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Length (other)
Length in its basic meaning is the long dimension of an object. Length may also refer to: Mathematics *Arc length, the distance between two points along a section of a curve. * Length of a sequence or tuple, the number of terms. (The length of an '-tuple is ') *Length of a module, in abstract algebra * Length of a polynomial, the sum of the magnitudes of the coefficients of a polynomial * Length of a vector, the size of a vector Other uses *Length (phonetics), in phonetics **Vowel length, the perceived duration of a vowel sound **Geminate consonant, the articulation of a consonant for a longer period of time than that of a single instance *Line and length, the direction and point of bouncing on the pitch of a delivery in cricket *Horse length A horse length, or simply length, is a unit of measurement for the length of a horse from nose to tail, approximately . Use in horse racing The length is commonly used in Thoroughbred horse racing, where it describes the distance between h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Length
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre. Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in. Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object. Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc Length
ARC may refer to: Business * Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s * Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services * Airport Regions Conference, a European organization of major airports * Amalgamated Roadstone Corporation, a British stone quarrying company * American Record Company (1904–1908, re-activated 1979), one of two United States record labels by this name * American Record Corporation (1929–1938), a United States record label also known as American Record Company * ARC (American Recording Company) (1978-present), a vanity label for Earth, Wind & Fire * ARC Document Solutions, a company based in California, formerly American Reprographics Company * Amey Roadstone Construction, a former British construction company * Aqaba Railway Corporation, a freight railway in Jordan * ARC/Architectural Resources Cambridge, Inc., Cambridge, Massachusett ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an ''arbitrary'' index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be ''finite'', as in these examples, or ''infi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defined inductively using the construction of an ordered pair. Mathematicians usually write tuples by listing the elements within parentheses "" and separated by a comma and a space; for example, denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "nbsp; or angle brackets "⟨ ⟩". Braces "" are used to specify arrays in some programming languages but not in mathematical expressions, as they are the standard notation for sets. The term ''tuple'' can often occur when discussing other mathematical objects, such as vectors. In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Length Of A Module
In abstract algebra, the length of a module is a generalization of the dimension of a vector space which measures its size. page 153 In particular, as in the case of vector spaces, the only modules of finite length are finitely generated modules. It is defined to be the length of the longest chain of submodules. Modules with ''finite'' length share many important properties with finite-dimensional vector spaces. Other concepts used to 'count' in ring and module theory are depth and height; these are both somewhat more subtle to define. Moreover, their use is more aligned with dimension theory whereas length is used to analyze finite modules. There are also various ideas of ''dimension'' that are useful. Finite length commutative rings play an essential role in functorial treatments of formal algebraic geometry and deformation theory where Artin rings are used extensively. Definition Length of a module Let M be a (left or right) module over some ring R. Given a chain of submo ... [...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] |
Norm (mathematics)
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance of a vector from the origin is a norm, called the Euclidean norm, or 2-norm, which may also be defined as the square root of the inner product of a vector with itself. A seminorm satisfies the first two properties of a norm, but may be zero for vectors other than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a ''seminormed vector space''. The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm". A pseudonorm may satisfy the same axioms as a norm, with the equality replaced by an inequality "\,\leq\," in the homogeneity axiom. It can also re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Length (phonetics)
In phonetics, length or quantity is a feature of sounds that have distinctively extended duration compared with other sounds. There are long vowels as well as long consonants (the latter are often called ''geminates''). Many languages do not have distinctive length. Among the languages that have distinctive length, there are only a few that have both distinctive vowel length and distinctive consonant length. It is more common that there is only one or that they depend on each other. The languages that distinguish between different lengths have usually long and short sounds. The Mixe languages are widely considered to have three distinctive levels of vowel length, as do Estonian, some Low German/Low Saxon varieties in the vicinity of Hamburg and some Moselle Franconian and Ripuarian Franconian varieties. Strictly speaking, a pair of a long sound and a short sound should be identical except for their length. In certain languages, however, there are pairs of phonemes that ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vowel Length
In linguistics, vowel length is the perceived length of a vowel sound: the corresponding physical measurement is duration. In some languages vowel length is an important phonemic factor, meaning vowel length can change the meaning of the word, for example in: Arabic, Estonian, Finnish, Fijian, Kannada, Malayalam, Japanese, Latin, Old English, Scottish Gaelic, and Vietnamese. While vowel length alone does not change word meaning in most dialects of English, it is said to do so in a few dialects, such as Australian English, Lunenburg English, New Zealand English, and South African English. It also plays a lesser phonetic role in Cantonese, unlike in other varieties of Chinese. Many languages do not distinguish vowel length phonemically, meaning that vowel length does not change meaning, and the length of a vowel is conditioned by other factors such as the phonetic characteristics of the sounds around it, for instance whether the vowel is followed by a voiced or a voiceless conso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geminate Consonant
In phonetics and phonology, gemination (), or consonant lengthening (from Latin 'doubling', itself from ''gemini'' 'twins'), is an articulation of a consonant for a longer period of time than that of a singleton consonant. It is distinct from stress. Gemination is represented in many writing systems by a doubled letter and is often perceived as a doubling of the consonant.William Ham, ''Phonetic and Phonological Aspects of Geminate Timing'', p. 1-18 Some phonological theories use "doubling" as a synonym for gemination, others describe two distinct phenomena. Consonant length is a distinctive feature in certain languages, such as Arabic, Berber, Danish, Estonian, Hindi, Hungarian, Italian, Japanese, Kannada, Punjabi, Polish and Turkish. Other languages, such as English, do not have word-internal phonemic consonant geminates. Consonant gemination and vowel length are independent in languages like Arabic, Japanese, Finnish and Estonian; however, in languages like Italian, No ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line And Length
Line and length in cricket refers to the direction and point of bouncing on the pitch of a delivery. The two concepts are frequently discussed together. Line The line of a delivery is the direction of its trajectory measured in the horizontal plane. More simply, it is a measure of how far to the left or right the ball is travelling, compared to a line drawn straight down the pitch. It is usually referred to in terms of the directions off (away in front of the batsman) and leg (in towards or behind the batsman), rather than left and right, however. Different lines that the ball may be said to be travelling on may be towards off stump, middle stump or leg stump, outside leg stump, or outside off stump. Balls on a line outside off stump may be said to be in the " corridor of uncertainty" if they are within 12 inches of the line of off stump. Wider deliveries may be said to be giving a batsman "width". Balls delivered on a line outside leg stump are often referred to as "going down ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horse Length
A horse length, or simply length, is a unit of measurement for the length of a horse from nose to tail, approximately . Use in horse racing The length is commonly used in Thoroughbred horse racing, where it describes the distance between horses in a race. Horses may be described as winning by several lengths, as in the notable example of Secretariat, who won the 1973 Belmont Stakes by 31 lengths. In 2013, the New York Racing Association placed a blue-and-white checkered pole at Belmont Park to mark that winning margin; using Equibase's official measurement of a length——the pole was placed from the finish line. More often, winning distances are merely a fraction of a length, such as half a length. In British horse racing, the distances between horses are calculated by converting the time between them into lengths by a scale of lengths-per-second. The actual number of lengths-per-second varies according to the type of race and the going conditions. For example, in a flat turf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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