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An approximation 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. Accuracy, in science, engineering, industry and statistics, is the degree of conformity of a measured/calculated quantity to its actual (true) value. ... A number is an abstract entity that represents a count or measurement. ... Partial plot of a function f. ... In geometry, two sets have the same shape if one can be transformed to another by a combination of translations, rotations and uniform scalings. ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ...

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. Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ...

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. Many famous physicists of the 20th and 21st century are found on the list of recipients of the Nobel Prize in physics. ... Earth (often referred to as the earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ... A sphere (< Greek σφαίρα) is a perfectly symmetrical geometrical object. ... Gravity is a force of attraction that acts between bodies that have mass. ...

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. Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ...

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 scientific method refers to a body of techniques for investigating phenomena and acquiring new knowledge of the natural world, as well as the correction and integration of previous knowledge, based on observable, empirical, measurable evidence, and subject to laws of reasoning. ... Various meters Measurement is the process of estimating the ratio of a magnitude of a quantity to a unit of the same type. ...

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. Philosophy of science is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of science, including the formal sciences, natural sciences, and social sciences. ... Various meters Measurement is the process of estimating the ratio of a magnitude of a quantity to a unit of the same type. ... The history of science investigates the historical record of human events that are pertinent to the cultural context and the secular development of what is currently called science, namely, a body of empirical and theoretical knowledge, produced by a global community of researchers, making use of specific techniques for the...

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. In mathematics, the concept of a limit is used to describe the behavior of a function as its argument either gets close to some point, or as it becomes larger and larger; or the behavior of a sequences elements, as their index becomes larger and larger. ... In the scientific method, an experiment (Latin: ex-+-periri, of (or from) trying), is a set of actions and observations, performed in the context of solving a particular problem or question, to support or falsify a hypothesis or research concerning phenomena. ... Various meters Measurement is the process of estimating the ratio of a magnitude of a quantity to a unit of the same type. ... In physics, the correspondence principle is a principle, first invoked by Niels Bohr in 1923, which states that the behavior of quantum mechanical systems reduce to classical physics in the limit of large quantum numbers. ...

Mathematics

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". In mathematics and computer science, a numerical digit is a symbol, e. ... In mathematics, approximation theory is concerned with how functions can be approximated with other, simpler, functions, and with characterising in a quantitative way the errors introduced thereby. ... Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ... In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. ... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ...

See also

• Approximation error
• Congruence
• Estimation
• Fermi estimate
• Linear approximation
• Newton's method
• Numerical analysis
• Orders of approximation
• Runge-Kutta methods
• Taylor series