Quadrature

Quadrature, derived from Latin quadrare, is a term with various meanings:

Quadrature amplitude modulation (QAM), a modulation method of using both a carrier wave and a 'quadrature' carrier wave that is 90° out of phase with the main carrier
Oscillations are said to be in quadrature if they are separated in phase by 90° (π/2, or λ/4). See Quadrature phase.
A quadrature filter is the analytic signal of a real-valued filter.

Quadrature of the circle (also squaring the circle), in geometry, the problem of constructing a square and circle of equal area, possible using only an unmarked straight-edge and compass
In mathematics, summing in quadrature means summing the squares of numbers, then taking the square root, as used in error analysis
Numerical quadrature is the numerical calculation of the area under a curve, or more generally, using numerical integration to calculate a definite integral.

Other Applications

In motion control, quadrature encoder is a rotary encoder giving both the relative position and the direction of motion of a shaft.
In astronomy, quadrature occurs when two celestial bodies appear 90° apart from one another as viewed from a third celestial body. As an example, the Moon and the Sun are in quadrature with respect to the Earth when the Moon is in its exact first quarter or last quarter phases. The symbol for astronomical quadrature is a hollow square.