What Is a Tessellation?
A tessellation, also known as a tiling, is a pattern created by repeating one or more geometric shapes to completely cover a flat surface without any gaps or overlaps. The shapes must fit together perfectly, like the tiles on a floor or the pieces of a jigsaw puzzle.
Section 2: The Key Rule of Tessellations
For a pattern to be a true tessellation, the corners (vertices) of the shapes must meet at a single point. The sum of the angles of all the shapes meeting at that vertex must be exactly 360 degrees. This ensures that the shapes lie flat and do not create gaps or overlaps.
Section 3: A Practical Example
A simple and common example of a tessellation is a checkerboard, which is made by tiling squares. Another excellent example from nature is a honeycomb, which is a natural tessellation of hexagons. These shapes are used because they are highly efficient for building strong, stable structures.
Section 4: Importance and Applications
Tessellations are important in mathematics for studying symmetry and geometric properties. They also have many practical applications in art, such as the famous works of M.C. Escher, and in architecture and design for creating patterns on floors, walls, fabrics, and mosaics.