Information om | Engelska ordet QUADRIC

Exempel på hur man kan använda QUADRIC i en mening

• A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters.
• In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).
• 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.
• Among these features are mapping between screen- and world-coordinates, generation of texture mipmaps, drawing of quadric surfaces, NURBS, tessellation of polygonal primitives, interpretation of OpenGL error codes, an extended range of transformation routines for setting up viewing volumes and simple positioning of the camera, generally in more human-friendly terms than the routines presented by OpenGL.
• More generally, a smooth quadric (degree 2) hypersurface X of any dimension n is rational, by stereographic projection.
• Geometrically, an isotropic line of the quadratic form corresponds to a point of the associated quadric hypersurface in projective space.
• Arthur Cayley (1873) "On the superlines of a quadric surface in five-dimensional space", Collected Mathematical Papers 9: 79–83.
• If f:A→B is the blowup of the origin of a quadric cone B in affine 3-space, then f×f:A×A→B×B cannot be produced by an étale local resolution procedure, essentially because the exceptional locus has 2 components that intersect.
• The quadric parameterizes oriented (n – 1)-spheres in n-dimensional space, including hyperplanes and point spheres as limiting cases.
• Analogously to the classical Möbius and Laguerre planes, there exists a 3-dimensional model: The classical Minkowski plane is isomorphic to the geometry of plane sections of a hyperboloid of one sheet (non-degenerate quadric of index 2) in 3-dimensional projective space.
• Early mathematical research papers written by Coble when he was teaching at Johns Hopkins University, include: On the relation between the three-parameter groups of a cubic space curve and a quadric surface (1906); An application of the form-problems associated with certain Cremona groups to the solution of equations of higher degree (1908); An application of Moore's cross-ratio group to the solution of the sextic equation (1911); An application of finite geometry to the characteristic theory of the odd and even theta functions (1913); and Point sets and allied Cremona groups (1915).
• More technically, the set of points that are zeros of a quadratic form (in any number of variables) is called a quadric, and the irreducible quadrics in a two dimensional projective space (that is, having three variables) are traditionally called conics.
• In 2016 Hans Havlicek showed that there is a one-to-one correspondence between Clifford parallelisms and planes external to the Klein quadric.
• Stodola established experimentally that the relationship between these three parameters as represented in the Cartesian coordinate system has the shape of a degenerate quadric surface, the cone directrix being an ellipse.
• Abrosimov proved that holomorphic automorphisms of a quadric of codimension two are furnished by birational transformations of degree two.
• A simple ovoid in real 3-space can be constructed by glueing together two suitable halves of different ellipsoids, such that the result is not a quadric.
• The spinor bundle on a quadric 3-fold X is the natural rank-2 subbundle on X viewed as the isotropic Grassmannian of 2-planes in a 4-dimensional symplectic vector space.

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