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2 unusual facts about Approximation


Approximation

(U+2245), another combination of "≈" and "=", which is used to indicate isomorphism or sometimes congruence

Körting Hannover

At its peak before the Great Depression, Körting employed approximately 1,700 workers and 400 staff.


Bootable business card

The first version of the LNX-BBC that was independent from Linuxcare was 1.618 (a number suggested by team member Seth Schoen, an approximation of the golden ratio, or phi (φ), and a tribute to Donald Knuth who uses successively more precise approximations of π for versioning his TeX typesetting system).

Boussinesq approximation

Turbulence modeling and eddy viscosity: in modelling the turbulence Reynolds stresses, the Boussinesq approximation results in the use of an eddy viscosity concept

Cube rule

The approximation can work well; it matched the 2002 U.S. House elections to within one seat.

Delay calculation

(These are very closely related - see Laplace transform.) It can also be thought of a generalization of Elmore delay, which matches the first moment in the time domain (or computes a one-pole approximation in the frequency domain - they are equivalent).

Eikonal

Eikonal approximation, a method of approximation useful in wave scattering equations.

El Yunque National Forest

The forest is commonly known as El Yunque, which may be attributed to either a Spanish approximation of the aboriginal Taíno word yu-ke which means "white lands", or the word "anvil," which is yunque in Spanish.

Elliott Ward Cheney, Jr.

Cheney was awarded grants for his research on approximation theory from the National Science Foundation, United States Air Force and United States Army as well as the UK Research Councils and the Italian Scientific Research Council, among others.

Equatorial Rossby wave

Equatorial Rossby waves, often called planetary waves, are very long, low frequency waves found near the equator and are derived using the equatorial Beta plane approximation, f = \beta y, where "β" is the variation of the Coriolis parameter with latitude, \beta = \frac{\partial f}{\partial y}.

Fermi–Pasta–Ulam problem

In the Summer of 1953 Fermi, Pasta, Ulam and Mary Tsingou conducted numerical experiments (i.e. computer simulations) of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third).

François Budan de Boislaurent

Budan's work on approximation was studied by Horner in preparing his celebrated article in the Philosophical Transactions of the Royal Society of London in 1819 that gave rise to the term Horner's method; Horner comments there and elsewhere on Budan's results, at first being sceptical of the value of Budan's work, but later warming to it.

Gardner's relation

The constants \alpha and \beta are usually calibrated from sonic and density well log information but in the absence of these, Gardner's constants are a good approximation.

Golden ratio

The first known approximation of the (inverse) golden ratio by a decimal fraction, stated as "about 0.6180340", was written in 1597 by Michael Maestlin of the University of Tübingen in a letter to his former student Johannes Kepler.

Golomb

Golomb is a surname derived from a phonetical approximation of the Polish word Gołąb (meaning "dove").

Homotopy analysis method

The HAM is an analytic approximation method designed for the computer era with the goal of "computing with functions instead of numbers." In conjunction with a computer algebra system such as Mathematica or Maple, one can gain analytic approximations of a highly nonlinear problem to arbitrarily high order by means of the HAM in only a few seconds.

Horner's method

As it also happened, Henry Atkinson, of Newcastle, devised a similar approximation scheme in 1809; he had consulted his fellow Geordie, Charles Hutton, another specialist and a senior colleague of Barlow at the Royal Military Academy, Woolwich, only to be advised that, while his work was publishable, it was unlikely to have much impact.

Kenning

John Steinbeck used an approximation of kennings in his 1950 novella Burning Bright, which was adapted into a Broadway play that same year.

Lab color space

Though color management software, such as that built into image editing applications, will pick the closest in-gamut approximation, changing lightness, chroma, and sometimes hue in the process, author Dan Margulis claims that this access to imaginary colors is useful, going between several steps in the manipulation of a picture.

Less-than sign

The less-than sign plus the equals sign (<=) is used for an approximation of the less-than-or-equal-to sign (≤).

Liouville number

The following lemma is usually known as Liouville's theorem (on diophantine approximation), there being several results known as Liouville's theorem.

Navarro–Frenk–White profile

The NFW profile is an approximation to the equilibrium configuration of dark matter produced in simulations of collisionless dark matter particles by numerous groups of scientists.

No No Never

Written and composed by Australian-born band member Jane Comerford, the unusual choice of country as the genre resulted in BBC commentator Terry Wogan asking jokingly and with a rough approximation of the appropriate accent "are we in Athens, Georgia?" at the end of the performance (the Contest was held in Athens, Greece).

Politics of Northern Ireland

Once established under the Government of Ireland Act 1920, Northern Ireland, since it was an approximation of that area on the island of Ireland where those favouring remaining part of the UK were in the majority, was structured geographically to guarantee a unionist majority in its government.

Polythiophene

As an approximation, the conjugated backbone can be considered as a real-world example of the "electron-in-a-box" solution to the Schrödinger equation; however, the development of refined models to accurately predict absorption and fluorescence spectra of well-defined oligo(thiophene) systems is ongoing.

Pseudolikelihood

One use of the pseudolikelihood measure is as an approximation for inference about a Markov or Bayesian network, as the pseudolikelihood of an assignment to X i may often be computed more efficiently than the likelihood, particularly when the latter may require marginalization over a large number of variables.

Rational approximation

Diophantine approximation, the approximation of real numbers by rational numbers.

Rigid rotor

This selection rule arises from a first-order perturbation theory approximation of the time-dependent Schrödinger equation.

Robert Dean Frisbie

In Tahiti, Frisbie (dubbed: “Ropati,” a phonetic approximation of “Robert” en: Writer) met Charles Nordhoff and James Norman Hall, well-known co-authors of the Mutiny on the Bounty series.

Sharp-P-complete

Jerrum, Valiant, and Vazirani showed that every #P-complete problem either has an FPRAS, or is essentially impossible to approximate; if there is any polynomial-time algorithm which consistently produces an approximation of a #P-complete problem which is within a polynomial ratio in the size of the input of the exact answer, then that algorithm can be used to construct an FPRAS.

Slave boson

It is mainly used as an approximation for the Anderson impurity model in the limit that the Coulombic repulsion tends to infinity.

Stochastic simulation

The Poisson Distribution depends on only one parameter, λ, and can be interpreted as an approximation to the binomial distribution when the parameter p is a small number.

Thue's theorem

Thue–Siegel–Roth theorem, also known as Roth's theorem, is a foundational result in diophantine approximation to algebraic numbers.

Transition layer

In mathematics, a mathematical approach to finding an accurate approximation to a problem's solution.

Unscented transform

In 1994 Jeffrey Uhlmann noted that the EKF takes a nonlinear function and partial distribution information (in the form of a mean and covariance estimate) of the state of a system but applies an approximation to the known function rather than to the imprecisely-known probability distribution.

Valentinus Otho

In 1573 he came to Wittenberg, proposing to Johannes Praetorius an approximation of Pi as \pi \approx \tfrac {355} {113} .

Wald test

The other reason is that the Wald test uses two approximations (that we know the standard error, and that the distribution is chi-squared), whereas the likelihood ratio test uses one approximation (that the distribution is chi-squared).

William George Horner

His contribution to approximation theory is honoured in the designation Horner's method, in particular respect of a paper in Philosophical Transactions of the Royal Society of London for 1819.


see also