What is a tessellation?

A tessellation is a repeating pattern of shapes that completely covers a surface without any gaps or overlaps. These shapes can be simple, such as triangles or squares, or more complex, such as animals or other objects. Tessellations are often used in art and design to create visually interesting and geometrically pleasing patterns.

A tessellation is a pattern of shapes that completely cover a surface without overlapping or leaving any gaps. The shapes used in a tessellation are usually regular polygons, such as squares, triangles, or hexagons. Tessellations can be found in nature, art, and architecture.

Examples of tessellations:

- A honeycomb is a tessellation of hexagons.
- A tiled floor is a tessellation of squares or rectangles.
- A stained glass window is a tessellation of triangles and other polygons.

Properties of tessellations:

- Tessellations must cover the entire surface without any gaps or overlaps.
- The shapes used in a tessellation must be regular polygons.
- The angles at each vertex of a tessellation must add up to 360 degrees.

Uses of tessellations:

Tessellations are used in a variety of applications, including:

- Art and design: Tessellations can be used to create beautiful and intricate works of art.
- Architecture: Tessellations can be used to create strong and durable structures.
- Mathematics: Tessellations can be used to study geometry and topology.

Tessellations are a fascinating and versatile mathematical concept with a wide range of applications. They can be found all around us, from nature to art to architecture.