What does quadrature mean?
Quadrature is a mathematical term for determining the area of a geometric figure, particularly by expressing that area through squares or through the multiplication of relevant lengths. In modern analysis, it commonly refers to the process of evaluating a definite integral, as in numerical quadrature, where a complex area under a curve is approximated by simpler calculations. Historically, the “quadrature of the circle” meant constructing an exact square with the same area as a circle, a problem that occupied Greek and later mathematicians for centuries. The word is specialized and usually appears in geometry, calculus, numerical analysis, or the history of mathematics rather than in everyday conversation. Its enduring interest lies in the connection between curved figures and the simpler mathematics used to measure them.
The mathematical process of finding the area of a plane figure, especially a square or a circle.
"The book explains the geometric principles of quadrature."
The phrase “quadrature of the circle” refers to the classical problem of constructing a square equal in area to a circle.
The symbolic or numerical evaluation of a definite integral.
"Numerical quadrature provides an efficient way to estimate the integral."
This sense is common in analysis, numerical methods, and signal processing.
Used when referring to multiple areas, mathematical methods, or integral evaluations.
"The article compares different numerical quadratures for estimating the integral."
For ancient mathematicians, quadrature was the challenge of expressing the area of a curved figure through the mathematics of straight lines and squares.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does quadrature come from?
The word comes through Latin quadratura, a noun formed from quadratus, “squared” or “square.” The underlying root quadr-, meaning “four” or “four-sided,” also appears in related English words such as quadrilateral, quadrangle, and quadratic. In early mathematical usage, quadrature referred broadly to the squaring of a geometric figure, before developing into a technical term for the evaluation of integrals.
How quadrature is actually used
In modern mathematics, quadrature most often refers to numerical integration or to a method for approximating an integral. In geometry and its history, it can refer more broadly to the squaring or area-determination of a figure.
Easily confused with quadrature
Quadrature is the calculation of an area or integral, whereas a quadrant is one of four sections into which a plane or coordinate system is divided.