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Height (other)
Height is the measurement of vertical distance. Height may also refer to: Mathematics and computer science * Height (abelian group), an invariant that captures the divisibility properties of an element * Height (ring theory), a measurement in commutative algebra * Height (triangle) or altitude * Height function, a function that quantifies the complexity of mathematical objects * Height of a field, exponent of torsion in the Witt group * Height, the logarithm of the first nonzero term in the formal power series * Tree height, length of the longest root-to-leaf path in a tree data structure Music * Height (musician), Baltimore hip hop artist * ''Height'' (album), an album by John Nolan People * Amy Height (c. 1866–1913), African-American music hall entertainer in the UK * Bob Height, 19th century African-American blackface minstrel performer * Dorothy Height (1912–2010), civil rights activist See also * The Heights (other) The Heights or Heights may refer t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height
Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is about 10,000 m". For example, "Christopher Columbus is 5 foot 2 inches in vertical height." When the term is used to describe vertical position (of, e.g., an airplane) from sea level, height is more often called ''altitude''. Furthermore, if the point is attached to the Earth (e.g., a mountain peak), then altitude (height above sea level) is called ''elevation''. In a two-dimensional Cartesian space, height is measured along the vertical axis (''y'') between a specific point and another that does not have the same ''y''-value. If both points happen to have the same ''y''-value, then their relative height is zero. In the case of three-dimensional space, height is measured along the vertical ''z'' axis, describing a distance from (or "above") t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height (abelian Group)
In mathematics, the height of an element ''g'' of an abelian group ''A'' is an invariant that captures its divisibility properties: it is the largest natural number ''N'' such that the equation ''Nx'' = ''g'' has a solution ''x'' ∈ ''A'', or the symbol ∞ if there is no such ''N''. The ''p''-height considers only divisibility properties by the powers of a fixed prime number ''p''. The notion of height admits a refinement so that the ''p''-height becomes an ordinal number. Height plays an important role in Prüfer theorems and also in Ulm's theorem, which describes the classification of certain infinite abelian groups in terms of their Ulm factors or Ulm invariants. Definition of height Let ''A'' be an abelian group and ''g'' an element of ''A''. The ''p''-height of ''g'' in ''A'', denoted ''h''''p''(''g''), is the largest natural number ''n'' such that the equation ''p''''n''''x'' = ''g'' has a solution in ''x'' ∈ ''A'', or the symbol ∞ if a solution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height (ring Theory)
In commutative algebra, the Krull dimension of a commutative ring ''R'', named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules. The Krull dimension was introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety defined by an ideal ''I'' in a polynomial ring ''R'' is the Krull dimension of ''R''/''I''. A field ''k'' has Krull dimension 0; more generally, ''k'' 'x''1, ..., ''x''''n''has Krull dimension ''n''. A principal ideal domain that is not a field has Krull dimension 1. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent. There are several other ways that have been used to define the dimension of a ring. Most of them coinc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height (triangle)
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the ''extended base'' of the altitude. The intersection of the extended base and the altitude is called the ''foot'' of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as ''dropping the altitude'' at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. Thus, the longest altitude is perpendicular to the shortest side of the triangle. The altitudes are also related to the sides of the triangle through the trigonometr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height Function
A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers. For instance, the ''classical'' or ''naive height'' over the rational numbers is typically defined to be the maximum of the numerators and denominators of the coordinates (e.g. for the coordinates ), but in a logarithmic scale. Significance Height functions allow mathematicians to count objects, such as rational points, that are otherwise infinite in quantity. For instance, the set of rational numbers of naive height (the maximum of the numerator and denominator when expressed in lowest terms) below any given constant is finite despite the set of rational numbers being infinite. In this sense, height functions can be used to prove asymptotic results such as Baker's t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height Of A Field
In mathematics, a Witt group of a field, named after Ernst Witt, is an abelian group whose elements are represented by symmetric bilinear forms over the field. Definition Fix a field ''k'' of characteristic not equal to two. All vector spaces will be assumed to be finite-dimensional. We say that two spaces equipped with symmetric bilinear forms are equivalent if one can be obtained from the other by adding a metabolic quadratic space, that is, zero or more copies of a hyperbolic plane, the non-degenerate two-dimensional symmetric bilinear form with a norm 0 vector.Milnor & Husemoller (1973) p. 14 Each class is represented by the core form of a Witt decomposition.Lorenz (2008) p. 30 The Witt group of ''k'' is the abelian group ''W''(''k'') of equivalence classes of non-degenerate symmetric bilinear forms, with the group operation corresponding to the orthogonal direct sum of forms. It is additively generated by the classes of one-dimensional forms.Milnor & Husemoll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Group Law
In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations. Formal groups are intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology. Definitions A one-dimensional formal group law over a commutative ring ''R'' is a power series ''F''(''x'',''y'') with coefficients in ''R'', such that # ''F''(''x'',''y'') = ''x'' + ''y'' + terms of higher degree # ''F''(''x'', ''F''(''y'',''z'')) = ''F''(''F''(''x'',''y''), ''z'') (associativity). The simplest example is the additive formal group law ''F''(''x'', ''y'') = ''x'' + ''y''. The idea of the definition is that ''F'' should be something like the formal power series expansion of the product of a Lie group, where we choose coordinates so that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (data Structure)
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent. These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes in a single straight line. Binary trees are a commonly used type, which constrain the number of children for each parent to exactly two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height (musician)
Height Keech is the stage name of Baltimore rapper and podcaster Dan Keech (born September 22, 1981). Stereogum. 26 January 2015. He is best known as the founder and frontman for the group Height With Friends. Before forming Height With Friends, he released three solo albums and six EPs between 2000 and 2009. Keech interviews artists and musicians on his weekly podcast Height Zone World, which debuted in July 2014. Height founded Cold Rhymes Records in 2012. The label supports a variety of North American artists. A natural-born storyteller, Height has toured extensively over his musical career. In 2023 Height produced |
Height (album)
John Thomas Nolan (born February 24, 1978) is an American musician best known as the guitarist and co-lead vocalist of Taking Back Sunday, and the former lead singer, pianist, and guitarist of Straylight Run. Nolan left Taking Back Sunday in 2003 along with bassist Shaun Cooper, with whom he formed Straylight Run. During March 2010, he and Cooper rejoined Taking Back Sunday, reforming the ''Tell All Your Friends''-era lineup. Nolan is also a solo artist and has recorded an album called ''Height'' and "Live at Looney Tunes." Biography John Thomas Nolan was born in Baltimore, Maryland, then at three, moved to Rockville Centre, Nassau County, New York, United States. As member of the band Taking Back Sunday he performs lead guitar, vocals and keyboards, in Straylight Run he performs lead vocals, piano, and guitar. Taking Back Sunday In 1999, John was recruited into Taking Back Sunday by Jesse Lacey. He later would invite Adam Lazzara to join the band. In 2002 the ban ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amy Height
Amy Height (c. 1866 – 21 March 1913) was an American music hall entertainer in the UK. She was an unusual black actor and comedian who introduced herself to British audiences first in pantomime and also in straight theatre. Life Height was born in Boston, Massachusetts, around 1866. In 1886, she was acting in Barnsley in northern England. In 1883 she was in the pantomime Robinson Crusoe as his "squaw", Topsy. The critics favourably described her powerful singing voice and her comic delivery. She became a music-hall entertainer in the UK. She appeared with banjoists James and George Bohee who were African Americans on their British tour in 1888 and she was still singing soprano semi-comic songs for them in 1889. She was an unusual black actor who introduced herself to British audiences first in pantomime and also in straight theatre. She was described a "beautiful octaroon" when in Cardiff who was "the only" black female music hall actor. This is not likely. Roles were created ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bob Height
Bob Height was an American 19th century African-American blackface minstrel performer. He was a standout talent in the companies with which he performed, although frustrations eventually drove him to pursue a career in Europe. Later writers have compared him to his contemporary, Bert Williams.Toll 203. Height joined with Charles Hicks in the late 1860s to form Hicks and Height's Georgia Minstrels. This company proved quite popular among African Americans, particularly in the Washington, D.C. area. Eventually, both Hicks and Height joined Sam Hague's Slave Troupe of Georgia Minstrels. Height became a featured talent and accompanied the troupe on a European tour in the early 1870s. Upon the troupe's return to the US in 1872, Charles Callender purchased it and changed the name to Callender's Original Georgia Minstrels. The new owner helped lead the company to great success, and Height enjoyed high billing alongside Billy Kersands and Pete Devonear Pete or Petes or ''variation'', m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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