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  2. 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 ...

  3. 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.

  4. Quartic surface - Wikipedia

    en.wikipedia.org/wiki/Quartic_surface

    This is a surface in affine space A 3. On the other hand, a projective quartic surface is a surface in projective space P 3 of the same form, but now f is a homogeneous polynomial of 4 variables of degree 4, so for example ⁠ f ( x , y , z , w ) = x 4 + y 4 + x y z w + z 2 w 2 − w 4 {\displaystyle f(x,y,z,w)=x^{4}+y^{4}+xyzw+z^{2}w^{2}-w^{4

  5. Quadric geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Quadric_geometric_algebra

    Attempting to rotate a QGA quadric surface may result in a different type of quadric surface, or a quadric surface that is rotated and distorted in an unexpected way. Attempting to rotate a QGA point may produce a value that projects as the expected rotated vector, but the produced value is generally not a correct embedding of the rotated vector.

  6. Plücker coordinates - Wikipedia

    en.wikipedia.org/wiki/Plücker_coordinates

    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 ⁠ ⁠.

  7. List of complex and algebraic surfaces - Wikipedia

    en.wikipedia.org/wiki/List_of_complex_and...

    Labs surface, a certain septic with 99 nodes; Endrass surface, a certain surface of degree 8 with 168 nodes; Sarti surface, a certain surface of degree 12 with 600 nodes; Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue ...

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