quadrature

plural quadratures

1. countableuncountableThe process of making something square; squaring.
2. countableuncountablemathematicsThe act or process of constructing a square that has the same area as a given plane figure, or of computing that area.

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   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 […] .

3. countableuncountablenumerical analysismathematicsThe calculation of a definite integral by numerical means.

   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.

   2015, Bernard Shizgal, Spectral Methods in Chemistry and Physics, Springer, page 71

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   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 ∫_ΓF(t)dt/(t-x), x∈Γ, where Γ is an arc in the complex plane. Under suitable assumptions on F, the quadrature errors are of order O(e), where N is the number of quadrature nodes and c is a constant independent of N.

   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.

   2011, Narayan Kovvali, Theory and Applications of Gaussian Quadrature Methods, Morgan & Claypool, page 37

   For a function of one independent variable, the basic idea of a quadrature rule is to replace the definite integral by a sum of the integrand evaluated at certain points (called quadrature points ) multiplied by a number (called quadrature weights ).

   (Can we date this quote?), “Numerical Quadrature”, in Florida State University, archived from the original on 22 Feb 2016, page 2

4. countableuncountablemathematical analysisThe act or process of solving an indefinite integral by symbolic means.
5. countableuncountableastronomyA 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. countableuncountablenatural sciencesThe condition in which the phase angle between two alternating quantities is 90°.

   If ν_(IN) has 50% duty-cycle, then the outputs are in quadrature.

   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

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   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.

   2011, M. V. Deshpande, Electrical Machines, PHI Learning, page 315

   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.

   2015, Mohammad Elbadry, Ramesh Harjani, Quadrature Frequency Generation for Wideband Wireless Applications, Springer, page 7

7. countableuncountableartA painting painted on a wooden panel.