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147 (number)
147 (one hundred ndforty-seven) is the natural number following 146 and preceding 148. In mathematics 147 is the fourth centered icosahedral number. These are a class of figurate numbers that represent points in the shape of a regular icosahedron or alternatively points in the shape of a cuboctahedron, and are magic numbers for the face-centered cubic lattice. Separately, it is also a magic number for the diamond cubic. It is also the fourth Apéry number a_3, where a_n=\sum_^n\binom^2\binom. There are 147 different ways of representing one as a sum of unit fractions with five terms, allowing repeated fractions, and 147 different self-avoiding polygonal chains of length six using horizontal and vertical segments of the integer lattice. In other fields 147 is the highest possible break in snooker, in the absence of fouls and refereeing errors. In some traditions, there are 147 psalms. However, current Christian and Jewish traditions list a larger number, leading to the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal numbers'', and numbers used for ordering are called ''ordinal numbers''. Natural numbers are sometimes used as labels, known as '' nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by succ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diamond Cubic
The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adopt this structure, including α-tin, the semiconductors silicon and germanium, and silicon–germanium alloys in any proportion. There are also crystals, such as the high-temperature form of cristobalite, which have a similar structure, with one kind of atom (such as silicon in cristobalite) at the positions of carbon atoms in diamond but with another kind of atom (such as oxygen) halfway between those (see :Minerals in space group 227). Although often called the diamond lattice, this structure is not a lattice in the technical sense of this word used in mathematics. Crystallographic structure Diamond's cubic structure is in the Fdm space group (space group 227), which follows the face-centered cubic Bravais lattice. The lattice describes the repeat pattern; for diamond cubic c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psalms
The Book of Psalms ( or ; he, תְּהִלִּים, , lit. "praises"), also known as the Psalms, or the Psalter, is the first book of the ("Writings"), the third section of the Tanakh, and a book of the Old Testament. The title is derived from the Greek translation, (), meaning "instrumental music" and, by extension, "the words accompanying the music". The book is an anthology of individual Hebrew religious hymns, with 150 in the Jewish and Western Christian tradition and more in the Eastern Christian churches. Many are linked to the name of David, but modern mainstream scholarship rejects his authorship, instead attributing the composition of the psalms to various authors writing between the 9th and 5th centuries BC. In the Quran, the Arabic word ‘Zabur’ is used for the Psalms of David in the Hebrew Bible. Structure Benedictions The Book of Psalms is divided into five sections, each closing with a doxology (i.e., a benediction). These divisions were probably intr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Snooker
Snooker (pronounced , ) is a cue sport played on a rectangular table covered with a green cloth called baize, with six pockets, one at each corner and one in the middle of each long side. First played by British Army officers stationed in India in the second half of the 19th century, the game is played with twenty-two balls, comprising a , fifteen red balls, and six other balls—a yellow, green, brown, blue, pink, and black—collectively called the colours. Using a cue stick, the individual players or teams take turns to strike the white to other balls in a predefined sequence, accumulating points for each successful pot and for each time the opposing player or team commits a . An individual of snooker is won by the player who has scored the most points. A snooker ends when a player reaches a predetermined number of frames. Snooker gained its identity in 1875 when army officer Sir Neville Chamberlain, stationed in Ootacamund, Madras, and Jabalpur, devised a set of r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Break
A maximum break (also known as a maximum, a 147, or orally, a one-four-seven) is the highest possible in a single of snooker. A player compiles a maximum break by potting all 15 with 15 for 120 points, followed by all six for a further 27 points. Compiling a maximum break is regarded as a particularly significant achievement in the game of snooker, and may be compared to a nine-dart finish in darts or a 300 game in ten-pin bowling. The first officially recognised maximum break was made by Joe Davis in a 1955 exhibition match in London. At the Classic in January 1982, Steve Davis achieved the first recognised maximum in professional competition, which was also the first maximum to occur during a televised match. The following year, Cliff Thorburn became the first player to make a maximum at the World Snooker Championship. At the UK Championship in December 2013, Mark Selby compiled the 100th recognised maximum break in professional competition. Ronnie O'Sullivan hold ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Lattice
In mathematics, the -dimensional integer lattice (or cubic lattice), denoted , is the lattice in the Euclidean space whose lattice points are -tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice. Automorphism group The automorphism group (or group of congruences) of the integer lattice consists of all permutations and sign changes of the coordinates, and is of order 2''n'' ''n''!. As a matrix group it is given by the set of all ''n''×''n'' signed permutation matrices. This group is isomorphic to the semidirect product :(\mathbb Z_2)^n \rtimes S_n where the symmetric group ''S''''n'' acts on (Z2)''n'' by permutation (this is a classic example of a wreath product). For the square lattice, this is the group of the square, or the dihedral group of order 8; for the three-dimensional cubic lattice, we get the group of the cub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygonal Chain
In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points (A_1, A_2, \dots, A_n) called its vertices. The curve itself consists of the line segments connecting the consecutive vertices. Name A polygonal chain may also be called a polygonal curve, polygonal path, polyline,. piecewise linear curve, broken line or, in geographic information systems, a linestring or linear ring. Variations A simple polygonal chain is one in which only consecutive (or the first and the last) segments intersect and only at their endpoints. A closed polygonal chain is one in which the first vertex coincides with the last one, or, alternatively, the first and the last vertices are also connected by a line segment. A simple closed polygonal chain in the plane is the boundary of a simple polygon. Often the term "polygon" is used in the meaning of "closed polygonal chain", but in some cases it is important to d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Egyptian Fraction
An Egyptian fraction is a finite sum of distinct unit fractions, such as \frac+\frac+\frac. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number \tfrac; for instance the Egyptian fraction above sums to \tfrac. Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including \tfrac and \tfrac as summands, were used as a serious notation for rational numbers by the ancient Egyptians, and continued to be used by other civilizations into medieval times. In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation. However, Egyptian fractions continue to be an object of study in modern number theory and recreational mathematics, as well as in modern historical studies of ancient mathematics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Face-centered Cubic Lattice
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc, and alternatively called ''cubic close-packed'' or ccp) Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the primitive unit cells often are not. Bravais lattices The three Bravais lattices in the cubic crystal system are: The primitive cubic lattice (cP) consists of one lattice point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cube ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
146 (number)
146 (one hundred ndforty-six) is the natural number following 145 and preceding 147. In mathematics 146 is an octahedral number, the number of spheres that can be packed into in a regular octahedron with six spheres along each edge. For an octahedron with seven spheres along each edge, the number of spheres on the surface of the octahedron is again 146. It is also possible to arrange 146 disks in the plane into an irregular octagon with six disks on each side, making 146 an octo number. There is no integer with exactly 146 coprimes less than it, so 146 is a nontotient. It is also never the difference between an integer and the total of coprimes below it, so it is a noncototient. And it is not the sum of proper divisors of any number, making it an untouchable number. There are 146 connected partially ordered set In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Number (chemistry)
The concept of magic numbers in the field of chemistry refers to a specific property (such as stability) for only certain representatives among a distribution of structures. It was first recognized by inspecting the intensity of mass-spectrometric signals of rare gas cluster ions. In case a gas condenses into clusters of atoms, the number of atoms in these clusters that are most likely to form varies between a few and hundreds. However, there are peaks at specific cluster sizes, deviating from a pure statistical distribution. Therefore, it was concluded that clusters of these specific numbers of rare gas atoms dominate due to their exceptional stability. The concept was also successfully applied to explain the monodispersed occurrence of thiolate-protected gold clusters; here the outstanding stability of specific cluster sizes is connected with their respective electronic configuration. The term magic numbers is also used in the field of nuclear physics. In this context, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboctahedron
A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral. Its dual polyhedron is the rhombic dodecahedron. The cuboctahedron was probably known to Plato: Heron's ''Definitiones'' quotes Archimedes as saying that Plato knew of a solid made of 8 triangles and 6 squares. Synonyms *''Vector Equilibrium'' (Buckminster Fuller) because its center-to-vertex radius equals its edge length (it has radial equilateral symmetry). Fuller also called a cuboctahedron built of rigid struts and flexible vertices a ''jitterbug''; this object can be progressively transformed into an icosahedron, octahedron, and tetrahedron by folding along the diagonals of its square s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
