{"id":"circle","domain":"geometry","type":"Concept","title":"Circle","slug":"circle","url":"/mathematics/geometry/circle/","summary":"Set of points equidistant from a centre. C=2*pi*r, A=pi*r^2. Multi-civilisational history of computing pi.","formal_definition":"(x-h)^2+(y-k)^2=r^2","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Coxeter, H.S.M. and Greitzer, S.L. (1967). Geometry Revisited. MAA."},{"tier":1,"citation":"Beckmann, P. (1971). A History of Pi. St. Martin's Press."},{"tier":2,"citation":"Fejes Tóth, L. (1972). Lagerungen in der Ebene, auf der Kugel und im Raum. 2nd ed."},{"tier":3,"citation":"Blatner, D. (1997). The Joy of Pi. Walker Publishing."}],"relationships":[{"type":"ratio_defines","target":"irrational-number","label":"Irrational Number — π"},{"type":"special_case_of","target":"conic-sections","label":"Conic Sections"},{"type":"bounded_by","target":"archimedes","label":"Archimedes"},{"type":"computed_by","target":"madhava","label":"Mādhava"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.9"}