Theorems in geometry
•
Projective geometry
Theorems in projective geometry
Fundamental theorem of projective geometry
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which they are derived. It is a bijection that maps lines to lines, and...
Cayley–Bacharach theorem
Cayley–Bacharach theorem - Wikipedia
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 holomor...
Birkhoff–Grothendieck theorem - Wikipedia
Intersection theorem
In projective geometry, an intersection theorem or incidence theorem is an incidence structure consisting of points, lines, and possibly higher-dimensional objects and their incidences, together with ...
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 (i.e., ellipse, parabola or hyperbola) and joined by...
Pascal's theorem - Wikipedia
Bruck–Ryser–Chowla theorem
The Bruck–Ryser–Chowla theorem is a result on the combinatorics of block designs. It states that if a (v, b, r, k, λ)-design exists with v = b (a symmetric block design), then: The theorem was proved ...
Veblen–Young theorem
In mathematics, the Veblen–Young theorem, proved by Oswald Veblen and John Wesley Young (1908, 1910, 1917), states that a projective space of dimension at least 3 can be constructed a...
Steiner's theorem (geometry)
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 ...
Steiner's theorem (geometry) - Wikipedia
Desargues' theorem
In projective geometry, Desargues' theorem, named after Girard Desargues, states:Denote the three vertices of one triangle by a, b, and c, and those of the other by A, B, and C. Axial perspectivity ...
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. ...
Gerbaldi's theorem
In linear algebra and projective geometry, Gerbaldi's theorem, proved by Gerbaldi (1882), states that one can find six pairwise apolar linearly independent nondegenerate ternary quadratic forms. ...
Projective linear transformation
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which they are derived. It is a bijection that maps lines to lines, and...
Projective linear transformation - Wikipedia
De Bruijn–Erdős theorem (incidence geometry)
In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős (1948), states a lower bound on the number of lines determined by n points in ...
De Bruijn–Erdős theorem (incidence geometry) - Wikipedia