{"id":"conic-sections","domain":"geometry","type":"Concept","title":"Conic Sections","slug":"conic-sections","url":"/mathematics/geometry/conic-sections/","summary":"Circle, ellipse, parabola, hyperbola — curves from slicing a cone. Studied by Apollonius c.200BCE; later shown by Kepler/Newton to govern planetary orbits.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Heath, T.L. (1961 reprint). Apollonius of Perga: Treatise on Conic Sections. Cambridge University Press."},{"tier":1,"citation":"Newton, I. (1687). Philosophiae Naturalis Principia Mathematica."},{"tier":2,"citation":"Coxeter, H.S.M. (2003). Projective Geometry. 2nd ed. Springer."},{"tier":3,"citation":"Stillwell, J. (2010). Mathematics and Its History. 3rd ed."}],"relationships":[{"type":"special_case","target":"circle","label":"Circle — eccentricity zero"},{"type":"built_on","target":"euclidean-geometry","label":"Euclidean Geometry"},{"type":"related_to","target":"polynomial","label":"Polynomial — second-degree equations"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.9"}