Linked from

The 66 pages that link to Projective geometry, each with the reason it gives.

• David HilbertRelated: Its synthetic methods shaped Hilbert’s axiomatic treatment of geometry.

• Linear perspectiveRelated: It formalizes how perspective maps spatial points and lines onto a picture.

• Conic sectionRelated: It unifies conic types by treating them as projectively related curves.

• Coordinate geometryRelated: It extends coordinate methods to relationships that ordinary Euclidean coordinates treat awkwardly.

• Field (mathematics)Related: Coordinates over fields construct projective spaces and their points.

• Projective planeNarrower topic: The projective plane is a fundamental space studied by this geometry.

• Analytic geometryRelated: It extends coordinate methods to include points at infinity and projection.

• Felix KleinRelated: Klein treated projective geometry as a broad setting in which other geometries could be described.

• Affine spaceRelated: Affine spaces embed into projective spaces by adding points at infinity.

• Arthur CayleyRelated: Cayley connected projective geometry with metric geometry through an invariant-based approach.

• GeometryRelated: It treats perspective and intersections as primary while setting aside ordinary measurements.

• Synthetic geometryRelated: Its synthetic methods extend classical figure reasoning beyond Euclidean distance and parallelism.

• Affine geometryRelated: Affine geometry developed in close relation to projective geometry and its points at infinity.

• Projective transformationNarrower topic: Projective transformations are its coordinate representations of incidence-preserving changes.

• Ceva's theoremNarrower topic: Ceva's incidence condition has a projective interpretation through side intersections.

• Convex geometryCompared with: Its incidence-based viewpoint differs from convexity's focus on segments and containment.

• Line (geometry)Related: It changes how parallel lines intersect without changing their straightness.

• Apollonius of PergaCompared with: It unifies conics through incidence and projection, a different framework from Apollonius's treatment.

• Cross-ratioNarrower topic: The cross-ratio supplies a numerical invariant where projective geometry otherwise preserves few measurements.

• Pascal's theoremNarrower topic: Pascal's theorem became a foundational result in this broader geometry.

• FieldRelated: Coordinates over a field construct projective spaces and their points.

• Jakob SteinerNarrower topic: Steiner’s synthetic investigations helped establish this field as a coherent mathematical discipline.

• Sophus LieNarrower topic: Projective transformations formed part of the geometric landscape Lie sought to generalize.

• Elliptic geometryRelated: Elliptic geometry uses projective incidence while adding a metric.

• AnamorphosisRelated: Its transformations describe how an image can be warped and still reconstruct correctly.

• Complete quadrilateralNarrower topic: The complete quadrilateral became a standard configuration in this geometric tradition.

• Descriptive geometryCompared with: It shares projection as a foundation but studies broader invariant relationships than Monge's constructions.

• Point (geometry)Related: Its expanded point concept makes projective transformations preserve incidence.

• Brianchon's theoremNarrower topic: Its incidence language explains concurrency without requiring distances or angles.

• Miquel's theoremNarrower topic: The theorem's quadrilateral setup connects to projective treatments of conics and incidence.

• August Ferdinand MöbiusNarrower topic: Möbius helped establish this field through his work on homogeneous coordinates and geometric transformations.

• Homogeneous polynomialRelated: Homogeneous equations define zero sets that are unchanged when coordinates are scaled together.

• Jean-Victor PonceletNarrower topic: It is the field Poncelet helped restore and develop.

• Miquel pointNarrower topic: The point's incidence relations sit within the broader history of synthetic geometry.

• Vector geometryCompared with: Its central relations survive projection even when Euclidean lengths and angles do not.

• Menelaus's theoremRelated: Menelaus's relation is a classical incidence theorem with a projective-geometric formulation.

• Erlangen programBroader topic: Projective transformations preserve fewer structures than Euclidean motions, yielding a broader geometry.

• History of geometryRelated: Renaissance perspective and later algebraic methods enlarged geometry beyond measurement and congruence.

• Girard DesarguesNarrower topic: Desargues’s work helped establish this broader geometry of projection and perspective.

• Intercept theoremCompared with: Unlike Euclidean proportionality, projective geometry does not preserve ordinary lengths or ratios.

• Pasch's axiomCompared with: Its incidence-focused setting highlights which order properties Pasch's axiom adds.

• Chasles' theoremRelated: Chasles developed influential geometric methods in the nineteenth-century setting from which the theorem emerged.

• CoplanarityNarrower topic: Projective methods preserve whether points and lines lie in a common plane.

• Inversive geometryCompared with: Projective transformations preserve lines as lines, whereas inversion can turn lines into circles.

• Line–line intersectionCompared with: Its added points at infinity recast parallel lines as intersecting.

• Oswald VeblenRelated: Veblen’s axioms and textbook work helped give projective geometry a rigorous foundation.

• Pappus's hexagon theoremNarrower topic: Pappus's theorem is a foundational statement about incidence in this geometry.

• Pavel FlorenskyRelated: Florensky drew on projective geometry when considering perspective and the construction of pictorial space.

• Poncelet–Steiner theoremRelated: Nineteenth-century projective methods shaped the mathematical setting in which the theorem was proved.

• Solid geometryCompared with: It studies incidence and projection while setting aside ordinary distance and angle.