Tessellations as Classroom Projects

Tessellate means to form or arrange small squares in a pattern. From Greek "tesseres," and then translated into English means "four." The first tessellations were made from square tiles. A regular polygon has sides and angles equal. The regular tessellation is made up of congruent regular polygons. Congruent tessellations are polygons put together so all are the same size and shape. There are only three regular polygons that tessellate in the Euclidean plane: squares, triangles or hexagons. Some examples are shown in the graphic. From Latin in comes to us as meaning a square tablet and the process of tessellation has been used to produce many beautiful mosaic art displays. A mosaic is a pattern that extends over a given area without leaving an uncovered region.

In space science, the term could even be applied to space or hyperspace which is a kind of mosaic extending over the vast regions of the universe. In a classroom however, if you had large numbers of tile pieces you could have students create patterns on their desks and students could work together to form patterns created by the group. Many aspects of nature have qualities of tessellation. The patterns of coloration of animals and plants have repeating patterns.

Some types of tessellations have repeating patterns that are partially in one tile section and continue into another tile section. When we use wallpaper, the patterns may tessellate to cover the entire wall to give the appearance of a continuous scene or pattern. The pattern produced by a herd of Zebras is a kind of tessellation pattern and it is believed that when the herd is attacked and they begin to run, the different speeds causes confusion in the attacker and gives the animals a slight edge. The attacker has a bit more difficulty focusing in on a particular animal because the pattern "extends" throughout the entire group of animals, but also changes as they move.

Even the movement of schools of fish has a similar characteristic, a pattern extending over a large area. When viewed from the top of the ocean large groups of fish also create patterns as seen from above and when viewed from above they also blend in somewhat with the darker deeper waters. When viewed from the bottom of the ocean many fish have much lighter undersides again forming a pattern and blending in with the lighter surface of the water.

A great deal more could be done with the use of tessellations in a variety of subjects. Naturally tessellations could be used in art or mathematics classes, but as shown here they could also be used in biology classes. In social studies there are many patterns that have been woven into cloth which are also tessellations. The American Indians had many intricate patterns that repeated in the cloth they produced.

The concept of tessellation has been extended beyond just squares, triangles and hexagons and a search of the internet will yield a lot of examples. As a science teacher the concept may allow the integration of art into the science curriculum in a dynamic new way and with the aid of the computer tessellations are easier that ever to produce.