tessellatsioonit

Tessellations are the tiling of a plane using one or more geometric shapes, called tiles, without overlapping and with no gaps between them. This concept has been studied in mathematics for centuries, with ancient civilizations such as the Greeks and Babylonians being familiar with it.

In order for a shape to be used in a tessellation, it must have certain properties. It must be able to be repeated without overlapping and it must not have any gaps between the tiles. This means that the sum of the interior angles of the shape must be a multiple of 360 degrees, and the shape must be able to be translated and rotated to fit perfectly around the other tiles.

Examples of shapes that can be used in tessellations include squares, triangles, and hexagons. These shapes are often referred to as "regular" tessellations, because they have the same shape and size and can fit together in a repeating pattern with no gaps. Other shapes, such as pentagons and heptagons, can also be used to create tessellations, but these are often referred to as "irregular" tessellations because they have different shapes and sizes.

Tessellations have many real-world applications, including in the design of mosaics, tile patterns, and other forms of decorative art. They are also studied in mathematics and art for their aesthetic and geometric properties. Additionally, tessellations have been used to create complex and intricate patterns in architectural designs, such as in the famous Islamic geometric patterns found in many mosques and palaces.