quadrature

English

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)

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', 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 x₁ = −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 . Two common techniques for quadrature generation are divide-by-two frequency dividers, and polyphase filters.
(art) A painting painted on a wooden panel.