A tessellation is a tiled pattern made repeatedly repeating a shape with no gaps or overlaps. A tile floor, which is covered in square tiles, is a classic example of a tessellation. Tessellations can be found in a variety of works of art, as well as architecture, and they are also interesting mathematically. Tessellations can be found in a variety of places, and once people start looking for them, they tend to see them everywhere, including in nature.
Tessellations are mosaic patterns that are created repeating polygonal shapes. They can be used to tile a flat surface as well as a sculpted one. The tessellation can theoretically be repeated indefinitely in all cases, with the pattern remaining consistent and the shapes maintaining their relative positions. Because the pattern eventually reaches a point where shapes start to interlock or gaps form, certain shapes will not tessellate or cannot tessellate infinitely.
A single shape is used to tessellate in regular tessellations, also known as periodic tessellations. In a regular tessellation, only equilateral triangles, squares, and hexagons can be used. There are two or more shapes in semi-regular or non-periodic versions. M. C. Escher’s art frequently uses non-periodic tessellation as a stylistic element, sometimes with extremely complex shapes like interlocking animals. This type of tessellation is also used to introduce students to a variety of concepts in geometry and other math classes.
The tessellation’s mathematics background may explain why it is such a popular design element. Many recurring themes in art can be mathematically described, implying that mathematically bounded and described concepts have universal appeal. Tessellation can be found everywhere, in a variety of levels of complexity, from the cobblestoned streets of Paris to the complex tessellated designs of Islamic art. Math, like art, can be a universal language that anyone can understand, and it’s fascinating to see how radically different styles of artwork can be linked to mathematical concepts.
Exploring tessellation can help children learn about shapes and basic math, and these patterns can provide students with interesting, fun, or engaging projects. Students can experiment with visual illusions created with specific shapes and colors in a tessellation, as well as see how many colors they need to ensure that shapes of the same color do not touch.