{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","description":"This cluster of papers covers a wide range of topics in geometric mathematics, including hyperbolic geometry, loops, billiards in ellipses, Poncelet's theorem, Moufang loops, trigonometry, algebraic structures, and their applications in relativity and inversive geometry.","keywords":[{"id":"https://openalex.org/keywords/plane-geometry","display_name":"plane geometry","score":0.4847},{"id":"https://openalex.org/keywords/geometry","display_name":"geometry","score":0.2055},{"id":"https://openalex.org/keywords/conic-sections","display_name":"conic sections","score":0.5205},{"id":"https://openalex.org/keywords/projective-geometry","display_name":"projective geometry","score":0.4509},{"id":"https://openalex.org/keywords/triangle-geometry","display_name":"triangle geometry","score":0.8354},{"id":"https://openalex.org/keywords/analytic-geometry","display_name":"analytic geometry","score":0.3856},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4357},{"id":"https://openalex.org/keywords/solid-geometry","display_name":"solid geometry","score":0.2584},{"id":"https://openalex.org/keywords/geometric-construction","display_name":"geometric construction","score":0.3773},{"id":"https://openalex.org/keywords/trigonometry","display_name":"trigonometry","score":0.2969},{"id":"https://openalex.org/keywords/circle-geometry","display_name":"circle geometry","score":0.5035},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"non-Euclidean geometry","score":0.3631},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":0.2612},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"trigonometric functions","score":0.2529},{"id":"https://openalex.org/keywords/triangles","display_name":"triangles","score":0.296},{"id":"https://openalex.org/keywords/trigonometric-identities","display_name":"trigonometric identities","score":0.5008},{"id":"https://openalex.org/keywords/triangle-centers","display_name":"triangle centers","score":0.9043},{"id":"https://openalex.org/keywords/circle","display_name":"circle","score":0.2766},{"id":"https://openalex.org/keywords/plane-curves","display_name":"plane curves","score":0.2404},{"id":"https://openalex.org/keywords/geometric-problems","display_name":"geometry problems","score":0.4469},{"id":"https://openalex.org/keywords/geometric-proof","display_name":"geometric proof","score":0.3918},{"id":"https://openalex.org/keywords/quadric-surfaces","display_name":"quadric surfaces","score":0.3915},{"id":"https://openalex.org/keywords/spherical-trigonometry","display_name":"spherical trigonometry","score":0.4533},{"id":"https://openalex.org/keywords/right-triangles","display_name":"right triangles","score":0.5017},{"id":"https://openalex.org/keywords/ellipse","display_name":"ellipse","score":0.3517}],"legacy_keywords":"Geometry; Hyperbolic; Loops; Billiards; Poncelet; Moufang; Trigonometry; Algebraic; Relativity; Inversive","ids":{"openalex":"https://openalex.org/T12504","wikipedia":"https://en.wikipedia.org/wiki/Geometry"},"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"},"siblings":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory"},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models"},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology"},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory"},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications"},{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis"},{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory"},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds"},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems"},{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry"}],"works_count":140221,"cited_by_count":259665,"works_api_url":"https://api.openalex.org/works?filter=topics.id:T12504","updated_date":"2026-10-20T03:01:21","created_date":"2024-01-23T15:27:14"}