In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second

degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...

, or equations or formulas that involve such terms. ''Quadratus'' is Latin for ''square''.

Mathematics

Algebra (elementary and abstract)

Quadratic function In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before 20th century, the distinction was unclear between a polynomial ...

(or quadratic polynomial), a polynomial function that contains terms of at most second degree ** Complex quadratic polynomials, are particularly interesting for their sometimes chaotic properties under iteration * Quadratic equation, a polynomial equation of degree 2 (reducible to 0 = ''ax''² + ''bx'' + ''c'') * Quadratic formula, calculation to solve a quadratic equation for the independent variable (''x'') * Quadratic field, an algebraic number field of degree two over the field of rational numbers * Quadratic irrational or "quadratic surd", an irrational number that is a root of a quadratic polynomial

Calculus

Quadratic integral In mathematics, a quadratic integral is an integral of the form \int \frac. It can be evaluated by completing the square in the denominator. \int \frac = \frac \int \frac. Positive-discriminant case Assume that the discriminant ''q'' = ''b''2& ...

, the integral of the reciprocal of a second-degree polynomial

Statistics and stochastics

Quadratic form (statistics) In multivariate statistics, if \varepsilon is a vector of n random variables, and \Lambda is an n-dimensional symmetric matrix, then the scalar quantity \varepsilon^T\Lambda\varepsilon is known as a quadratic form in \varepsilon. Expectation It ...

, scalar quantity ε'Λε for an ''n''-dimensional square matrix *

Quadratic mean In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...

, the square root of the mean of the squares of the data * Quadratic variation, in stochastics, useful for the analysis of Brownian motion and martingales

Number theory

* Quadratic reciprocity, a theorem from number theory *

Quadratic residue In number theory, an integer ''q'' is called a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; i.e., if there exists an integer ''x'' such that: :x^2\equiv q \pmod. Otherwise, ''q'' is called a quadratic no ...

, an integer that is a square modulo ''n'' *

Quadratic sieve The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerab ...

, a modern integer factorization algorithm

Other mathematics

* Quadratic convergence, in which the distance to a convergent sequence's limit is squared at each step *

Quadratic differential In mathematics, a quadratic differential on a Riemann surface is a section of the symmetric square of the holomorphic cotangent bundle. If the section is holomorphic, then the quadratic differential is said to be holomorphic. The vector space of ho ...

, a form on a Riemann surface that locally looks like the square of an

abelian differential In mathematics, ''differential of the first kind'' is a traditional term used in the theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic varieties), for everywhere-regular differential 1 ...

Quadratic form In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to a ...

, a homogeneous polynomial of degree two in any number of variables * Quadratic programming, a special type of mathematical optimization problem * Quadratic growth, an asymptotic growth rate proportional to a quadratic function *

Periodic points of complex quadratic mappings This article describes periodic points of some complex quadratic maps. A map is a formula for computing a value of a variable based on its own previous value or values; a quadratic map is one that involves the previous value raised to the powers o ...

, a type of graph that can be used to explore stability in control systems * Quadratic bézier curve, a type of bezier curve

Computer science

Quadratic probing Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking the original hash index and adding successive values of an arbitrary quadratic polynomial unti ...

, a scheme in computer programming for resolving collisions in hash tables *

Quadratic classifier In statistics, a quadratic classifier is a statistical classifier that uses a quadratic decision surface to separate measurements of two or more classes of objects or events. It is a more general version of the linear classifier. The classific ...

, used in machine learning to separate measurements of two or more classes of objects * Quadratic time, in referring to algorithms with quadratic time complexity

Other

* ''Quadratic'' (collection), a 1953 collection of science fiction novels by Olaf Stapledon and Murray Leinster