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Indeterminate (other)
Indeterminate may refer to: In mathematics * Indeterminate (variable), a symbol that is treated as a variable * Indeterminate system, a system of simultaneous equations that has more than one solution * Indeterminate equation, an equation that has more than one solution * Indeterminate form, an algebraic expression with certain limiting behaviour in mathematical analysis Other * Indeterminate growth, a term in biology and especially botany * Indeterminacy (philosophy), describing the shortcomings of definition in philosophy * Indeterminacy (music), music for which the composition or performance is determined by chance * Statically indeterminate In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations force and moment equilibrium conditions are insufficient for determining the internal forces and reactions on that structure. Mathemati ..., in statics, describing a structure for which the static equilibrium equations are insuf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indeterminate (variable)
In mathematics, an indeterminate or formal variable is a Variable (mathematics), variable (a mathematical symbol, symbol, usually a letter) that is used purely formally in a mathematical expression, but does not stand for any value. In mathematical analysis, analysis, a mathematical expression such as is usually taken to represent a quantity whose value is a function (mathematics), function of its variable , and the variable itself is taken to represent an unknown or changing quantity. Two such functional expressions are considered equal whenever their value is equal for every possible value of within the Domain of a function, domain of the functions. In abstract algebra, algebra, however, expressions of this kind are typically taken to represent mathematical object, objects in themselves, elements of some algebraic structure – here a polynomial, element of a polynomial ring. A polynomial can be formally defined as the sequence of its coefficients, in this case , and the expr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indeterminate System
In mathematics, particularly in number theory, an indeterminate system has fewer equations than unknowns but an additional a set of constraints on the unknowns, such as restrictions that the values be integers. In modern times indeterminate equations are often called Diophantine equations. Examples Linear indeterminate equations An example linear indeterminate equation arises from imagining two equally rich men, one with 5 rubies, 8 sapphires, 7 pearls and 90 gold coins; the other has 7, 9, 6 and 62 gold coins; find the prices (y, c, n) of the respective gems in gold coins. As they are equally rich: 5y + 8c + 7n + 90 = 7y + 9c + 6n + 62 Bhāskara II gave an general approach to this kind of problem by assigning a fixed integer to one (or N-2 in general) of the unknowns, e.g. n=1, resulting a series of possible solutions like (y, c, n)=(14, 1, 1), (13, 3, 1). For given integers , and , the general linear indeterminant equation is ax + by = n with unknowns and restricted to in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indeterminate Form
Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus, it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function. For example, \begin \lim_ \bigl(f(x) + g(x)\bigr) &= \lim_ f(x) + \lim_ g(x), \\ mu\lim_ \bigl(f(x)g(x)\bigr) &= \lim_ f(x) \cdot \lim_ g(x), \end and likewise for other arithmetic operations; this is sometimes called the algebraic limit theorem. However, certain combinations of particular limiting values cannot be computed in this way, and knowing the limit of each function separately does not suffice to determine the limit of the combination. In these particular situations, the limit is said to take an indeterminate form, described by one of the informal expressions \frac 00,~ \frac,~ 0\times\infty,~ \infty - \infty,~ 0^0,~ 1^\infty, \text \infty^0, among a wide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indeterminate Growth
In biology and botany, indeterminate growth is growth that is not terminated, in contrast to determinate growth that stops once a genetically predetermined structure has completely formed. Thus, a plant that grows and produces flowers and fruit until killed by frost or some other external factor is called indeterminate. For example, the term is applied to tomato varieties that grow in a rather gangly fashion, producing fruit throughout the growing season. In contrast, a determinate tomato plant grows in a more bushy shape and is most productive for a single, larger harvest, then either tapers off with minimal new growth or fruit or dies. Inflorescences In reference to an inflorescence (a shoot specialised for bearing flowers, and bearing no leaves other than bracts), an indeterminate type (such as a raceme) is one in which the first flowers to develop and open are from the buds at the base, followed progressively by buds nearer to the growing tip. The growth of the shoot is not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indeterminacy (philosophy)
Indeterminacy, in philosophy, can refer both to common scientific and mathematical concepts of uncertainty and their implications and to another kind of indeterminacy deriving from the nature of definition or meaning. It is related to deconstructionism and to Nietzsche's criticism of the Kantian noumenon. Indeterminacy in philosophy Introduction The problem of indeterminacy arises when one observes the eventual circularity of virtually every possible definition. It is easy to find loops of definition in any dictionary, because this seems to be the only way that certain concepts, and generally very important ones such as that of existence, can be defined in the English language. A definition is a collection of other words, and in any finite dictionary if one continues to follow the trail of words in search of the precise meaning of any given term, one will inevitably encounter this linguistic indeterminacy. Philosophers and scientists generally try to eliminate indeterminate terms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indeterminacy (music)
Indeterminacy is a composing approach in which some aspects of a musical work are left open to chance or to the interpreter's free choice. John Cage, a pioneer of indeterminacy, defined it as "the ability of a piece to be performed in substantially different ways". The earliest significant use of music indeterminacy features is found in many of the compositions of American composer Charles Ives in the early 20th century. Henry Cowell adopted Ives's ideas during the 1930s, in works allowing players to arrange the fragments of music in a number of different possible sequences. Beginning in the early 1950s, the term came to refer to the (mostly American) movement which grew up around Cage. This group included the other members of the New York School. In Europe, following the introduction of the expression " aleatory music" by Werner Meyer-Eppler, the French composer Pierre Boulez was largely responsible for popularizing the term. Definition Describing indeterminacy, composer John C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statically Indeterminate
In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations force and moment equilibrium conditions are insufficient for determining the internal forces and reactions on that structure. Mathematics Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are: : \sum \mathbf F = 0 : the vectorial sum of the forces acting on the body equals zero. This translates to: :: \sum \mathbf H = 0 : the sum of the horizontal components of the forces equals zero; :: \sum \mathbf V = 0 : the sum of the vertical components of forces equals zero; : \sum \mathbf M = 0 : the sum of the moments (about an arbitrary point) of all forces equals zero. In the beam construction on the right, the four unknown reactions are , , , and . The equilibrium equations are: : \begin \sum \mathbf V = 0 \quad & \implies \quad \mathbf V_A - \mathbf F_v + \mathbf V_B + \mathbf V_C = 0 \\ \sum \mathbf H = 0 \quad & \implies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
