In Latin, tessella is a small cubical piece of clay, stone, or glass used to make mosaics. Other prominent contributors include Alexei Vasilievich Shubnikov and Nikolai Belov (1964), and Heinrich Heesch and Otto Kienzle (1963). Fyodorov's work marked the unofficial beginning of the mathematical study of tessellations. Some two hundred years later in 1891, the Russian crystallographer Yevgraf Fyodorov proved that every periodic tiling of the plane features one of seventeen different groups of isometries. He wrote about regular and semiregular tessellations in his Harmonices Mundi he was possibly the first to explore and to explain the hexagonal structures of honeycomb and snowflakes. In 1619, Johannes Kepler made an early documented study of tessellations. ĭecorative mosaic tilings made of small squared blocks called tesserae were widely employed in classical antiquity, sometimes displaying geometric patterns. Tessellations were used by the Sumerians (about 4000 BC) in building wall decorations formed by patterns of clay tiles. History A temple mosaic from the ancient Sumerian city of Uruk IV (3400–3100 BC), showing a tessellation pattern in coloured tiles Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs. 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 (an aperiodic set of prototiles). 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 can find the invention tessellation resource here.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. I had so much fun creating artistic tessellations with my kids that I created a simple “I” tessellation research project for inventions! A list of 50+ inventions is included that students can research and report on in a fun way. Reflection or Mirror Tessellation Use a Collaborative Tessellation for a Research Project There are some videos for making rotational and mirror tessellations on YouTube once your students have mastered the simpler translation tessellation: square piece of paper (a small sticky note works well).You can also create complex tessellations by combining multiple operations. Rotation tessellations are accomplished by (you guessed it!) rotating the tessellated shape. This is the type of tessellation you can make easily with a sticky note (as shown below). Translation can be thought of as sliding the shape along a plane. They can be made by positioning the same shape with one of these three operations: Tessellations are patterns resulting from arranging, or tiling, shapes without any gaps. Certain basic shapes can be easily tessellated:Ĭombination shapes, complicated shapes, and animals such as the ones found on these sites are also examples to print and color: Tessellations are a fun, hands-on way to explore STEAM, whether you are in art class, math class, or in a STEM or STEAM classroom.
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