quadrature

noun

Etymology: Etymology tree Latin quadrātūrabor. English quadrature Borrowed from Latin quadrātūra.

1. The process of making something square; squaring.
2. 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 […] .”

3. 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 ∫_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.”

4. The act or process of solving an indefinite integral by symbolic means.
5. 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. The 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.”

   “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.”

7. A painting painted on a wooden panel.