TrueType fonts use Bézier splines composed of quadratic Bézier curves.

A quadratic Bézier curve is the path traced by the function B ( t ), given points P < sub > 0 </ sub >, P < sub > 1 </ sub >, and P < sub > 2 </ sub >,

Writing B < sub > P < sub > i </ sub >, P < sub > j </ sub >, P < sub > k </ sub ></ sub >( t ) for the quadratic Bézier curve defined by points P < sub > i </ sub >, P < sub > j </ sub >, and P < sub > k </ sub >, the cubic Bézier curve can be defined as a linear combination of two quadratic Bézier curves:

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

A Bézier triangle is a special type of Bézier surface, which is created by ( linear, quadratic, cubic or higher degree ) interpolation of control points.

File: Circle and quadratic bezier. svg | Eight-segment quadratic Bézier spline ( red ) approximating a circle ( black ) with control points

* a curve shape was a single quadratic Bézier curve defined by three control points.

* a path shape which was a sequence of quadratic Bézier curves.

But if no two lines of the regulus of multiple secants of **zg can intersect, then the regulus must be quadratic, or in other words, **zg must be either a Af or a Af curve on a nonsingular quadric surface.

The red curve is the initial state at time zero at which the string is " let free " in a predefined shape The initial state for " Investigation by numerical methods " is set with quadratic splines as follows:

Following von Koch's concept, several variants of the Koch curve were designed, considering right angles ( quadratic ), other angles ( Césaro ) or circles and their extensions to higher dimensions ( Sphereflake ):

This is a quadratic form in the tangent plane to the surface at a point whose value at a particular tangent vector X to the surface is the normal component of the acceleration of a curve along the surface tangent to X ; that is, it is the normal curvature to a curve tangent to X ( see above ).

However, wherever a minimum occurs in the dispersion relation, the minimum can be approximated by a quadratic curve in the small region around that minimum, for example:

The integrand is the restriction to the curve of the square root of the ( quadratic ) differential

Six terms will be needed to vanish a quadratic curve and so on given the other constraints to be included.

It can be parameterized by drawing a line with slope t through the rational point, and intersection with the plane quadratic curve ; this gives a polynomial with F-rational coefficients and one F-rational root, hence the other root is F-rational ( i. e., belongs to F ) also.

with rational coefficients must satisfy the simple quadratic curve

An accelerating or decelerating rate of response would lead to a quadratic ( or similar ) curve.

In mathematics, a degenerate conic is a conic ( degree-2 plane curve, the zeros of a degree-2 polynomial equation, a quadratic ) that fails to be an irreducible curve.

The most obvious of these is the quadratic complex of tangents to Q, each line of which is transformed into the entire pencil of lines tangent to Q at the image of the point of tangency of the given line.

If the quadratic polynomial is monic then the roots are quadratic integers.

The case where X is F, and we have a bilinear form, is particularly useful ( see for example scalar product, inner product and quadratic form ).

As a parabola is a conic section, some sources refer to quadratic Béziers as " conic arcs ".

One of these, Itō's lemma, expresses the composite of an Itō process ( or more generally a semimartingale ) dX < sub > t </ sub > with a twice-differentiable function f. In Itō's lemma, the derivative of the composite function depends not only on dX < sub > t </ sub > and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way.

The set of constructible numbers can be completely characterized in the language of field theory: the constructible numbers form the quadratic closure of the rational numbers: the smallest field extension of which is closed under square root and complex conjugation.

This is a quadratic equation which we can solve.

There is no evidence that suggests Diophantus even realized that there could be two solutions to a quadratic equation.

Formulas for the eccentricity of an ellipse that is expressed in the more general quadratic form are described in the article dedicated to conic sections.

The Earley parser executes in cubic time in the general case, where n is the length of the parsed string, quadratic time for unambiguous grammars, and linear time for almost all LR ( k ) grammars.

A quadratic equation is one which includes a term with an exponent of 2, for example,, and no term with higher exponent.

In general, a quadratic equation can be expressed in the form, where is not zero ( if it were zero, then the equation would not be quadratic but linear ).

Because of this a quadratic equation must contain the term, which is known as the quadratic term.

A geometric algebra is the Clifford algebra of a vector space over the field of real numbers endowed with a quadratic form.

Given a finite dimensional real quadratic space with quadratic form, the geometric algebra for this quadratic space is the Clifford algebra Cℓ ( V, Q ).

Comparisons can also look at tests of trend, such as linear and quadratic relationships, when the independent variable involves ordered levels.

* Gaussian integers: those complex numbers where both and are integers are also quadratic integers.

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin, Arithmetical Investigations ), which, among things, introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon ( 17-sided polygon ) can be constructed with straightedge and compass.

He also considered simultaneous quadratic equations.

The generalized mean, also known as the power mean or Hölder mean, is an abstraction of the quadratic, arithmetic, geometric and harmonic means.

Grover's algorithm can also be used to obtain a quadratic speed-up over a brute-force search for a class of problems known as NP-complete.

Zhu also found square and cube roots by solving quadratic and cubic equations, and added to the understanding of series and progressions, classifying them according to the coefficients of the Pascal triangle.

The two primes, p and q, should both be congruent to 3 ( mod 4 ) ( this guarantees that each quadratic residue has one square root which is also a quadratic residue ) and gcd ( φ ( p-1 ), φ ( q-1 )) should be small ( this makes the cycle length large ).

Again, since both quadratic forms are scalars and hence their product is a scalar, the expectation of their product is also a scalar.

This is a quadratic equation in x, which is also equal to the solubility.

In mathematics, the root mean square ( abbreviated RMS or rms ), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity.

The Ulam spiral, or prime spiral ( in other languages also called the Ulam Cloth ) is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes.

Every quadratic space is also an inner product space ( see below ).

An alternative characterization of the Wiener process is the so-called Lévy characterization that says that the Wiener process is an almost surely continuous martingale with W < sub > 0 </ sub > = 0 and quadratic variation = t ( which means that W < sub > t </ sub >< sup > 2 </ sup > − t is also a martingale ).

He also found negative solutions of quadratic equations and gave rules regarding operations involving negative numbers and zero, such as " A debt cut off from nothingness becomes a credit ; a credit cut off from nothingness becomes a debt.

In the 12th century AD in India, Bhāskara II also gave negative roots for quadratic equations but rejected them because they were inappropriate in the context of the problem.

* Algebraic form ( homogeneous polynomial ), which generalises quadratic forms to degrees 3 and more, also known as quantics or simply forms

The Kalman filter, also known as linear quadratic estimation ( LQE ), is an algorithm which uses a series of measurements observed over time, containing noise ( random variations ) and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those that would be based on a single measurement alone.

For this reason some authors add to the definition that a quadratic residue q must not only be a square but must also be relatively prime to the modulus n.