Linked from

The 137 pages that link to Euclidean geometry, each with the reason it gives.

• Linear perspectiveNarrower topic: Perspective constructions use geometric relations among the viewer, scene, and image plane.

• Projective geometryCompared with: Projective geometry retains incidence but not Euclidean lengths or angles.

• TriangleNarrower topic: The familiar 180-degree angle sum follows from the parallel postulate of this geometry.

• Differential geometryCompared with: It is the flat model that differential geometry generalizes to curved spaces.

• Euclidean spaceRelated: It develops the geometric consequences of the space's metric and affine structure.

• Gödel's incompleteness theoremsRelated: A complete first-order theory, proving incompleteness is not universal to all axiom systems.

• Euclid's ElementsNarrower topic: The treatise's geometric books became the classical foundation of this subject.

• Non-Euclidean geometryCompared with: Its parallel postulate is the one non-Euclidean systems replace.

• EuclidBroader topic: Euclid’s name became attached to the geometric system organized in the Elements.

• Mathematical proofRelated: Its propositions illustrate systematic derivation from explicit geometric assumptions.

• Thomas HobbesRelated: Hobbes admired demonstrative reasoning and sought comparable certainty in political argument.

• Deductive reasoningBroader topic: Its axiomatic proofs are a foundational example of systematic deduction.

• Coordinate geometryNarrower topic: Coordinate geometry is one method for studying the familiar geometry of Euclidean space.

• Hyperbolic geometryCompared with: Its parallel postulate is the assumption hyperbolic geometry replaces.

• Incidence geometryCompared with: Unlike Euclidean geometry, incidence geometry can ignore distances and angles entirely.

• Riemannian geometryCompared with: It is the zero-curvature model that Riemannian geometry extends locally.

• Spherical geometryCompared with: Its triangle angles sum to 180 degrees, unlike spherical triangles.

• Quadratic equationRelated: Geometric constructions and length constraints have historically generated quadratic equations.

• Law of cosinesNarrower topic: The familiar law assumes the flat geometry that spherical versions modify.

• Analytic geometryRelated: Its familiar figures become equations when placed in coordinates.

• Light coneCompared with: Its distance-based geometry lacks the light-speed causal boundary that structures spacetime.

• TrigonometryNarrower topic: Classical triangle trigonometry is formulated within Euclidean geometry.

• Ancient GreeceRelated: Greek mathematical reasoning became a durable foundation for geometry.

• CircumcenterNarrower topic: The usual circumcenter construction relies on Euclidean distance and perpendicularity.

• GeometryBroader topic: It is the classical framework for familiar flat-plane geometry.

• Synthetic geometryNarrower topic: Synthetic geometry is most often practiced within Euclidean geometry’s axiomatic framework.

• Ancient Greek mathematicsBroader topic: Its axioms and deductive propositions became the clearest model of Greek mathematical reasoning.

• Omar KhayyamRelated: Khayyam expressed algebraic solutions through constructions in the geometric tradition of Euclid.

• FractalCompared with: Fractals challenge its usual reliance on smooth shapes and integer dimensions.

• Inscribed angle theoremNarrower topic: The theorem is proved within the standard geometry of the plane.

• Perpendicular bisectorNarrower topic: The familiar midpoint, angle, and distance properties assume this geometric setting.

• Plane (geometry)Narrower topic: The plane is the central setting for ordinary Euclidean geometry.

• Affine geometryCompared with: Affine geometry retains parallelism but does not preserve Euclidean lengths or angles.

• Line segmentNarrower topic: Line segments are basic objects in the geometry of ordinary flat space.

• Parallel linesNarrower topic: Its parallel postulate makes the familiar constant-distance definition possible.

• Parallel postulateNarrower topic: The postulate distinguishes Euclidean geometry from geometries with different parallel behavior.

• Greek mathematicsBroader topic: Its axiomatic presentation became the clearest model of Greek deductive mathematics.

• Interior angleNarrower topic: Interior-angle theorems are standard results in Euclidean geometry.

• Triangle geometryNarrower topic: Most classical triangle centers and circle theorems assume this geometry.

• Vector graphicsNarrower topic: Vector illustrations use familiar geometric primitives and relationships.

• MidpointNarrower topic: The ordinary midpoint relies on Euclidean notions of segments and length.

• Perpendicular linesNarrower topic: The familiar four-right-angle definition applies within Euclidean geometry.

• RectangleNarrower topic: The usual rectangle properties hold in the Euclidean plane.

• Triangle areaNarrower topic: The familiar triangle-area formulas assume ordinary flat Euclidean geometry.

• Angle bisectorNarrower topic: Angle bisectors are defined and studied within this geometric system.

• Apollonius of PergaRelated: Apollonius expressed conic properties through geometric constructions and proofs.

• Spherical trigonometryCompared with: Spherical geometry violates the parallel postulate, changing triangle properties.

• Axiomatic methodBroader topic: It is the canonical theory whose axiom choices prompted comparison with alternative geometries.

• Geometric constructionNarrower topic: Classical constructions developed within the geometric tradition formalized by Euclid.

• Angle trisectionNarrower topic: The classical trisection problem is posed within Euclidean geometric construction.