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  2. Quadric - Wikipedia

    en.wikipedia.org/wiki/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.

  3. Quadric (algebraic geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadric_(algebraic_geometry)

    The two families of lines on a smooth (split) quadric surface. In 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 examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...

  4. Intersection curve - Wikipedia

    en.wikipedia.org/wiki/Intersection_curve

    It is an easy task to determine the intersection points of a line with a quadric (i.e. line-sphere); one only has to solve a quadratic equation. So, any intersection curve of a cone or a cylinder (they are generated by lines) with a quadric consists of intersection points of lines and the quadric (see pictures).

  5. Quadric geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Quadric_geometric_algebra

    Quadric geometric algebra (QGA) is a geometrical application of the , geometric algebra.This algebra is also known as the , Clifford algebra.QGA is a super-algebra over , conformal geometric algebra (CGA) and , spacetime algebra (STA), which can each be defined within sub-algebras of QGA.

  6. Algebraic surface - Wikipedia

    en.wikipedia.org/wiki/Algebraic_surface

    For more examples see the list of algebraic surfaces. The first five examples are in fact birationally equivalent. That is, for example, a cubic surface has a function field isomorphic to that of the projective plane, being the rational functions in two indeterminates. The Cartesian product of two curves also provides examples.

  7. Plücker coordinates - Wikipedia

    en.wikipedia.org/wiki/Plücker_coordinates

    It corresponds to a curve on the Klein quadric. For example, a hyperboloid of one sheet is a quadric surface in ⁠ ⁠ ruled by two different families of lines, one line of each passing through each point of the surface; each family corresponds under the Plücker map to a conic section within the Klein quadric in ⁠ ⁠.

  8. Kummer surface - Wikipedia

    en.wikipedia.org/wiki/Kummer_surface

    Any such surface is the Kummer variety of the Jacobian variety of a smooth hyperelliptic curve of genus 2; i.e. a quotient of the Jacobian by the Kummer involution x ↦ −x. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface.

  9. Analytic geometry - Wikipedia

    en.wikipedia.org/wiki/Analytic_geometry

    A quadric, or quadric surface, is a 2-dimensional surface in 3-dimensional space defined as the locus of zeros of a quadratic polynomial. In coordinates x 1 , x 2 , x 3 , the general quadric is defined by the algebraic equation [ 21 ]

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