Hyperplane section
Hyperplane section In mathematics, a hyperplane section of a subset X of projective space ... is the intersection of X with some hyperplane H — in other words we ...
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Lefschetz hyperplane theorem
Lefschetz hyperplane theorem In mathematics, the Lefschetz hyperplane theorem states that a hyperplane section W of a non-singular complex algebraic ... product with the cohomology class of a hyperplane. This is the hard Lefschetz theorem ( ...
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Image:24cell section anim.gif
Image:24cell section anim.gif Image File history File links 24cell_section_anim.gif Animated cross section of a 24-cell. Shows the intersection ... the 24-cell and a 3-d hyperplane as the hyperplane passes through the 24-cell from corner ...
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Convex cone
... condition of α, β. Half-spaces An hyperplane of V is a maximal proper linear ... from V to its scalar field. The hyperplane defined by L(v) = 0 is the bounding hyperplane of H. Half-spaces (open or closed ... a perfect half-space of the bounding hyperplane of H. Every perfect half-space is ... and projections of a convex set Flat section An affine hyperplane of V is ...
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Poincaré map
... dynamical systems, a Poincaré map or Poincaré section is the intersection of a trajectory of ... of at least three dimensions, with a hyperplane of one fewer dimension. More precisely, one ... the return of the trajectory to the hyperplane which starts at a given point of it. The Poincaré section refers to the hyperplane, and the Poincaré map refers to ...
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Regular polytope
... XIII). H.S.M. Coxeter (Coxeter, 1948, Section 1.9) credits Plato (400 BC) with ... fold out nets mentioned in the previous section have higher-dimensional equivalents. Some of these ... de Bruxelles). An animated cut-away cross-section of the 24-cell. The intersection of ... dimensional regular polytope with a three-dimensional hyperplane will be a polytope (not necessarily regular). If the hyperplane is moved through the shape, the ...
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3-sphere
... a 3-sphere with a three-dimensional hyperplane is a 2-sphere (unless the hyperplane is tangent to the 3-sphere, in ... sphere moves through a given three-dimensional hyperplane, the intersection starts out as a point ... which reaches its maximal size when the hyperplane cuts right through the "middle" of the ... point as the 3-sphere leaves the hyperplane. Topological construction Two convenient constructions for ...
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User:Mathbot/List of mathematical redlinks (S)
... Local Government and Regional Planning -- Sectio canonis -- Section 47 -- Section of a vector bundle -- Secure multi-party ... metric -- Smooth morphism -- Smooth (rapper) -- SM Smooth section -- Smooth variety -- Smoothed octagon -- Smoothing -- Snake in ... of a module -- Support vector regression -- Supporting hyperplane -- Supporting hyperplane theorem -- Supporting line -- Supposition -- Supraflüssigkeit -- Supreme ...
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Lefschetz pencil
... variety, and the divisors on V are hyperplane sections. Suppose given hyperplanes H and H′ ... forms L and L′, and the general hyperplane section is V intersected with λL + μ L′ ... where Bertini's lemma applies, the general hyperplane section will be smooth). A Lefschetz pencil ...
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Energy conditions
... is the projection tensor onto the spatial hyperplane elements orthogonal to the four-velocity, at each event. (Notice that these hyperplane elements will not form a spatial hyperslice ... of those mentioned above) are discussed in Section 2.1. Carroll, Sean M. (2004). Spacetime ... 3. Various energy conditions are discussed in Section 4.6. Wald, Robert M. (1984). General ... 2. Common energy conditions are discussed in Section 9.2.
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