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Approximation

Approximation Ap*prox`i*ma"tion n. [Cf. F. approximation, LL. approximatio.] 1. The act of approximating; a drawing, advancing or being near; approach; also, the result of approximating. The largest capacity and the most noble dispositions are but an approximation to the proper standard and true symmetry of human nature. --I. Taylor. 2. An approach to a correct estimate, calculation, or conception, or to a given quantity, quality, etc. 3. (Math.) (a) A continual approach or coming nearer to a result; as, to solve an equation by approximation. (b) A value that is nearly but not exactly correct.

Approximation Ap*prox`i*ma"tion n. [Cf. F. approximation, LL. approximatio.] 1. The act of approximating; a drawing, advancing or being near; approach; also, the result of approximating. The largest capacity and the most noble dispositions are but an approximation to the proper standard and true symmetry of human nature. --I. Taylor. 2. An approach to a correct estimate, calculation, or conception, or to a given quantity, quality, etc. 3. (Math.) (a) A continual approach or coming nearer to a result; as, to solve an equation by approximation. (b) A value that is nearly but not exactly correct.

- calculations easier. Approximations might also be used if incomplete information prevents use of exact representations. The type of approximation used depends...

- generate successive best rational approximations. These approximations are the best possible rational approximations of π relative to the size of their...

- but since the ruler does not use decimals, you round it to 5 cm.) or approximations are used instead of the real data (e.g., 3.14 instead of π). In the...

- second-order approximation is also called "paraxial". The approximations above for sine and tangent do not change for the "second-order" paraxial approximation (the...

- phenomenon. The expression order of approximation is expected to indicate progressively more refined approximations of a function in a specified interval...

- basis of the paraxial approximation), cartography, astronomy, computer science, and so on. The accuracy of the approximations can be seen below in Figure...

- Taylor polynomials) of the series can be used as approximations of the function. These approximations are good if sufficiently many terms are included...

- {\displaystyle n^{n}} and double exponential functions) in n. Most approximations for n! are based on approximating its natural logarithm ln n ! = ∑...

- Diophantine approximations and transcendental number theory are very close areas that share many theorems and methods. Diophantine approximations also have...

- If f {\displaystyle f} is concave up, the approximation will be an underestimate. Linear approximations for vector functions of a vector variable are...

- generate successive best rational approximations. These approximations are the best possible rational approximations of π relative to the size of their...

- but since the ruler does not use decimals, you round it to 5 cm.) or approximations are used instead of the real data (e.g., 3.14 instead of π). In the...

- second-order approximation is also called "paraxial". The approximations above for sine and tangent do not change for the "second-order" paraxial approximation (the...

- phenomenon. The expression order of approximation is expected to indicate progressively more refined approximations of a function in a specified interval...

- basis of the paraxial approximation), cartography, astronomy, computer science, and so on. The accuracy of the approximations can be seen below in Figure...

- Taylor polynomials) of the series can be used as approximations of the function. These approximations are good if sufficiently many terms are included...

- {\displaystyle n^{n}} and double exponential functions) in n. Most approximations for n! are based on approximating its natural logarithm ln n ! = ∑...

- Diophantine approximations and transcendental number theory are very close areas that share many theorems and methods. Diophantine approximations also have...

- If f {\displaystyle f} is concave up, the approximation will be an underestimate. Linear approximations for vector functions of a vector variable are...

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