quadrature

English

Quadrature of a sphere

Etymology

Borrowed from Latin quadrātūra.

Pronunciation

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

Noun

quadrature (countable and uncountable, plural quadratures)

1. The process of making something square; squaring.
2. (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's translation]} there gathering a variety of techniques of rational algebraic quadrature and arc-rectification […] .

3. (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 x₁ = −1 and x_N = 1 analogous to the Lobatto quadratures of the next section.

4. (mathematics, mathematical analysis) The act or process of solving an indefinite integral by symbolic means.
5. (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.

6. (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.

7. (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

squaring

• Danish: kvadrering c
• Georgian: კვადრატურა (ḳvadraṭura)
• German: Quadrieren n
• Greek: τετραγωνισμός (el) m (tetragonismós)
• Spanish: cuadratura f

mathematics

• Danish: kvadratur c
• French: quadrature (fr) f
• Georgian: კვადრატურა (ḳvadraṭura)
• German: Quadratur (de) f
• Greek: τετραγωνισμός (el) m (tetragonismós)
• Romanian: cvadratură (ro) f
• Russian: квадрату́ра (ru) f (kvadratúra)
• Spanish: cuadratura f

astronomy

• Danish: kvadratur c
• French: quadrature (fr) f
• Georgian: კვადრატურა (ḳvadraṭura)
• German: Quadratur (de) f
• Japanese: 矩 (ja) (く, ku), 西矩 (ja) (せいく, seiku), 西方矩 (せいほうく, seihōku), 下矩 (かく, kaku)
• Romanian: cvadratură (ro) f
• Sanskrit: तरवी (sa) (taravī)
• Spanish: cuadratura f

physics: condition in which the phase angle is 90 degrees

• Korean: 직교 (jikgyo)

See also

• cubature
• square the circle

French

Etymology

Borrowed from Latin quadrātūra. Doublet of carrure.

Pronunciation

• IPA^(key): /kwa.dʁa.tyʁ/, /ka.dʁa.tyʁ/

• Audio:

  (file)

Noun

quadrature f (plural quadratures)

1. 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

1. plural of quadratura

Latin

Participle

quadrātūre

1. vocative masculine singular of quadrātūrus