MMW 3.3- Tessellations

Tesselation

• the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps

• derived from the Latin word tessella (small square), a small cubical piece of clay, stone, or glass to make mosaics.

• Tessares (greek), means four

• Pattern in which geometric figures repeat and fit perfectly together

• Can stretch in every direction on the coordinate plane

Tessellations are also called?

• Pavings

• Parquetings

• Mosaics

Pavings

Outdoor floor, superficial surface covering

Parquetings

Flooring composed of wooden blocks arranged in geometric pattern

Mosaics

piece art made from small pieces of materials

Types of Tessellation

• Regular Tessellation

• Semiregular Tessellation

• Irregular Tessellation

Regular Tessellation

formed by only one type of regular polygon

Shapes that form regular tessellations:

• Square

• Equilateral Triangle

• Regular Hexagon

Regular Tessellation Derivation

its interior angle must be divided evenly into 360 degrees

Semi-regular Tessellation

• made from two or more regular polygons

• also called archimedian tessellation

Irregular Tessellation

• can be formed from almost any kind of geometric shapes

• M.C. Escher, a Dutch artist, is famous for making tessellations with irregular interlocking tiles shaped like animals and other objects

Where to find tessellations?

• first houses, churches, and castles were built by broken stones made up by random tessellations

• Window-panes in gothic architecture

• Different sorts of parquetings