quadric surface - translation to ρωσικά
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quadric surface - translation to ρωσικά

LOCUS OF ZEROS OF A QUADRATIC POLYNOMIAL (AFFINE OR PROJECTIVE, NOT NECESSARILY REAL)
Quadric surface; Quadric (projective geometry); Quadric (Projective Geometry); Quadratic surface; Quadric hypersurface; Hyperbolic quadric; Quadric cone; Quadratic hypersurface; Quadrics

quadric surface         

математика

поверхность второго порядка

квадрика

quadratic hypersurface         

математика

гиперповерхность второго порядка

quadratic surface         

математика

квадратичная поверхность

Ορισμός

Quadric
·adj Of or pertaining to the second degree.
II. Quadric ·noun A quantic of the second degree. ·see Quantic.
III. Quadric ·noun A surface whose equation in three variables is of the second degree. Spheres, spheroids, ellipsoids, paraboloids, hyperboloids, also cones and cylinders with circular bases, are quadrics.

Βικιπαίδεια

Quadric

In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections. When the defining polynomial is not absolutely irreducible, the zero set is generally not considered a quadric, although it is often called a degenerate quadric or a reducible quadric.

In coordinates x1, x2, ..., xD+1, the general quadric is thus defined by the algebraic equation

i , j = 1 D + 1 x i Q i j x j + i = 1 D + 1 P i x i + R = 0 {\displaystyle \sum _{i,j=1}^{D+1}x_{i}Q_{ij}x_{j}+\sum _{i=1}^{D+1}P_{i}x_{i}+R=0}

which may be compactly written in vector and matrix notation as:

x Q x T + P x T + R = 0 {\displaystyle xQx^{\mathrm {T} }+Px^{\mathrm {T} }+R=0\,}

where x = (x1, x2, ..., xD+1) is a row vector, xT is the transpose of x (a column vector), Q is a (D + 1) × (D + 1) matrix and P is a (D + 1)-dimensional row vector and R a scalar constant. The values Q, P and R are often taken to be over real numbers or complex numbers, but a quadric may be defined over any field.

A quadric is an affine algebraic variety, or, if it is reducible, an affine algebraic set. Quadrics may also be defined in projective spaces; see § Normal form of projective quadrics, below.

Μετάφραση του &#39quadric surface&#39 σε Ρωσικά