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Rose Petals Wallpaper Biography

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Flowers are the beautiful gift of nature. The rose, yellow, tulip, orchid and other flowers are best gift item for someone very dear. Not only whole flower but its petals are highly used for decoration, fragrance and other purposes. We have used the theme of yellow and red rose petals to design some lovely collection of free wallpapers. Watch out some of our exclusive collection of rose petals wallpaper and background for the valentine’s day.A tessellation is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions.
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. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups.
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.
In the real world, a tessellation is a tiling made of physical materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the decorative tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher often made use of tessellations for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.Tessellations were used by the Sumerians (about 4000 BC) in building wall decorations formed by patterns of clay tiles.[1]
In 1619 Johannes Kepler made one of the first documented studies of tessellations when he wrote about regular and semiregular tessellation, which are coverings of a plane with regular polygons, in his Harmonices Mundi.[2] 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.[3][4] Fyodorov's work marked the unofficial beginning of the mathematical study of tessellations. Other prominent contributors include Shubnikov and Belov (1951); and Heinrich Heesch and Otto Kienzle (1963).
Etymology[edit]
In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics.[5] The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word "τέσσερα" for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations, often made of glazed clay.Tessellation or tiling is the branch of mathematics that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps. There are only three "regular" tessellations using exactly one kind of identical regular polygons arranged edge-to-edge, but many other types of tessellations are possible, differing in the constraints that are chosen to apply. For example, there are nine types of tessellations made with more than one kind of regular polygon, but having the same arrangement of polygons at every corner. These were described by the Swiss geometer Ludwig Schläfli in the 1850s. Tessellations can also be made from other shapes such as rectangles, polyominoes and in fact almost any kind of geometric shape. The artist M. C. Escher is famous for making tessellations with irregular interlocking tiles, shaped like animals and other natural objects. If suitable contrasting colours are chosen for the tiles of differing shape, striking patterns are formed, and these can be used to form physical surfaces such as church floors.[6]
More formally, a tessellation or tiling is a partition of the Euclidean plane into a countable number of closed sets called tiles, such that the tiles intersect only on their boundaries. These tiles may be polygons or any other shapes.[a] Many tessellations are formed from a finite number of prototiles; all tiles in the tessellation are congruent to one of the given prototiles. If a geometric shape can be used as a prototile to create a tessellation, the shape is said to tessellate or to tile the plane. Mathematicians have found no general rule for determining if a given shape can tile the plane or not, which means there are many unsolved problems concerning tessellations.[7] For example, the types of convex pentagons that can tile the plane remains an unsolved problem.
Mathematically, tessellations can be extended to spaces other than the Euclidean plane.[8] Schläfli pioneered this by defining polyschemes, which mathematicians nowadays call polytopes; these are the analogues to polygons and polyhedra in spaces with more dimensions. He further defined the Schläfli symbol notation to make it easy to describe polytopes. For example, the Schläfli symbol for an equilateral triangle is {3}, while that for a square is {4}.[9] The Schläfli notation makes it possible to describe tilings compactly. For example, a tiling of regular hexagons has three six-sided polygons at each vertex, so its Schläfli symbol is {6,3}.[10]
Other methods also exist for describing polygonal tilings. When the tessellation is made of regular polygons, the most common notation is the vertex configuration, which is simply a list of the number of sides of the polygons around a vertex. The square tiling has a vertex configuration of 4.4.4.4, or 44. The tiling of regular hexagons is noted 6.6.6, or 66.[7]:59
In mathematics