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The vanishing point theorem is the principal theorem in the science of perspective. It says that the image in a picture plane π of a line L in space, not parallel to the picture, is determined by its intersection with π and its vanishing point. Some authors have used the phrase, "the image of a line includes its vanishing point".
Ramanujam vanishing theorem (algebraic geometry) Ramanujan–Skolem's theorem (Diophantine equations) Ramsey's theorem (graph theory, combinatorics) Rank–nullity theorem (linear algebra) Rao–Blackwell theorem ; Rashevsky–Chow theorem (control theory) Rational root theorem (algebra, polynomials) Rationality theorem
its vanishing point, found at the intersection between the parallel line from the eye point and the picture plane. The principal vanishing point is the vanishing point of all horizontal lines perpendicular to the picture plane. The vanishing points of all horizontal lines lie on the horizon line. If, as is often the case, the picture plane is ...
In algebraic geometry, the Kawamata–Viehweg vanishing theorem is an extension of the Kodaira vanishing theorem, on the vanishing of coherent cohomology groups, to logarithmic pairs, proved independently by Viehweg [1] and Kawamata [2] in 1982.
In algebraic geometry, a vanishing theorem gives conditions for coherent cohomology groups to vanish. Andreotti–Grauert vanishing theorem; Bogomolov–Sommese vanishing theorem; Grauert–Riemenschneider vanishing theorem; Kawamata–Viehweg vanishing theorem; Kodaira vanishing theorem; Le Potier's vanishing theorem; Mumford vanishing theorem
A classic example of this is the twisted cubic in : it is a smooth local complete intersection meaning in any chart it can be expressed as the vanishing locus of two polynomials, but globally it is expressed by the vanishing locus of more than two polynomials.
The strange car-chase movie 'Vanishing Point' has had an equally strange afterlife, as detailed in this new book about the film and its star, a 1970 Dodge Challenger R/T 440.
According to the hairy ball theorem, there is a p such that v(p) = 0, so that s(p) = p. This argument breaks down only if there exists a point p for which s(p) is the antipodal point of p, since such a point is the only one that cannot be stereographically projected onto the tangent plane of p.