TESSELLATION ART SQUARES TRIAL

Tessellation in two dimensions, also called planar tiling, is a topic in geometry that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps, according to a given set of rules. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.Ī rhombitrihexagonal tiling: tiled floor in the Archeological Museum of Seville, Spain, using square, triangle, and hexagon prototiles Tessellations are sometimes employed for decorative effect in quilting. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor, or wall coverings. A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.Ī real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons.

An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern. A tiling that lacks a repeating pattern is called 'non-periodic'. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.Ī periodic tiling has a repeating pattern. You'll be amazed that the 'conservation of shape' we are demonstrating also means that the shapes do continue to tessellate! Try it on a scrap of copy paper.An example of non‑periodicity due to another orientation of one tile out of an infinite number of identical tiles.Ī tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. Do we really have to match up those corners? Try it, trace it, and see what happens. Cut a square from one corner to an adjacent corner, pull it across and tape it down.

TESSELLATION ART SQUARES TRIAL

It's this trial and error that fuels STEAM education in art.įor example, the Translation method is the most common for tessellations. Experimentation is something we can do more of in our classes.

Most people work with just squares, but did you know many of the same techniques work just as well with rectangles? We have been told to 'line up the corners,' but in actuality, for many techniques, you don't have to. By expanding the techniques beyond the basic square and rudimentary techniques, life can be breathed back into the work and even offer opportunities for expression. Though tessellations can be fun, with great connections to math and geometry, they can become tedious and mechanical.

Tessellation art squares