Approximation

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approximation

[ə¦präk·sə¦mā·shən]
(mathematics)
A result that is not exact but is near enough to the correct result for some specified purpose.
A procedure for obtaining such a result.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Approximation

 

replacement of certain mathematical objects by others which are in one sense or another close to the initial objects. Approximation makes it possible to study the numerical characteristics and qualitative properties of the object, reducing the problem to a study of simpler or more convenient objects—for example, objects whose characteristics are easily computed or whose properties are already known. The theory of numbers studies Diophantine approximations—in particular, approximations of irrational numbers by rational numbers. Approximations of curves, surfaces, spaces, and mappings are investigated in geometry and topology. Some branches of mathematics are wholly devoted to approximations, as, for example, the approximation and interpolation of functions and numerical methods of analysis. The role of approximation in mathematics is continually growing. Presently, approximation can be viewed as one of the basic concepts of mathematics.

S. B. STECHKIN

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
According to the above initial data for ATPs of the used damped sinusoidal current pulse of the microsecond range and (1), the critical section for the tested copper wire is approximately equal to [S.sub.CC1] [approximately equal to] 3.34 [mm.sup.2].
As a result, the total nominal power capacitance of a powerful generator of artificial lightning current type [GAMMA]TM -10/350 is approximately equal to 1.15 MJ [19].
The calculated estimation from (4) of the numerical value of the temperature [T.sub.m] of the <<metallic plasma>> for the experimental case of air EE of a thin circular copper conductor of radius [r.sub.0] [approximately equal to] 0.1 mm and length [l.sub.0] [approximately equal to] 110 mm under the influence of the HPC of the microsecond time range described in [8] ([J.sub.k] = 1.95 x [10.sup.17] [A.sup.2] x s x [m.sup.-4]; [U.sub.e] [approximately equal to] 10 V; [S.sub.0] [approximately equal to] 3.14 x [10.sup.-8] [m.sup.2]; [I.sub.m] [approximately equal to] 190 kA; [omega] [approximately equal to] 26.18 x [10.sup.3] [s.sup.-1]) shows that in the considered approximation it will be approximately equal to 92.67 x [10.sup.3] K.
From (2) at [h.sub.sm] [approximately equal to] 2 mm, [[rho].sub.s] [approximately equal to] 72.5 x [10.sup.-8] [OHM] x m, [D.sub.se] [approximately equal to] 80 mm and [D.sub.si] [approximately equal to] 10 mm it follows that the sought value of RS0 is approximately equal to 0.12 m[OHM].

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