Category: Theorems in projective geometry

Cayley–Bacharach theorem
In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane P2. The original form states: Assume that two cubics C1 and C2 in
De Bruijn–Erdős theorem (incidence geometry)
In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős, states a lower bound on the number of lines determined by n points in a projective
Five points determine a conic
In Euclidean and projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve). There are additional subtleties f
Brianchon's theorem
In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point.
Bruck–Ryser–Chowla theorem
The Bruck–Ryser–Chowla theorem is a result on the combinatorics of block designs that implies nonexistence of certain kinds of design. It states that if a (v, b, r, k, λ)-design exists with v = b (a s
Steiner conic
The Steiner conic or more precisely Steiner's generation of a conic, named after the Swiss mathematician Jakob Steiner, is an alternative method to define a non-degenerate projective conic section in
Desargues's theorem
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in perspective centrally. Denote the three vertices
Fundamental theorem of projective geometry
No description available.
Gerbaldi's theorem
In linear algebra and projective geometry, Gerbaldi's theorem, proved by Gerbaldi, states that one can find six pairwise apolar linearly independent nondegenerate ternary quadratic forms. These are pe
Veblen–Young theorem
In mathematics, the Veblen–Young theorem, proved by Oswald Veblen and John Wesley Young , states that a projective space of dimension at least 3 can be constructed as the projective space associated t
Birkhoff–Grothendieck theorem
In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over is a direct sum of holomorp
Intersection theorem
In projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and possibly higher-dimensional objects and their i
Qvist's theorem
In projective geometry, Qvist's theorem, named after the Finnish mathematician , is a statement on ovals in finite projective planes. Standard examples of ovals are non-degenerate (projective) conic s
Segre's theorem
In projective geometry, Segre's theorem, named after the Italian mathematician Beniamino Segre, is the statement: * Any oval in a finite pappian projective plane of odd order is a nondegenerate proje
Pascal's theorem
In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in a
Pappus's hexagon theorem
In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that * given one set of collinear points and another set of collinear points then the intersection points of line