{"id":"euclidean-geometry","domain":"geometry","type":"Concept","title":"Euclidean Geometry","slug":"euclidean-geometry","url":"/mathematics/geometry/euclidean-geometry/","summary":"The geometry of flat space, built from Euclid's 5 postulates. Believed unique for 2000+ years until 19th-century non-Euclidean discoveries.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Hartshorne, R. (2000). Geometry: Euclid and Beyond. Springer."},{"tier":1,"citation":"Greenberg, M.J. (2008). Euclidean and Non-Euclidean Geometries. 4th ed. W.H. Freeman."},{"tier":2,"citation":"Bonola, R. (1955 reprint). Non-Euclidean Geometry. Dover."},{"tier":3,"citation":"Trudeau, R.J. (1987). The Non-Euclidean Revolution. Birkhäuser."}],"relationships":[{"type":"built_from","target":"euclids-elements","label":"Euclid's Elements"},{"type":"proves","target":"pythagorean-theorem","label":"Pythagorean Theorem"},{"type":"contrasted_by","target":"topological-space","label":"Topological Space"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.7"}