What does quadric surface mean?
Definitions for quadric surface
quadric sur·face
This dictionary definitions page includes all the possible meanings, example usage and translations of the word quadric surface.
Princeton's WordNet
quadric, quadric surfacenoun
a curve or surface whose equation (in Cartesian coordinates) is of the second degree
Wikipedia
quadric surface
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:
ChatGPT
quadric surface
A quadric surface is a two-dimensional geometric figure defined by a second degree equation in three variables - x, y, and z. This equation is generally represented in the following form: Ax² + By² + Cz² + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0. Examples of quadric surfaces include ellipsoids, paraboloids, hyperboloids, cones, cylinders, and planes.
Matched Categories
Numerology
Chaldean Numerology
The numerical value of quadric surface in Chaldean Numerology is: 1
Pythagorean Numerology
The numerical value of quadric surface in Pythagorean Numerology is: 2
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"quadric surface." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/quadric+surface>.
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