### What does **quadric** mean?

# Definitions for quadric

ˈkwɒd rɪkquadric

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **quadric**.

### Princeton's WordNet

quadric, quadric surfacenoun

a curve or surface whose equation (in Cartesian coordinates) is of the second degree

### Wiktionary

quadricnoun

A surface whose shape is defined in terms of a quadratic equation

### Wikipedia

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:

### ChatGPT

quadric

A quadric, or quadric surface, is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a type of surface in three-dimensional space defined by an equation of the second degree in three variables x, y, and z. These shapes include ellipsoids, hyperboloids, paraboloids, and others. They are the three-dimensional counterparts of the conic sections in two dimensions.

### Webster Dictionary

Quadricadjective

of or pertaining to the second degree

Quadricnoun

a quantic of the second degree. See Quantic

Quadricnoun

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

### Wikidata

Quadric

In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in-dimensional space defined as the locus of zeros of a quadratic polynomial. In coordinates {x1, x2, ..., xD+1}, the general quadric is defined by the algebraic equation which may be compactly written in vector and matrix notation as: where x = {x1, x2, ..., xD+1} is a row vector, xT is the transpose of x, Q is a × matrix and P is a-dimensional row vector and R a scalar constant. The values Q, P and R are often taken to be real numbers or complex numbers, but in fact, a quadric may be defined over any ring. In general, the locus of zeros of a set of polynomials is known as an algebraic variety, and is studied in the branch of algebraic geometry. A quadric is thus an example of an algebraic variety. For the projective theory see quadric.

### Chambers 20th Century Dictionary

Quadric

kwod′rik,

*adj.*(*alg.*) of the second degree, quadratic—esp. in solid geometry and where there are more than two variables.—*n.***Quad′ricone**, a quadric cone.

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### Usage in printed sources**From:**

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### Anagrams for quadric »

acquir'd

### Numerology

Chaldean Numerology

The numerical value of quadric in Chaldean Numerology is:

**9**Pythagorean Numerology

The numerical value of quadric in Pythagorean Numerology is:

**1**

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## Translations for **quadric**

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"quadric." *Definitions.net.* STANDS4 LLC, 2024. Web. 3 Oct. 2024. <https://www.definitions.net/definition/quadric>.

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