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Tiling With Rectangles
A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of side ratio. The tilings with straight polyominoes of shapes such as , and tilings with polyominoes of shapes such as fall also into this category. Congruent rectangles Some tiling of rectangles include: Tilings with non-congruent rectangles The smallest square that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 11 × 11 square, and the tiling uses five rectangles. The smallest rectangle that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 9 × 13 rectangle, and the tiling uses five rectangles. See also * Squaring the square * Tessellation * Tiling puzzle Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps). Some tiling puz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A 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. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. 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. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An '' aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles). A '' tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangle
In Euclidean geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a ''square''. The term "wikt:oblong, oblong" is used to refer to a non-square rectangle. A rectangle with Vertex (geometry), vertices ''ABCD'' would be denoted as . The word rectangle comes from the Latin ''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' (angle). A #Crossed rectangles, crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domino Tiling
In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by domino (mathematics), dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a matching (graph theory), perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they correspond to adjacent squares. Height functions For some classes of tilings on a regular grid in two dimensions, it is possible to define a height function associating an integer to the vertex (graph theory), vertices of the grid. For instance, draw a chessboard, fix a node A_0 with height 0, then for any node there is a path from A_0 to it. On this path define the height of each node A_ (i.e. corners of the squares) to be the height of the previous node A_n plus one if the square on the right of the path from A_n to A_ is black, and minus one otherwise. More details can be found in . Thurston's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in popular puzzles since at least 1907, and the enumeration of pentominoes is dated to antiquity. Many results with the pieces of 1 to 6 squares were first published in '' Fairy Chess Review'' between the years 1937 and 1957, under the name of "dissection problems." The name ''polyomino'' was invented by Solomon W. Golomb in 1953, and it was popularized by Martin Gardner in a November 1960 " Mathematical Games" column in ''Scientific American''. Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stacked Bond
''Stacked'' is an American television sitcom that aired on Fox Broadcasting Company, Fox from April 13, 2005, to January 11, 2006. Premise ''Stacked'' was described as the opposite of ''Cheers'', instead of a smart person in a "dumb" place, it is based on the concept of a dumb person in a "smart" place. A workplace, ensemble comedy, ''Stacked'' revolves around Skyler Dayton (Pamela Anderson), who is tired of her non-stop partying lifestyle and bad choices in boyfriends. Wanting a major life change, she wanders into Stacked Books - a small, family-run bookstore in the San Francisco area - owned by Gavin Miller (Elon Gold) and his brother, Stuart (Brian Scolaro). Divorced and unlucky in love himself, Gavin's inclined to regard Skyler as an embodiment of the vacuous, image-obsessed culture he has come to abhor. Stuart, however, is dazzled by Skyler's beauty and - much to Gavin's horror - offers her a job at their store, which she happily accepts as the first step in her quest for a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wallpaper Group-cmm-1
Wallpaper is used in interior decoration to cover the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" to help cover uneven surfaces and minor wall defects, "textured", plain with a regular repeating pattern design, or with a single non-repeating large design carried over a set of sheets. The smallest wallpaper rectangle that can be tiled to form the whole pattern is known as the pattern repeat. Wallpaper printing techniques include surface printing, rotogravure, screen-printing, rotary printing press, and digital printing. Modern wallpaper Modern wallpaper is made in long rolls which are hung vertically on a wall. Patterned wallpapers are designed so that the pattern "repeats", and thus pieces cut from the same roll can be hung next to each other so as to continue the pattern without it being easy to see where the join between two pieces occurs. In the ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basketweave
Basketweave is a structure that exists in many textile arts. It consists of multiple horizontal strands and vertical strands, resulting in a square pattern associated with woven baskets. It is used in the following textile arts: * Basket weaving * Basketweave in weaving * Basketweave in knitting * Basketweave in knot making * Basketweave as a variant of tent stitch in needlepoint * Basketweave in crochet See also * Plain weave * Seed/moss stitch * Monk's cloth Monk's cloth is a loosely woven cotton or linen fabric made of coarser yarns that drape well. Basketweave The Monk's cloth was woven with basketweave, usually with 2×2 or 4×4. Basketweave is a plain weave Plain weave (also called tab ... Textile arts Crafts {{Textile-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herringbone Bond
Brickwork is masonry produced by a bricklayer, using bricks and Mortar (masonry), mortar. Typically, rows of bricks called ''Course (architecture), courses'' are laid on top of one another to build up a structure such as a brick wall. Bricks may be differentiated from blocks by size. For example, in the UK a brick is defined as a unit having dimensions less than and a block is defined as a unit having one or more dimensions greater than the largest possible brick. Brick is a popular medium for constructing buildings, and examples of brickwork are found through history as far back as the Bronze Age. The fired-brick faces of the ziggurat of ancient Dur-Kurigalzu in Iraq date from around 1400 BC, and the brick buildings of ancient Mohenjo-daro in modern day Pakistan were built around 2600 BC. Much older examples of brickwork made with dried (but not fired) bricks may be found in such ancient locations as Jericho in Palestine, Çatalhöyük, Çatal Höyük in Anatolia, and Mehrg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herringbone Pattern
The herringbone pattern is an arrangement of rectangles used for floor tilings and road pavement, so named for a fancied resemblance to the bones of a fish such as a herring. The blocks can be rectangles or parallelograms. The block edge length ratios are usually 2:1, and sometimes 3:1, but need not be even ratios. The herringbone pattern has a symmetry of wallpaper group pgg, as long as the blocks are not of different color (i.e., considering the borders alone). Herringbone patterns can be found in wallpaper, mosaics, seating, cloth and clothing ( herringbone cloth), shoe tread, security printing, herringbone gears, jewellery, sculpture, and elsewhere. Examples Related tilings As a geometric tessellation, the herringbone pattern is topologically identical to the regular hexagonal tiling. This can be seen if the rectangular blocks are distorted slightly. In parquetry, more casually known as flooring, herringbone patterns can be accomplished in wood, brick, and til ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squaring The Square
Squaring the square is the problem of tessellation, tiling an integral square using only other integral squares. (An integral square is a square (geometry), square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set. The most studied restriction is that the squaring be perfect, meaning the sizes of the smaller squares are all different. A related problem is squaring the plane, which can be done even with the restriction that each natural number occurs exactly once as a size of a square in the tiling. The order of a squared square is its number of constituent squares. Perfect squared squares A "perfect" squared square is a square such that each of the smaller squares has a different size. Perfect squared squares were studied by R. Leonard Brooks, R. L. Brooks, Cedric Smith (statistician), C. A. B. Smith, Arthur Harold Stone, A. H. Stone and W. T. Tutte (wr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
