Tetromino
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Tetromino
A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners). Tetrominoes, like dominoes and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally. A popular use of tetrominoes is in the video game ''Tetris'' created by the Soviet game designer Alexey Pajitnov, which refers to them as tetriminos. The tetrominoes used in the game are specifically the one-sided tetrominoes. The tetrominoes Free tetrominoes Polyominos are formed by joining unit squares along their edges. A free polyomino is a polyomino considered up to congruence. That is, two free polyominos are the same if there is a combination of translations, rotations, and reflections that turns one into the other. A free tetromino is a free polyomino made from four squares. There are five free tetrominoes. The free tetrominoes have the following symmetry: * ...
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Tetromino Tetracube Packing
A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners). Tetrominoes, like dominoes and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally. A popular use of tetrominoes is in the video game ''Tetris'' created by the Soviet game designer Alexey Pajitnov, which refers to them as tetriminos. The tetrominoes used in the game are specifically the one-sided tetrominoes. The tetrominoes Free tetrominoes Polyominos are formed by joining unit squares along their edges. A free polyomino is a polyomino considered up to congruence. That is, two free polyominos are the same if there is a combination of translations, rotations, and reflections that turns one into the other. A free tetromino is a free polyomino made from four squares. There are five free tetrominoes. The free tetrominoes have the following symmetry: ...
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Tetris
''Tetris'' (russian: link=no, Тетрис) is a puzzle video game created by Soviet software engineer Alexey Pajitnov in 1984. It has been published by several companies for multiple platforms, most prominently during a dispute over the appropriation of the rights in the late 1980s. After a significant period of publication by Nintendo, the rights reverted to Pajitnov in 1996, who co-founded the Tetris Company with Henk Rogers to manage licensing. In ''Tetris'', players complete lines by moving differently shaped pieces (tetrominoes), which descend onto the playing field. The completed lines disappear and grant the player points, and the player can proceed to fill the vacated spaces. The game ends when the uncleared lines reach the top of the playing field. The longer the player can delay this outcome, the higher their score will be. In multiplayer games, players must last longer than their opponents; in certain versions, players can inflict penalties on opponents by completi ...
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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 to 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, the s ...
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Free Polyomino
A polyomino is a Shape, 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 to 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), Mathematical Games" column in ''Scientific American''. Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhex (mathematics), polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cube (geometry), cubes to form polycubes, ...
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Pentomino
Derived from the Greek word for ' 5', and " domino", a pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 12 different '' free'' pentominoes. When reflections are considered distinct, there are 18 '' one-sided'' pentominoes. When rotations are also considered distinct, there are 63 ''fixed'' pentominoes. Pentomino tiling puzzles and games are popular in recreational mathematics. Usually, video games such as '' Tetris'' imitations and ''Rampart'' consider mirror reflections to be distinct, and thus use the full set of 18 one-sided pentominoes. Each of the twelve pentominoes satisfies the Conway criterion; hence every pentomino is capable of tiling the plane. Each chiral pentomino can tile the plane without being reflected. History The earliest puzzle containing a complete set of pentominoes appeared in ...
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Pentomino
Derived from the Greek word for ' 5', and " domino", a pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 12 different '' free'' pentominoes. When reflections are considered distinct, there are 18 '' one-sided'' pentominoes. When rotations are also considered distinct, there are 63 ''fixed'' pentominoes. Pentomino tiling puzzles and games are popular in recreational mathematics. Usually, video games such as '' Tetris'' imitations and ''Rampart'' consider mirror reflections to be distinct, and thus use the full set of 18 one-sided pentominoes. Each of the twelve pentominoes satisfies the Conway criterion; hence every pentomino is capable of tiling the plane. Each chiral pentomino can tile the plane without being reflected. History The earliest puzzle containing a complete set of pentominoes appeared in ...
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Alexey Pajitnov
Alexey Leonidovich Pajitnov. (born 16 April 1955) is a Russian-born American computer engineer and video game designer. He is best-known for designing and developing ''Tetris'' in 1984 while working at the Dorodnitsyn Computing Centre under the Academy of Sciences of the Soviet Union (now the Russian Academy of Sciences). In 1996, five years after his relocation to the United States from the Soviet Union, Pajitnov founded The Tetris Company alongside Dutch video game designer Henk Rogers; Pajitnov did not receive royalties from ''Tetris'' prior to this time, despite the game's high popularity. Early life and education Pajitnov was born to parents who were both writers; his father was a critic of the arts, and his mother was a journalist who wrote for both newspapers and a film magazine. It was through his parents that Pajitnov gained exposure to the arts, eventually developing a passion for cinema. He accompanied his mother to many film screenings, including the Moscow Film F ...
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Chirality (mathematics)
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be ''achiral''. A chiral object and its mirror image are said to be enantiomorphs. The word ''chirality'' is derived from the Greek (cheir), the hand, the most familiar chiral object; the word ''enantiomorph'' stems from the Greek (enantios) 'opposite' + (morphe) 'form'. Examples Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule. Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves and shoes. Right shoes differ from left shoes only by being mirror images of each other. In contrast thin gloves may not be considered chiral if you can wear them inside-out. The J, L, S and Z-shaped ''tetrominoes'' of the popula ...
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Polyforms
In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. For example, a square basic polygon results in the well-known polyominoes. Construction rules The rules for joining the polygons together may vary, and must therefore be stated for each distinct type of polyform. Generally, however, the following rules apply: #Two basic polygons may be joined only along a common edge, and must share the entirety of that edge. #No two basic polygons may overlap. #A polyform must be connected (that is, all one piece; see connected graph, connected space). Configurations of disconnected basic polygons do not qualify as polyforms. #The mirror image of an asymmetric polyform is not consider ...
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Soma Cube
The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes. The pieces of the Soma cube consist of all possible combinations of three or four unit cubes, joined at their faces, such that at least one inside corner is formed. There is one combination of three cubes that satisfies this condition, and six combinations of four cubes that satisfy this condition, of which two are mirror images of each other (see Chirality). Thus, 3 + (6 × 4) is 27, which is exactly the number of cells in a 3×3×3 cube. The Soma cube was popularized by Martin Gardner in the September 1958 Mathematical Games column in ''Scientific American.'' The book '' Winning Ways for your Mathematical Plays'' also contains a detailed analysis of the Soma cube problem. Th ...
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Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic period (), and the Classical period (). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical periods of the language. From the Hellenistic period (), Ancient Greek was followed by Koine Greek, which is regarded as a separate historical stage, although its earliest form closely resembles Attic Greek and its latest form approaches Medieval Greek. There were several regional dialects of Ancient Greek, of which Attic Greek developed into Koi ...