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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".
Kleene fixed-point theorem (order theory) Kleene's recursion theorem (recursion theory) Knaster–Tarski theorem (order theory) Kneser's theorem (combinatorics) Kneser's theorem (differential equations) Kochen–Specker theorem ; Kodaira embedding theorem (algebraic geometry) Kodaira vanishing theorem (complex manifold) Koebe 1/4 theorem ...
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.
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
In graphical perspective, parallel (horizontal) lines in the plane intersect at a vanishing point (on the horizon).. In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity.
The point P is the vanishing point of lines perpendicular to the picture. If S is another point on the horizon, then it is the vanishing point for all lines parallel to OS. But Brook Taylor (1719) indicated that the horizon plane determined by O and the horizon was like any other plane:
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.
Beauville–Laszlo theorem; Behrend's trace formula; Belyi's theorem; Bézout's theorem; Birkhoff–Grothendieck theorem; Bogomolov–Sommese vanishing theorem; Borel fixed-point theorem; Borel's theorem