Dictionary Definition
approximation
Noun
1 an approximate calculation of quantity or
degree or worth; "an estimate of what it would cost"; "a rough idea
how long it would take" [syn: estimate, estimation, idea]
2 the quality of coming near to identity
(especially close in quantity)
3 an imprecise or incomplete account; "newspapers
gave only an approximation of the actual events"
4 the act of bringing near or bringing together
especially the cut edges of tissue [syn: bringing
close together]
User Contributed Dictionary
English
Pronunciation

 Rhymes: eɪʃǝn
Noun
Translations
act of approximating
 Dutch: benaderen, schatten
 Finnish: arviointi, approksimointi, lähentäminen
 Italian: approssimazione
imprecise solution
 Czech: přiblížení
 Dutch: benadering, schatting
 Finnish: approksimaatio, likiarvo
 Italian: approssimazione
act of bringing together tissues to be sutured
Derived terms
See also
Extensive Definition
An approximation (represented by the symbol ≈) is
an inexact
representation of something that is still close enough to be
useful. Although approximation is most often applied to numbers, it is also frequently
applied to such things as mathematical
functions, shapes, and
physical
laws.
Approximations may be used because incomplete
information prevents
use of exact representations. Many problems in physics are either
too complex to solve analytically, or impossible to solve. Thus,
even when the exact representation is known, an approximation may
yield a sufficiently accurate solution while reducing the
complexity of the problem significantly.
For instance, physicists often approximate
the shape of the Earth as a sphere even though more accurate
representations are possible, because many physical
behaviours—e.g. gravity—are much
easier to calculate for a sphere than for less regular
shapes.
The problem consisting of two or more planets
orbiting around a sun has no exact solution. Often, ignoring the
gravitational effects of the planets gravitational pull on each
other and assuming that the sun does not move achieve a good
approximation. The use of perturbations to correct for the errors
can yield more accurate solutions. Simulations of the motions of
the planets and the star also yields more accurate solutions.
The type of approximation used depends on the
available information, the degree of
accuracy required, the sensitivity of the problem to this data, and
the savings (usually in time and effort) that can be achieved by
approximation.
Science
The scientific method is carried out with a constant interaction between scientific laws (theory) and empirical measurements, which are constantly compared to one another.The approximation also refers to using a simpler
process. This model is used to make predictions easier. The most
common versions of philosophy
of science accept that empirical measurements are always
approximations—they do not perfectly represent what is
being measured. The history
of science indicates that the scientific laws commonly felt to
be true at any time in history are only approximations to some
deeper set of laws. For example, attempting to resolve a model
using outdated physical
laws alone incorporates an inherent source of error, which
should be corrected by approximating the quantum effects not
present in these laws.
Each time a newer set of laws is proposed, it is
required that in the limiting
situations in which the older set of laws were tested against
experiments, the
newer laws are nearly identical to the older laws, to within the
measurement
uncertainties of the older measurements. This is the correspondence
principle.
Mathematics
<div id="shortcut" class="noprint" style="border:1px solid #999; background:#fff; margin:0 0 .5em 1em; textalign:center; padding:5px; float:right; clear:right; fontsize:smaller;">≈ (formal)
~ (informal)
symbols representing approximation. Approximation usually occurs
when an exact form or an exact numerical number is unknown. However
some known form may exist and may be able to represent the real
form so that no significant deviation can be found. Numerical
approximations sometimes result from using a small number of
significant digits.
Approximation
theory is a branch of mathematics, a quantitative part of
functional
analysis. Diophantine
approximation deals with approximation to real numbers
by rational
numbers. The symbol "≈" means "approximately equal to"; tilde
(~) and the Libra
sign (* Congruence
References
approximation in Breton: Tostadur
approximation in Czech: Aproximace
approximation in Danish: Approksimation
approximation in German: Approximation
approximation in Esperanto: Proksimuma
kalkulado
approximation in French: Approximation
approximation in Icelandic: Námundun
approximation in Italian: Approssimazione
approximation in Dutch: Benadering
approximation in Japanese: 近似
approximation in Polish: Aproksymacja
approximation in Portuguese: Aproximação
approximation in Russian: Аппроксимация
approximation in Simple English:
Approximation
approximation in Finnish: Approksimaatio
approximation in Swedish: Approximation
approximation in Ukrainian:
Апроксимація
Synonyms, Antonyms and Related Words
access,
accession, accord, accordance, addition, adjunct, advance, advent, affairs, affiliation, affinity, afflux, affluxion, agreement, alikeness, alliance, allowance, analogy, aping, appraisal, appraisement, approach, approaching, appropinquation,
appulse, assemblage, assessment, assimilation, assize, assizement, association, bond, calculation, closeness, combination, coming, coming near, coming
toward, community,
comparability,
comparison, computation, confines, conformity, connectedness, connection, contiguity, contrariety, convergence, copying, correction, correspondence, dealings, deduction, determination, deviation, differentiation,
disjunction,
division, environs, equation, estimate, estimation, evaluation, evolution, extrapolation, filiation, flowing toward,
foreground, forthcoming, gauging, homology, identity, imitation, immediacy, immediate
foreground, imminence,
imprecision,
inaccuracy, inaccurateness, incorrectness, inexactitude, inexactness, instrumentation,
integration,
intercourse,
interpolation,
intimacy, inversion, involution, junction, laxity, liaison, likeness, likening, link, linkage, linking, looseness, measure, measurement, measuring, mensuration, metaphor, metric system,
mimicking, multiplication, mutual
attraction, nearing,
nearness, negligence, neighborhood, nighness, notation, oncoming, parallelism, parity, practice, precinct, predictable error,
probable error, propinquity, proportion, proximation, proximity, purlieus, quantification, quantization, rapport, rating, reduction, relatedness, relation, relations, relationship, resemblance, sameness, semblance, similarity, simile, similitude, simulation, standard
deviation, subtraction, survey, surveying, sympathy, telemetering, telemetry, tie, tiein, tolerance, transformation, triangulation, uncorrectness, unfactualness, union, unpreciseness, unrigorousness, valuation, vicinage, vicinity