English
quadrature
Pronunciation
  • IPA: /ˈkwɒd.ɹə.tjʊə(ɹ)/, /-t͡ʃə(ɹ)/
Noun

quadrature

  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, Tom 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 xN = 1 analogous to the Lobatto quadratures of the next section.
  4. (mathematics, 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 νIN 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. (arts) A painting painted on a wooden panel.
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