Negatiytilmallen

Negatiytilmallen, also known as negative tiling, is a mathematical concept that involves the arrangement of shapes in a plane such that no two shapes overlap and the entire plane is covered without gaps. Unlike positive tiling, which uses shapes that can tessellate without any gaps or overlaps, negative tiling uses shapes that cannot tessellate on their own but can be combined with other shapes to create a tiling.

The concept of negative tiling was first introduced by the mathematician H.S.M. Coxeter in the 1960s. It is a useful tool in the study of tiling theory and has applications in various fields, including computer graphics, art, and architecture.

One of the most well-known examples of negative tiling is the combination of a square and a regular hexagon. While neither shape can tessellate on its own, they can be combined to create a tiling pattern. The square and hexagon can be arranged in such a way that their vertices coincide, creating a pattern that covers the entire plane without gaps or overlaps.

Negative tiling can also be used to create more complex patterns by combining multiple shapes. For example, a combination of a square, a regular hexagon, and a regular dodecagon can be used to create a tiling pattern that has a higher degree of symmetry.

In conclusion, negative tiling is a fascinating concept in mathematics that has applications in various fields. It involves the arrangement of shapes in a plane such that no two shapes overlap and the entire plane is covered without gaps. While it may not be as well-known as positive tiling, it is a useful tool in the study of tiling theory and has the potential to create complex and beautiful patterns.