kvadratúrna

Kvadrátúrna, also known as "quadrature" in English, refers to the mathematical process of determining the area under a curve by dividing it into infinitesimally small shapes, typically rectangles or strips, whose areas can be summed to approximate the total area. This concept is foundational in calculus and integral calculus, where it serves as the basis for defining definite integrals.

The term originates from the ancient Greek word *quadrature*, meaning "squaring," which historically referred to the problem of constructing a square with the same area as a given shape, such as a circle or parabola. This problem was famously posed by the ancient Greeks, including Hippocrates of Chios, who successfully squared certain curvilinear shapes but not the circle, which remained unsolved until the 17th century with the development of calculus.

In modern mathematics, quadrature is primarily associated with numerical integration techniques used to approximate integrals when analytical solutions are difficult or impossible to obtain. Methods like the trapezoidal rule, Simpson’s rule, and Gaussian quadrature are widely employed in computational mathematics and engineering to estimate areas under curves with high precision.

The concept also extends to more advanced applications, such as solving partial differential equations in physics and engineering, where quadrature is used to evaluate integrals over complex domains. Additionally, quadrature techniques are essential in signal processing, statistics, and computational simulations, where accurate integration is critical for reliable results.