Transformation & Tessellation - Essay Example

Transformation and Tessellation Transformation, from the word "transform" means "to change". However, in mathematics (specifically geometry), it means to change the position of a shape on a plane, without changing the area of the shape, or the size of the angles and the lines. There are three types of transformation, namely rotation, reflection and translation. A fourth type, resizing, is also considered a type of transformation. However, it involves a change in size of the object (Pierce, 2009).

Rotation involves turning the object to any direction on the plane. By doing so, the position of the object changes, without changing any other attributes. Reflection involves flipping the object on the plane, creating a mirror image of the object on the same plane. Translation involves moving, or "sliding" the object within the plane, with the points moving on the same direction or with the same distance.Transformation can be applied in the real world in creating 3D images and models of objects, like houses, buildings, or even human beings.

In order to capture the real essence of the object being imitated (or transformed), the same dimensions should be used, however, on a smaller scale.Tessellation, on the other hand, occurs when objects in a plane create a pattern without overlapping with each other, and without leaving gaps in between the object (Seymour and Britton, 1989). These patterns are often a subject of artworks, and one can see a lot of these kinds of patterns on books and on the Internet, in pages where one is asked to count the number of polygons in a page.

One of the most common examples of this kind of patterns can be found on floor tiles, which follow the same principle: each tile should fit a given space, without overlapping with another tile, and without any gaps in between. The objects can be regularly shaped polygons, like squares, triangles, octagons, etc., with each side touching another objects side (Seymour and Britton, 1989). Irregularly shaped objects can also be used, which proves to be more complicated than using regular polygons.

Common objects such as soccer balls, jigsaw puzzles and honeycombs also have a tessellated pattern.ReferencesColgan, Lynda E. C. "Its Friezing in Here: Tessellations through Art, Architecture, and Cultural Artifacts." Mathematics Teaching in the Middle School 9.6 (2004): 334-338. Coxeter, H.S.M.. Regular Polytopes, Section IV : Tessellations and Honeycombs. Dover, 1973Lu, Peter J., and Paul J. Steinhardt. "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture." Science 315.

5815 (2007): 1106.Pierce, Rod. "Transformations" Math Is Fun. Ed. Rod Pierce. 21 Sep 2009.Seymour, Dale, and Jill Britton. Introduction to Tessellations. 1989.