Who Is M.C. Escher?
Tesselation information and facts about M.C. Escher.
A tessellation is a two-dimensional plane covered by the repition of geometric shapes with no gaps or overlaps. Tessellations often showed up in Escher's work, and tessella means "small square" in Latin. The first recorded study of tessellations was in 1618, and was recorded by Johannes Kepler when he wrote about semiregular and regular tessellations. A regular tessellation is made up of all congruent regular polygons, and a semiregular tessellation is made up of a variety of the eight regular polygons. Also there are edge to edge tessellation, which are made up of adjacent tiles that share full sides. There are also other tessellations such as regular versus irregular, periodic versus nonperiodic, symmetric versus asymmetric, and fractal tessellations, as well as other classifications. When assigning colors to tiles in a tessellation, you have to state whether colors ae part of the illustration or part of the tiling. The four color theroem says that for every tessellation in a normal [Euclid] plane, with a choice of four colors, colored in with one color so that no tiles of the same color meet at a length of poistive curve, but this will not generally respect the symmetry of the tessellation. If you want a color color choice that will, you may need up to seven colors.
Some transformations used in making a tessellation include translation, reflection, rotation, and glide reflection. A translation simply means to move an object. When you translate it, you need two things: a magnitude and a direction. Rotation is the spinning of an object or shape around a point called the center of rotation. The amount you turn the object is called angle of rotation and is measured in degrees. Reflection is the flipping of an object over a line or axis. The line that you flip it over is called the line of symmetry. Another type of reflection is glide reflection, and is simply a translation and reflection combined. It doesnt matter which oorder you do them in, they still come out the same product and are reffered to as glide reflection.