Definition of "quadrature" in 英语

noun

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', 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 ∫_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.

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°.

7. (art) A painting painted on a wooden panel.