quadrature

Borrowed from Latin quadrātūra.

• IPA^(key): /ˈkwɒd.ɹə.tjʊə(ɹ)/, /-t͡ʃə(ɹ)/

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 ${\displaystyle \textstyle \int _{\Gamma }F(t)dt/(t-x)}$ , ${\displaystyle \textstyle x\in \Gamma }$ , where ${\displaystyle \textstyle \Gamma }$ is an arc in the complex plane. Under suitable assumptions on F, the quadrature errors are of order ${\displaystyle \textstyle O(e^{-c{\sqrt {N}}})}$ , 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.

• differential quadrature
• Gaussian quadrature
• quadrature amplitude modulation
• quadrature domain

• quadrate
• quadratural
• quadraturist

• cubature
• square the circle

Borrowed from Latin quadrātūra. See also carrure.

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

quadrature f (plural quadratures)

1. quadrature

   quadrature du cercle – quadrature of the circle

• “quadrature” in le Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

quadrature f

1. plural of quadratura

quadrātūre

1. vocative masculine singular of quadrātūrus