quadrature

== English == === Etymology === Borrowed from Latin quadrātūra. === Pronunciation === (Received Pronunciation) IPA(key): /ˈkwɒd.ɹəˌtjʊə(ɹ)/, /ˈkwɒd.ɹə.t͡ʃə(ɹ)/ (General American, dialects of Canada) IPA(key): /ˈkwɑ.dɹəˌt͡ʃʊɚ/, /ˈkwɑ.dɹə.t͡ʃɚ/ (Canada, dialects of the US) IPA(key): /ˈkwɒd.ɹəˌt͡ʃʊɚ/, /ˈkwɒd.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',[editor's translation] 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 ∫ Γ F ( t ) d t / ( t − x ) {\displaystyle \textstyle \int _{\Gamma }F(t)dt/(t-x)} , x ∈ Γ {\displaystyle \textstyle x\in \Gamma } , where Γ {\displaystyle \textstyle \Gamma } is an arc in the complex plane. Under suitable assumptions on F, the quadrature errors are of order O ( e − c N ) {\displaystyle \textstyle O(e^{-c{\sqrt {N}}})} , where N is the number of quadrature nodes and c is a constant independent of N. (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. (physics) The condition in which the phase angle between two alternating quantities is 90°. (art) A painting painted on a wooden panel. ==== Derived terms ==== ==== Related terms ==== quadrate quadratural quadraturist ==== Translations ==== === See also === cubature square the circle == French == === Etymology === Borrowed from Latin quadrātūra. Doublet of carrure. === Pronunciation === IPA(key): /kwa.dʁa.tyʁ/, /ka.dʁa.tyʁ/ === Noun === quadrature f (plural quadratures) quadrature quadrature du cercle ― quadrature of the circle === Further reading === “quadrature”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012 == Italian == === Noun === quadrature f plural of quadratura == Latin == === Participle === quadrātūre vocative masculine singular of quadrātūrus