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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, the length of a horse in equestrianism *Length overall Length overall (LOA, o/a, o.a. or oa) is the maximum length of a vessel's hull measured parallel to the waterline. This length is important while docking the ship. It is the ... [...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 (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), 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 size, 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, width, breadth, and depth. ''Height'' is used when there is a base from which vertical measurements can be taken. ''Width'' and ''breadth'' usually refer to a shorter dimension than ''length''. ''Depth'' is used for the measure of a third dimension. Length is the measure of one spatial dimension, whereas area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc Length
Arc length is the distance between two points along a section of a curve. Development of a formulation of arc length suitable for applications to mathematics and the sciences is a problem in vector calculus and in differential geometry. In the most basic formulation of arc length for a vector valued curve (thought of as the trajectory of a particle), the arc length is obtained by integrating speed, the magnitude of the velocity vector over the curve with respect to time. Thus the length of a continuously differentiable curve (x(t),y(t)), for a\le t\le b, in the Euclidean plane is given as the integral L = \int_a^b \sqrt\,dt, (because \sqrt is the magnitude of the velocity vector (x'(t),y'(t)), i.e., the particle's speed). The defining integral of arc length does not always have a closed-form expression, and numerical integration may be used instead to obtain numerical values of arc length. Determining the length of an irregular arc segment by approximating the arc segment as ... [...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 '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An -tuple can be formally defined as the image of a function that has the set of the first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an -tuple can be identified with the ordered pair of its first elements and its t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Length Of A Module
In algebra, the length of a module over a ring R is a generalization of the dimension of a vector space which measures its size. page 153 It is defined to be the length of the longest chain of submodules. For vector spaces (modules over a field), the length equals the dimension. If R is an algebra over a field k, the length of a module is at most its dimension as a k-vector space. In commutative algebra and algebraic geometry, a module over a Noetherian commutative ring R can have finite length only when the module has Krull dimension zero. Modules of finite length are finitely generated modules, but most finitely generated modules have infinite length. Modules of finite length are Artinian modules and are fundamental to the theory of Artinian rings. The degree of an algebraic variety inside an affine or projective space is the length of the coordinate ring of the zero-dimensional intersection of the variety with a generic linear subspace of complementary dimension. More gene ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norm (mathematics)
In mathematics, a norm is a function (mathematics), 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 (mathematics), origin: it Equivariant map, commutes with scaling, obeys a form of the triangle inequality, and zero is only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the #Euclidean norm, Euclidean norm, the #p-norm, 2-norm, or, sometimes, the magnitude or length of the vector. This norm can 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 meaning ... [...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 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 are tradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vowel Length
In linguistics, vowel length is the perceived or actual length (phonetics), duration of a vowel sound when pronounced. Vowels perceived as shorter are often called short vowels and those perceived as longer called long vowels. On one hand, many languages do not distinguish vowel length phoneme, phonemically, meaning that vowel length alone does not change the meanings of words. However, the amount of time a vowel is uttered can change based on factors such as the phonetic characteristics of the sounds around it: the phonetic environment. An example is that vowels tend to be pronounced longer before a voiced consonant and shorter before a voiceless consonant in the standard accents of General American English, American and Received Pronunciation, British English. On the other hand, vowel length is indeed an important phonemic factor in certain languages, meaning vowel length can change word-meanings, for example in Arabic phonology#Vowels, Arabic, Czech phonology, Czech, Dravidia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geminate Consonant
In phonetics and phonology, gemination (; from Latin 'doubling', itself from '' gemini'' 'twins'), or consonant lengthening, 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, while others describe two distinct phenomena. Consonant length is a distinctive feature in certain languages, such as Japanese. Other languages, such as Greek, do not have word-internal phonemic consonant geminates. Consonant gemination and vowel length are independent in languages like Arabic, Japanese, Hungarian, Malayalam, and Finnish; however, in languages like Italian, Norwegian, and Swedish, vowel length and consonant length are interdependent. Fo ... [...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 tur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
