1482:. The predictions of a scientific theory can differ from actual measurements. This can be because there are factors in the real situation that are not included in the theory. For example, simple calculations may not include the effect of air resistance. Under these circumstances, the theory is an approximation to reality. Differences may also arise because of limitations in the measuring technique. In this case, the measurement is an approximation to the actual value.
1525:. In the first iteration, the planets' gravitational interactions are ignored, and the star is assumed to be fixed. If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others. This process may be repeated until a satisfactorily precise solution is obtained.
50:
322:, slide rules and calculators produce approximate answers to all but the simplest calculations. The results of computer calculations are normally an approximation expressed in a limited number of significant digits, although they can be programmed to produce more precise results. Approximation can occur when a decimal number cannot be expressed in a finite number of binary digits.
1940:
300:
being measured is 1,500,000 to the nearest hundred thousand (so the actual value is somewhere between 1,450,000 and 1,550,000); this is in contrast to the notation 1.500 × 10, which means that the true value is 1,500,000 to the nearest thousand (implying that the true value is somewhere between 1,499,500 and 1,500,500).
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Some problems in physics are too complex to solve by direct analysis, or progress could be limited by available analytical tools. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.
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Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain. However some known form may exist and may be able to represent the real form so that no significant deviation can be found. For example, 1.5 × 10 means that the true value of something
1520:
Approximation is also used to analyze the motion of several planets orbiting a star. This is extremely difficult due to the complex interactions of the planets' gravitational effects on each other. An approximate solution is effected by performing
253:
In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. An approximate model is used to make calculations easier. Approximations might also be used if incomplete
230:
The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock).
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is a key word generally employed within the title of a directive, for example the Trade Marks
Directive of 16 December 2015 serves "to approximate the laws of the Member States relating to trade marks". The
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420:. No consistent notation is used throughout mathematics and some texts use ≈ to mean approximately equal and ~ to mean asymptotically equal whereas other texts use the symbols the other way around.
1497:, a new scientific theory should reproduce the results of older, well-established, theories in those domains where the old theories work. The old theory becomes an approximation to the new theory.
1923:
Directive (EU) 2015/2436 of the
European Parliament and of the Council of 16 December 2015 to approximate the laws of the Member States relating to trade marks (recast) (Text with EEA relevance)
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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.
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value of a function, i.e. the value as one or more of a function's parameters becomes arbitrarily large. For example, the sum
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even though more accurate representations are possible, because many physical characteristics (e.g.,
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describes approximation of law as "a unique obligation of membership in the
European Union".
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Another combination of "≈" and "=", used to indicate equivalence or approximate equivalence.
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are used especially in technical or scientific contexts. In everyday
English, words such as
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Glossary of mathematical symbols § Equality, equivalence and similarity
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for new member states, and as a continuing process when required by an
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Guide to the
Approximation of European Union Environmental Legislation
730:), usually to indicate asymptotic equivalence between functions, like
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1014:), usually to indicate that two quantities are equal up to constants.
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832:), usually to indicate proportionality between functions, the same
1517:) are much easier to calculate for a sphere than for other shapes.
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are used with a similar meaning. It is often found abbreviated as
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678:), usually to indicate that numbers are not approximately equal (
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1635: – Estimation problem in physics or engineering education
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Another combination of "≈" and "=", which is used to indicate
43:
1689: – Simplification of the basic trigonometric functions
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Which can be used to represent the approach of a variable,
626:), usually to indicate approximation between numbers, like
1547:— they do not perfectly represent what is being measured.
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is anything that is intentionally similar but not exactly
1677: – Family of implicit and explicit iterative methods
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Which is also sometimes used to indicate proportionality.
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A combination of "≈" and "=", which is used to indicate
929:), usually to indicate congruence between figures, like
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is a branch of mathematics, and a quantitative part of
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The type of approximation used depends on the available
1925:, published 23 December 2015, accessed 15 November 2022
1912:, last updated 2 August 2019, accessed 15 November 2022
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would be wrong under this definition, despite wide use.
37:"Approximate" redirects here. Not to be confused with
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1333:{\displaystyle \lim _{x\to \infty }y(x)\doteq 0}
1297:
234:Although approximation is most often applied to
1796:"Approximately Equal — from Wolfram MathWorld"
1665: – Expressions for approximation accuracy
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981:{\displaystyle \Delta ABC\cong \Delta A'B'C'}
325:Related to approximation of functions is the
8:
1844:D & D Standard Oil & Gas Abbreviator
1750:Longman Dictionary of Contemporary English,
1605: – Varying methods used to calculate pi
1489:shows that earlier theories and laws can be
27:Something roughly the same as something else
1695: – Type of analog-to-digital converter
1671: – Approximation of a mathematical set
1629: – Process of finding an approximation
1204:NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO
407:{\displaystyle k/2+k/4+k/8+\cdots +k/2^{n}}
1647: – Approximation method in statistics
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134:Learn how and when to remove this message
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258:prevents use of exact representations.
1493:to some deeper set of laws. Under the
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310:. Calculations are likely to involve
7:
1639:Idealization (philosophy of science)
72:adding citations to reliable sources
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768:{\displaystyle f(n)\simeq 3n^{2}}
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645:{\displaystyle \pi \approx 3.14}
465:≅, ≅
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1847:. PennWell. 2006. p. 366.
1731:The Concise Oxford Dictionary,
797:{\displaystyle \pi \simeq 3.14}
697:{\displaystyle 1\not \approx 2}
267:the degree of accuracy required
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1464:GREATER-THAN OR APPROXIMATE
1053:{\displaystyle \gtrapprox }
416:is asymptotically equal to
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861:of the line above will be
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30:For the sound change, see
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1976:Comparison (mathematical)
1971:Equivalence (mathematics)
1687:Small-angle approximation
577:approximately equals sign
286:Diophantine approximation
1878:Correspondence principle
1495:correspondence principle
1446:LESS-THAN OR APPROXIMATE
1398:A reversed variation of
1258:ALMOST EQUAL OR EQUAL TO
615:{\displaystyle \approx }
304:Numerical approximations
1883:Encyclopædia Britannica
1591:Approximation algorithm
1136:ASYMPTOTICALLY EQUAL TO
1003:{\displaystyle \eqsim }
719:{\displaystyle \simeq }
562:ASYMPTOTICALLY EQUAL TO
1895:The three body problem
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1603:Approximations of π
1578:European Commission
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1240:NOT ALMOST EQUAL TO
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548:EQUALS SIGN
508:MINUS TILDE
424:Typography
273:Mathematics
263:information
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39:Approximant
1955:Categories
1828:2013-04-20
1805:2021-11-22
1781:2013-06-16
1719:References
1627:Estimation
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1503:Physicists
1169:congruence
1073:See also:
1062:\gtrapprox
569:See also:
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320:Log tables
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1515:gravity
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