Linked from

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

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

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

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

• 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.

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

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

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

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

• Elliptic geometryCompared with: Its parallel postulate is replaced by elliptic geometry's claim that no parallels exist.

• Complete quadrilateralCompared with: Metric properties are not intrinsic to the quadrilateral’s projective incidence structure.

• Nikolai LobachevskyCompared with: Its parallel postulate was the assumption Lobachevsky challenged.

• Projective dualityCompared with: Those metric properties are not what projective duality preserves.

• Hyperbolic planeCompared with: Its unique-parallel rule is the alternative that hyperbolic geometry rejects.

• Spherical law of cosinesCompared with: Its triangle identities omit the curvature corrections present in the spherical formula.

• Spherical excessCompared with: Its triangle angle sum of 180 degrees supplies the baseline for the excess.

• Egyptian mathematicsCompared with: It highlights the difference between Egyptian practical procedures and later axiomatic presentation.

• Euclid's theoremCompared with: It is the better-known subject of the same work, distinct from its number theory.

• Daina TaimiņaCompared with: Its familiar parallel-line rule contrasts with the geometry Taimiņa’s models illustrate.

• Hjelmslev's theoremCompared with: Euclidean triangles with the same angles can be differently sized and noncongruent.