In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas,...

mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental...

Quadrics was a supercomputer company formed in 1996 as a joint venture between Alenia Spazio and the technical team from Meiko Scientific. They produced...

ellipsoid is a quadric surface;  that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces...

space of lines in ⁠ P 3 {\displaystyle \mathbb {P} ^{3}} ⁠ and points on a quadric in ⁠ P 5 {\displaystyle \mathbb {P} ^{5}} ⁠ (projective 5-space). A predecessor...

are degenerate quadric surfaces. When the principal axes of a quadric are aligned with the reference frame (always possible for a quadric), a general equation...

In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from...

manifold known as the Lie quadric (a quadric hypersurface in projective space). Lie sphere geometry is the geometry of the Lie quadric and the Lie transformations...

of A, B, C, F, G and H are zero, is called a quadric surface. There are six types of non-degenerate quadric surfaces: Ellipsoid Hyperboloid of one sheet...

dimension d ≥ 3. Simple examples in a real projective space are hyperspheres (quadrics). The essential geometric properties of an ovoid O {\displaystyle {\mathcal...

class groups is a central goal of algebraic number theory. Let X be the quadric cone of dimension 2, defined by the equation xy = z2 in affine 3-space...

section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane section of the quadric, as this circle is the intersection...

Quadric geometric algebra (QGA) is a geometrical application of the G 6 , 3 {\displaystyle {\mathcal {G}}_{6,3}} geometric algebra. This algebra is also...

5-space, the points that represent each line in S lie on a quadric, Q known as the Klein quadric. If the underlying vector space of S is the 4-dimensional...

a quadric, and is easily seen to contain two one-parameter families of lines. Over the complex numbers this is a quite general non-singular quadric. Letting...

linear transformation of P(Rn+2) that leaves the quadric invariant. In a related construction, the quadric S is thought of as the celestial sphere at infinity...

Eckhard; Nozick, Vincent; Sugimoto, Akihiro (2019), "Three-dimensional quadrics in extended conformal geometric algebras of higher dimensions from control...

extension of the concept of confocal conics to surfaces leads to confocal quadrics. Any hyperbola or (non-circular) ellipse has two foci, and any pair of...

intersection of two planes, b) plane section of a quadric (sphere, cylinder, cone, etc.), c) intersection of two quadrics in special cases. For the general case...

as a 3-dimensional family of lines in P3. The linear line complex and quadric line complex are the cases when the hypersurface has degree 1 or 2; they...

hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, a hyperboloid...

{\displaystyle A+C=0} , the equation represents a rectangular hyperbola. A quadric, or quadric surface, is a 2-dimensional surface in 3-dimensional space defined...

of a quadric surface. Let P ( x , y , z ) {\displaystyle P(x,y,z)} be a polynomial of degree two in three variables that defines a real quadric surface...

obtains an elliptic cone (also called a conical quadric or quadratic cone), which is a special case of a quadric surface. A conical surface S {\displaystyle...

solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors. The camera...

ellipsoid (together with the stress director surface), and Cauchy's stress quadric are two-dimensional graphical representations of the state of stress at...

Augustin-Louis Cauchy saw how their work could be used to classify the quadric surfaces, and generalized it to arbitrary dimensions. Cauchy also coined...

generally, a smooth quadric (degree 2) hypersurface X of any dimension n is rational, by stereographic projection. (For X a quadric over a field k, X must...

} Since it can be expressed as a quadratic polynomial, a sphere is a quadric surface, a type of algebraic surface. Let a, b, c, d, e be real numbers...

plane P2 or a quadric P1×P1. Shavel (1978) constructed some "fake quadrics": surfaces of general type with the same Betti numbers as quadrics. Beauville...