mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas). In three-dimensional space, quadrics include...

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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

have an arbitrarily large number of variables. The set of its zero form a quadric, which is a surface in the case of three variables and a hypersurface in...

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...

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...

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...

bounded by the base or only to the lateral conic surface, a quadric called conical quadric or quadratic cone. In a three-dimensional Cartesian coordinate...

{\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...

also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes;...

{\displaystyle {\sqrt {2}}} . The eccentricity of a three-dimensional quadric is the eccentricity of a designated section of it. For example, on a triaxial...

etc.) or a quadric (sphere, cylinder, hyperboloid, etc.) lead to quadratic equations that can be easily solved. Intersections between quadrics lead to quartic...

divided into minimal surfaces, ruled surfaces, non-orientable surfaces, quadrics, pseudospherical surfaces, algebraic surfaces, and other types of surfaces...

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...

The image is algebraic, consisting of the intersection of a number of quadrics defined by the § Plücker relations (see below). The Plücker embedding was...

quadratic form (in any number of variables) is called a quadric, and the irreducible quadrics in a two dimensional projective space (that is, having three...

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...

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

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