# quadrature
## English
### Etymology

Borrowed from Latin quadrātūra.

### Pronunciation

* (UK) IPA: /ˈkwɒd.ɹəˌtjʊə(ɹ)/, /ˈkwɒd.ɹə.t͡ʃə(ɹ)/
* (US) IPA: /ˈkwɑd.ɹəˌt͡ʃʊɚ/, /ˈkwɑd.ɹə.t͡ʃɚ/

### Noun

quadrature (countable and uncountable, plural quadratures)
* The process of making something square; squaring.
* (mathematics) The act or process of constructing a square that has the same area as a given plane figure, or of computing that area.
** 1976, D. T. Whiteside (editor), The Mathematical Papers of Isaac Newton, Volume 7: 1691-1695, Cambridge University Press, page 3,
    Craige was then on the point of publishing a short tract wherein he expounded a systematic (if far from general) 'Method of determining the quadrature of figures comprehended by straight lines and curves',$^{[editor'stranslation]}$ there gathering a variety of techniques of rational algebraic quadrature and arc-rectification […] .
* (mathematics, numerical analysis) The calculation of a definite integral by numerical means.
** 1992, Bernard Bielecki, SINC Quadratures for Cauchy Principal Value Integrals, T.O. Espelid, Alan Genz, Springer, Numerical Integration: Recent Developments, Software and Applications, page 81,
    Three types of SINC quadratures are surveyed for the evaluation of Cauchy principal value integrals $\textstyle \int _{\Gamma }F(t)dt/(t-x)$, $\textstyle x\in \Gamma$, where $\textstyle \Gamma$ is an arc in the complex plane. Under suitable assumptions on F, the quadrature errors are of order $\textstyle O(e^{-c{\sqrt {N}}})$, where N is the number of quadrature nodes and c is a constant independent of N.
** 2011, Narayan Kovvali, Theory and Applications of Gaussian Quadrature Methods, Morgan & Claypool, page 37:In this chapter, we present some example applications of the Gaussian quadrature methods discussed in the previous chapters. […] Figure 4.1 shows the accuracy of the polynomial Gaussian quadratures used to evaluate the first two integrals as a function of N.
** 2015, Bernard Shizgal, Spectral Methods in Chemistry and Physics, Springer, page 71:The integral is thus given by a variant of the Fejér quadrature with two points at the interval boundaries, namely x$_1$ = −1 and x$_N$ = 1 analogous to the Lobatto quadratures of the next section.
* (mathematics, mathematical analysis) The act or process of solving an indefinite integral by symbolic means.
* (astronomy) A situation in which the directions of two celestial bodies (or a celestial body and the Sun) form a right angle from the perspective of the observer.
    When the Moon is in quadrature, it appears in the sky as a half-moon.
* (physics) The condition in which the phase angle between two alternating quantities is 90°.
** 2008, Luis B. Oliveira, Jorge R. Fernandes, Igor M. Filanovsky, Chris J. M. Verhoeven, Manuel M. Silva, Analysis and Design of Quadrature Oscillators, Springer, page 33:If ν$_{IN}$ has 50% duty-cycle, then the outputs are in quadrature.
** 2011, M. V. Deshpande, Electrical Machines, PHI Learning, page 315:The total mmf in a synchronous machine may be split up into two components—one along the pole axis or direct axis and the other at right angles to this or the quadrature axis. […] In the case of salient pole construction, however, the reluctances of the magnetic circuits on which the mmfs act are different along the direct axis and the quadrature axis.
** 2015, Mohammad Elbadry, Ramesh Harjani, Quadrature Frequency Generation for Wideband Wireless Applications, Springer, page 7:Quadrature LO generation is critical to the operation of direct-downconversion receivers [7]. Two common techniques for quadrature generation are divide-by-two frequency dividers, and polyphase filters.
* (art) A painting painted on a wooden panel.

#### Derived terms

* add in quadrature
* differential quadrature
* Gaussian quadrature
* quadrature amplitude modulation
* quadrature domain
* space quadrature

#### Related terms

* quadrate
* quadratural
* quadraturist

#### Translations
### See also

* cubature
* square the circle

## French
### Etymology

Borrowed from Latin quadrātūra. Doublet of carrure.

### Pronunciation

* IPA: /kwa.dʁa.tyʁ/, /ka.dʁa.tyʁ/
* Audio:(file)

### Noun

quadrature f (plural quadratures)
* quadrature
    quadrature du cercle ― quadrature of the circle

### Further reading

* “quadrature”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.

## Italian
### Noun

quadrature f
* plural of quadratura

## Latin
### Participle

quadrātūre
* vocative masculine singular of quadrātūrus