Quadratic

Encyclopedia

In mathematics, the term

, or equations or formulas that involve such terms.

for

Calculus

Statistics and stochastics

Number theory

Other

**quadratic**describes something that pertains to squares, to the operation of squaring, to terms of the second degreeDegree of a polynomial

The degree of a polynomial represents the highest degree of a polynominal's terms , should the polynomial be expressed in canonical form . The degree of an individual term is the sum of the exponents acting on the term's variables...

, or equations or formulas that involve such terms.

*Quadratus*is LatinLatin

Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

for

*square*.## Mathematics

Algebra (elementary and abstract)- Quadratic functionQuadratic functionA quadratic function, in mathematics, is a polynomial function of the formf=ax^2+bx+c,\quad a \ne 0.The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis....

, a polynomial function of degree 2 - Quadratic equationQuadratic equationIn mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...

, a polynomial equation of degree 2 (reducible to*y*=*ax*^{2}+*bx*+ c) - Quadratic formula, calculation to solve a quadratric equation for the independent variable (
*x*) - Quadratic polynomialQuadratic polynomialIn mathematics, a quadratic polynomial or quadratic is a polynomial of degree two, also called second-order polynomial. That means the exponents of the polynomial's variables are no larger than 2...

, a polynomial that contains terms of at most second degree- Complex quadratic polynomialComplex quadratic polynomialA complex quadratic polynomial is a quadratic polynomial whose coefficients are complex numbers.-Forms:When the quadratic polynomial has only one variable , one can distinguish its 4 main forms:...

s are particularly interesting for their sometimes chaotic properties under iteration

- Complex quadratic polynomial
- Quadratic fieldQuadratic fieldIn algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d ↦ Q is a bijection from the set of all square-free integers d ≠ 0, 1 to the set of all quadratic fields...

, an algebraic number field of degree two over the field of rational numbers - Quadratic irrationalQuadratic irrationalIn mathematics, a quadratic irrational is an irrational number that is the solution to some quadratic equation with rational coefficients...

or "quadratic surd", an irrational number that is a root of a quadratic polynomial

Calculus

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

Statistics and stochastics

- Quadratic form (statistics)Quadratic form (statistics)If \epsilon is a vector of n random variables, and \Lambda is an n-dimensional symmetric matrix, then the scalar quantity\epsilon^T\Lambda\epsilonis known as a quadratic form in \epsilon.-Expectation:It can be shown that...

, scalar quantity ε'Λε for a n-dimensional square matrix - Quadratic mean, the square root of the mean of the squares of the data
- Quadratic variationQuadratic variationIn mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and martingales. Quadratic variation is just one kind of variation of a process.- Definition :...

, in stochastics, useful for the analysis of Brownian motion and martingales

Number theory

- Quadratic reciprocityQuadratic reciprocityIn number theory, the law of quadratic reciprocity is a theorem about modular arithmetic which gives conditions for the solvability of quadratic equations modulo prime numbers...

, a theorem from number theory - Quadratic residue, an integer that is a square modulo
*n* - Quadratic sieveQuadratic sieveThe quadratic sieve algorithm is a modern integer factorization algorithm and, in practice, the second fastest method known . It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve...

, a modern integer factorization algorithm

Other

- Quadratic convergence, in which the distance to a convergent sequence's limit is squared at each step
- Quadratic differentialQuadratic differentialIn 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 differentialis said to be holomorphic...

, a form on a Riemann surface that locally looks like the square of an abelian differential - Quadratic formQuadratic formIn mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\!is a quadratic form in the variables x and y....

, a homogeneous polynomial of degree two in a number of variables - Quadratic programmingQuadratic programmingQuadratic programming is a special type of mathematical optimization problem. It is the problem of optimizing a quadratic function of several variables subject to linear constraints on these variables....

, a special type of mathematical optimization problem. - Quadratic growthQuadratic growthIn mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position, in the limit as the argument or sequence position goes to infinity...

, an asymptotic growth rate proportional to a quadratic function - Periodic points of complex quadratic mappingsPeriodic points of complex quadratic mappingsThis 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 one and two; and a complex map is one in which the...

, a type of graph that can be used to explore stability in control systems

## Computer science

- Quadratic probingQuadratic probingQuadratic probing is a scheme in computer programming for resolving collisions in hash tables.It is an open addressing method to handle overflows after a collision takes place in some bucket of a hash table....

, a scheme in computer programming for resolving collisions in hash tables. - Quadratic classifierQuadratic classifierA quadratic classifier is used in machine learning and statistical classification to separate measurements of two or more classes of objects or events by a quadric surface...

, 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)Quadratic (collection)Quadratic is a collection of four science fiction works by Olaf Stapledon and Murray Leinster. It was edited by William L. Crawford and published in 1953 by Fantasy Publishing Company, Inc. in an edition of 300 copies...

, a 1953 collection of science fiction novels by Olaf Stapledon and Murray Leinster

## See also

- QuadQuadQuad may refer to:-Architecture:*Quadrangle in architecture, e.g., on a university campus*Quad, a dormitory room or suite housing four residents...
- cubicCubicCubic may refer to:-Science and mathematics:* Cube , "cubic" measurement* Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex...

, relating to a cubeCubeIn geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

or degreeDegree of a polynomialThe degree of a polynomial represents the highest degree of a polynominal's terms , should the polynomial be expressed in canonical form . The degree of an individual term is the sum of the exponents acting on the term's variables...

3, as next higher above*quadratic* - linearLinearIn mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

, relating to a lineLine- Science and technology :* Line , a circuit or loop.** A power line for electric power transmission** line power or lines power, domestic mains electricity.** telephone line** RF transmission line...

or degree 1, as next lower below*quadratic*