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2. Quadric - Wikipedia

   en.wikipedia.org/wiki/Quadric

   A quadric is said to be non-degenerate if the matrix is invertible. A non-degenerate quadric is non-singular in the sense that its projective completion has no singular point (a cylinder is non-singular in the affine space, but it is a degenerate quadric that has a singular point at infinity).

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. 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 ⁠ ⁠.

5. Paraboloid - Wikipedia

   en.wikipedia.org/wiki/Paraboloid

   In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane section of a paraboloid made by a plane parallel to the axis of symmetry is a parabola.

6. List of surfaces - Wikipedia

   en.wikipedia.org/wiki/List_of_surfaces

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7. Hyperboloid - Wikipedia

   en.wikipedia.org/wiki/Hyperboloid

   A hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, a hyperboloid is characterized by not being a cone or a cylinder, having a center of symmetry, and intersecting many planes into hyperbolas.

8. Ruled surface - Wikipedia

   en.wikipedia.org/wiki/Ruled_surface

   The generators of any ruled surface coalesce with one family of its asymptotic lines. For developable surfaces they also form one family of its lines of curvature. It can be shown that any developable surface is a cone, a cylinder, or a surface formed by all tangents of a space curve. [5] Developable connection of two ellipses and its development

9. Sprouts (game) - Wikipedia

   en.wikipedia.org/wiki/Sprouts_(game)

   A 2-spot game of Sprouts. The game ends when the first player is unable to draw a connecting line between the only two free points, marked in green. The game is played by two players, [2] starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line between two spots (or from a spot to ...