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antipodal transformation

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  • Rotation group — This article is about rotations in three dimensional Euclidean space. For rotations in four dimensional Euclidean space, see SO(4). For rotations in higher dimensions, see orthogonal group. In mechanics and geometry, the rotation group is the… …   Wikipedia

  • Charts on SO(3) — In mathematics, the special orthogonal group in three dimensions, otherwise known as the rotation group SO(3), is a naturally occurring example of a manifold. The various charts on SO(3) set up rival coordinate systems: in this case there cannot… …   Wikipedia

  • Antipodes — For other uses, see Antipode (disambiguation). This map shows the antipodes of each point on the Earth s surface – the points where the blue and yellow overlap are land antipodes most land has its antipodes in the ocean. This map uses the Lambert …   Wikipedia

  • Projective space — In mathematics a projective space is a set of elements constructed from a vector space such that a distinct element of the projective space consists of all non zero vectors which are equal up to a multiplication by a non zero scalar. A formal… …   Wikipedia

  • Roman surface — The Roman surface (so called because Jakob Steiner was in Rome when he thought of it) is a self intersecting mapping of the real projective plane into three dimensional space, with an unusually high degree of symmetry. The mapping is not an… …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Duality (projective geometry) — A striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this metamathematical concept. There are two approaches to the subject of …   Wikipedia

  • Digon — A degenerate digon with two coinciding edges sharing the same vertices Edges and vertices 2 Schläfli symbol {2} …   Wikipedia

  • Quaternions and spatial rotation — Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to… …   Wikipedia

  • Geology of solar terrestrial planets — The geology of solar terrestrial planet mainly deals with the geological aspects of four planets of the Solar system namely, Mercury, Venus, Earth and Mars and one terrestrial dwarf planet, Ceres. Objects like Pluto are similar to terrestrial… …   Wikipedia

  • Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall …   Wikipedia

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