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Polycubes
upAll 8 one-sided tetracubes – if chirality is ignored, the bottom 2 in grey are considered the same, giving 7 free tetracubes in total A puzzle involving arranging nine L tricubes into a 3×3 cube A polycube is a solid figure formed by joining one or more equal cubes face to face. Polycubes are the three-dimensional analogues of the planar polyominoes. The Soma cube, the Bedlam cube, the Diabolical cube, the Slothouber–Graatsma puzzle, and the Conway puzzle are examples of packing problems based on polycubes. Enumerating polycubes A chiral pentacube Like polyominoes, polycubes can be enumerated in two ways, depending on whether chiral pairs of polycubes are counted as one polycube or two. For example, 6 tetracubes have mirror symmetry and one is chiral, giving a count of 7 or 8 tetracubes respectively. Unlike polyominoes, polycubes are usually counted with mirror pairs distinguished, because one cannot turn a polycube over to reflect it as one can a polyomino give ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetracube Categories
image:tetracube_categories.svg, upAll 8 one-sided tetracubes – if chirality is ignored, the bottom 2 in grey are considered the same, giving 7 free tetracubes in total image:9L cube puzzle solution.svg, A puzzle involving arranging nine L tricubes into a 3×3 cube A polycube is a solid figure formed by joining one or more equal cube (geometry), cubes face to face. Polycubes are the three-dimensional analogues of the planar polyominoes. The Soma cube, the Bedlam cube, the Diabolical cube, the Slothouber–Graatsma puzzle, and the Conway puzzle are examples of packing problems based on polycubes. Enumerating polycubes image:AGK-pentacube.png, A Chirality (mathematics), chiral pentacube Like polyominoes, polycubes can be enumerated in two ways, depending on whether Chirality (mathematics), chiral pairs of polycubes are counted as one polycube or two. For example, 6 tetracubes have Reflection symmetry, mirror symmetry and one is Chirality (mathematics), chiral, giving a coun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tesseract
In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, octahedroid, cubic prism, and tetracube. It is the four-dimensional hypercube, or 4-cube as a member of the dimensional family of hypercubes or measure polytopes. Coxeter labels it the \gamma_4 polytope. The term ''hypercube'' without a dimension reference is frequently treated as a synonym for this specific polytope. The ''Oxford English Dictionary'' traces the word ''tesseract'' to Charles Howard Hinton's 1888 book ''A New Era of Thought''. The term derives from the Greek ( 'four') and from ( 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also a leading authority on Lewis Carroll. ''The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Honeycomb (geometry)
In geometry, a honeycomb is a ''space filling'' or ''close packing'' of polyhedral or higher-dimensional ''cells'', so that there are no gaps. It is an example of the more general mathematical ''tiling'' or ''tessellation'' in any number of dimensions. Its dimension can be clarified as ''n''-honeycomb for a honeycomb of ''n''-dimensional space. Honeycombs are usually constructed in ordinary Euclidean ("flat") space. They may also be constructed in non-Euclidean spaces, such as hyperbolic honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space. Classification There are infinitely many honeycombs, which have only been partially classified. The more regular ones have attracted the most interest, while a rich and varied assortment of others continue to be discovered. The simplest honeycombs to build are formed from stacked layers or ''slabs'' of prisms based on some tessellations of the plane. In particula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
And He Built A Crooked House
or AND may refer to: Logic, grammar, and computing * Conjunction (grammar), connecting two words, phrases, or clauses * Logical conjunction in mathematical logic, notated as "∧", "⋅", "&", or simple juxtaposition * Bitwise AND, a boolean operation in programming, typically notated as "and" or "&" * Short-circuit ''and'', a short-circuit operator, notated "&&", "and", "and then", etc. * Ampersand, the symbol "&", representing "and" * AND gate, in electronics Music albums * ''And'' (John Martyn album), 1996 * ''And'' (Koda Kumi album), 2018 * '' A N D'', a 2015 album by Tricot * ''And'', a 2007 album by Jonah Matranga Businesses and organizations * Alberta New Democrats, now Alberta New Democratic Party *Academy of Nutrition and Dietetics, US * Automotive Navigation Data, digital map supplier * AND Corporation, biometrics * AND CO, software subsidiary of Fiverr Transportation * Anderson Regional Airport, South Carolina, US, IATA airport code * Anderston ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert A
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It can be use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nature (journal)
''Nature'' is a British weekly scientific journal founded and based in London, England. As a multidisciplinary publication, ''Nature'' features peer-reviewed research from a variety of academic disciplines, mainly in science and technology. It has core editorial offices across the United States, continental Europe, and Asia under the international scientific publishing company Springer Nature. ''Nature'' was one of the world's most cited scientific journals by the Science Edition of the 2019 ''Journal Citation Reports'' (with an ascribed impact factor of 42.778), making it one of the world's most-read and most prestigious academic journals. , it claimed an online readership of about three million unique readers per month. Founded in autumn 1869, ''Nature'' was first circulated by Norman Lockyer and Alexander Macmillan as a public forum for scientific innovations. The mid-20th century facilitated an editorial expansion for the journal; ''Nature'' redoubled its efforts in exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crucifixion (Corpus Hypercubus)
''Crucifixion (Corpus Hypercubus)'' is a 1954 oil-on-canvas painting by Salvador Dalí. A nontraditional, surrealist portrayal of the Crucifixion, it depicts Christ on a polyhedron net of a tesseract (hypercube). It is one of his best-known paintings from the later period of his career. Background During the 1940s and 1950s Dalí's interest in traditional surrealism diminished and he became fascinated with nuclear science, feeling that "thenceforth, the atom was isfavorite food for thought". The atomic bombing at the end of World War II left a lasting impression; his 1951 essay "Mystical Manifesto" introduced an art theory he called "nuclear mysticism" that combined his interests in Catholicism, mathematics, science, and Catalan culture in an effort to reestablish classical values and techniques, which he extensively utilized in ''Corpus Hypercubus''. That same year, to promote nuclear mysticism and explain the "return to spiritual classicism movement" in modern art, he tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salvador Dalí
Salvador Domingo Felipe Jacinto Dalí i Domènech, Marquess of Dalí of Púbol (; ; ; 11 May 190423 January 1989) was a Spanish Surrealism, surrealist artist renowned for his technical skill, precise draftsmanship, and the striking and bizarre images in his work. Born in Figueres, Catalonia, Spain, Dalí received his formal education in fine arts in Madrid. Influenced by Impressionism and the Renaissance art, Renaissance masters from a young age he became increasingly attracted to Cubism and avant-garde movements. He moved closer to Surrealism in the late 1920s and joined the Surrealist group in 1929, soon becoming one of its leading exponents. His best-known work, ''The Persistence of Memory'', was completed in August 1931, and is one of the most famous Surrealist paintings. Dalí lived in France throughout the Spanish Civil War (1936 to 1939) before leaving for the United States in 1940 where he achieved commercial success. He returned to Spain in 1948 where he announced his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-barred Cross
A two-barred cross is similar to a Latin cross but with an extra bar added. The lengths and placement of the bars (or "arms") vary, and most of the variations are interchangeably called the cross of Lorraine, the patriarchal cross, the Orthodox cross or the archiepiscopal cross. The two bars The two bars can be placed tight together (condensed) or far apart. They can be symmetrically spaced either around the middle, or above or below the middle. One asymmetrical variation has one bar near the top and the other just below the middle. Finally the bars can be of equal length, or with one shorter than the other. Decorations The ends of the arms can be decorated according to different styles. A style with round or rounded ends is called treflée or botonée (from French bouton) in heraldic use. The same style is called budded, apostles' or cathedral cross in religious use. A straight and pointy style called pattée also includes maltese cross variations, and finally a pointed style ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Cross
A Latin cross or ''crux immissa'' is a type of cross in which the vertical beam sticks above the crossbeam, with the three upper arms either equally long or with the vertical topmost arm shorter than the two horizontal arms, and always with a much longer bottom arm. If displayed upside down it is called St. Peter's Cross, because he was reputedly executed on this type of cross.Joyce Mori, ''Crosses of Many Cultures'' (Harrisburg, PA: Morehouse Publishing, 1998), p. 32 When displayed sideways it is called St. Philip's cross for the same reason. History In a broad sense, the Latin cross is used to represent all of Christianity and Christendom, given that it teaches that Jesus sacrificed himself for humanity upon it, atoning for the sins of the world. It is especially used among the denominations of Western Christianity, including the Roman Catholic tradition and several Protestant traditions, such as Lutheranism, Moravianism, Anglicanism, Methodism, and Reformed Christianity, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexomino
A hexomino (or 6-omino) is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hex(a)-. When rotations and reflections are not considered to be distinct shapes, there are 35 different ''free'' hexominoes. When reflections are considered distinct, there are 60 ''one-sided'' hexominoes. When rotations are also considered distinct, there are 216 ''fixed'' hexominoes. Symmetry The figure above shows all 35 possible free hexominoes, coloured according to their symmetry groups: * The twenty grey hexominoes have no symmetry. Their symmetry group consists only of the identity mapping. * The six red hexominoes have an axis of mirror symmetry parallel to the gridlines. Their symmetry group has two elements, the identity and a reflection in a line parallel to the sides of the squares. * The two green hexominoes have an axis of mirror symmetry at 45° to the gridlines. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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