On clear nights, we can see the stars as twinkling points of light in the sky. Today, nearly 1000 years after its inception, tangrams remain a popular pastime puzzle as well as a teaching aid for many elementary and not so elementary mathematical concepts. A tangram is a set of seven geometric shapes made up of five triangles, a square, and a parallelogram. “Tiling” is another word that is often used interchangeably to mean the same thing.Īs an art form, tessellations are rich in mathematics, particularly geometry!Ī tangram is a traditional Chinese puzzle consisting of a square cut into seven pieces (tans) that can be arranged into various shapes. These patterns are called tessellations.īy strict definition, a tessellation is an arrangement of shapes, closely fitted together without gaps or overlap. Examples range from a simple tiled floor or the hexagonal pattern of the honeycomb to the mathematically elaborate mosaics created by M.C. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.Patterns created by fitting together replicas of the same basic shape are visible in nature and in human design. Tessellations are sometimes employed for decorative effect in quilting. Escher often made use of tessellations for artistic effect. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative 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. In the real world, a tessellation is a tiling made of physical materials such as cemented ceramic squares or hexagons. In computer graphics, the term "tessellation" is used to describe the organization of information needed to render to give the appearance of the surfaces of realistic three-dimensional objects. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. Some special kinds of tessellations include regular, with tiles all of the same shape semi-regular, with tiles of more than one shape and aperiodic tilings, which use tiles that cannot form a repeating pattern. In mathematics, tessellations can be generalized to higher dimensions. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.įreebase Rate this definition: 0.0 / 0 votesĪ Tessellation is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. 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. 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". 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. Wikipedia Rate this definition: 0.0 / 0 votesĪ 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.
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