different between squaring vs quadrature

English

Verb

squaring

1. present participle of square

Noun

squaring (plural squarings)

1. The act or process by which something is squared (in various senses).

   Repeated squarings of the number 3 yield the value 6561.

English

Etymology

Borrowed from Latin quadr?t?ra.

Pronunciation

• IPA^(key): /?kw?d.??.tj??(?)/, /-t???(?)/

Noun

quadrature (countable and uncountable, plural quadratures)

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',^{[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 ${\displaystyle \textstyle \int _{\Gamma }F(t)dt/(t-x)}$, ${\displaystyle \textstyle x\in \Gamma }$, where ${\displaystyle \textstyle \Gamma }$ is an arc in the complex plane. Under suitable assumptions on F, the quadrature errors are of order ${\displaystyle \textstyle O(e^{-c{\sqrt {N}}})}$, 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 x_N = 1 analogous to the Lobatto quadratures of the next section.

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.

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 ?_IN 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. (art) A painting painted on a wooden panel.

Derived terms

• add in quadrature
• differential quadrature
• Gaussian quadrature
• quadrature amplitude modulation
• quadrature domain

Related terms

• quadrate
• quadratural
• quadraturist

Translations

See also

• cubature
• square the circle

French

Etymology

Borrowed from Latin quadr?t?ra. Doublet of carrure.

Pronunciation

• IPA^(key): /ka.d?a.ty?/, /kwa.d?a.ty?/

Noun

quadrature f (plural quadratures)

1. quadrature

   quadrature du cercle – quadrature of the circle

Further reading

• “quadrature” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Italian

Noun

quadrature f

1. plural of quadratura

Latin

Participle

quadr?t?re

1. vocative masculine singular of quadr?t?rus