Kvadratuuri

Kvadratuuri is a term used in mathematics to denote quadrature, the classical problem of determining a square with the same area as a given plane figure, or, more generally, the calculation of areas. The word derives from Latin quadratura, meaning to make square, and it is used across geometry and analysis.

In geometry, quadrature refers to the attempt to construct a square with equal area to a shape using only a straightedge and compass. The oldest and most famous instance is the squaring of the circle, which asks for a square with the same area as a circle. It was proven impossible to achieve with classical tools in 1882, after the realization that pi is transcendental.

In calculus and numerical analysis, quadrature denotes methods for evaluating definite integrals or areas under curves. Exact quadrature occurs for certain functions, while numerical quadrature uses discrete samples to approximate the integral. Common techniques include the trapezoidal rule, Simpson's rule, and Gaussian quadrature, each with known error bounds.

In technology and signal processing, quadrature also refers to components or signals that are 90 degrees out of phase, as in quadrature amplitude modulation or quadrature demodulation; this usage shares the underlying idea of decomposing a signal into orthogonal parts.

The term appears in various languages and academic contexts, sometimes focusing on geometric squaring and other times on numerical integration or signal processing, depending on the field and historical usage.