-regular tilings use two or more types of regular polygons, but the arrangement of the tiles follows a specific pattern. Irregular tilings, on the other hand, use irregular shapes or irregular arrangements of regular polygons.

The study of tiling has a rich history, with examples of tiling found in ancient art and architecture. In modern times, tiling has become an important tool in the fields of computer graphics and algorithm design. For example, tiling can be used to optimize the rendering of images or to design efficient algorithms for solving complex problems.