{"id":"https://openalex.org/W4230858366","doi":"https://doi.org/10.1007/978-3-030-42101-4_4","title":"Hyperbolic Plane","display_name":"Hyperbolic Plane","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W4230858366","doi":"https://doi.org/10.1007/978-3-030-42101-4_4"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-42101-4_4","doi":"https://doi.org/10.1007/978-3-030-42101-4_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-42101-4_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210218630","display_name":"Undergraduate texts in mathematics","issn_l":"0172-6056","issn":["0172-6056","2197-5604"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Undergraduate Texts in Mathematics","raw_type":"book-chapter"},"parent_works":[{"id":"https://openalex.org/W3022048614","display_name":"Geometry: from Isometries to Special Relativity","relationship":"volume"}],"lineage":["https://openalex.org/W4230858366","https://openalex.org/W3022048614"],"child_works_count":0,"type":"book-chapter","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101847738","display_name":"Nam\u2010Hoon Lee","orcid":"https://orcid.org/0000-0002-3781-5225","observed_orcids":["https://orcid.org/0000-0002-3781-5225"]},"institutions":[{"id":"https://openalex.org/I94588446","display_name":"Hongik University","ror":"https://ror.org/00egdv862","country_code":"KR","type":"education","lineage":["https://openalex.org/I94588446"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Nam-Hoon Lee","raw_affiliation_strings":["Department of Mathematics Education, Hongik University, Seoul, Korea (Republic of)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Hongik University, Seoul, Korea (Republic of)","institution_ids":["https://openalex.org/I94588446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101847738"],"corresponding_institution_ids":["https://openalex.org/I94588446"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"87","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9765999913215637,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9765999913215637,"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"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.009800000116229057,"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"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.006399999838322401,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperbolic-plane","display_name":"hyperbolic plane","score":0.925000011920929},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"hyperbolic geometry","score":1.0},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.9279999732971191},{"id":"https://openalex.org/keywords/hyperbolic-triangles","display_name":"hyperbolic triangles","score":0.722000002861023},{"id":"https://openalex.org/keywords/angle-sum","display_name":"angle sum","score":0.8489999771118164},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"non-Euclidean geometry","score":0.8489999771118164}],"concepts":[{"id":"https://openalex.org/C82673646","wikidata":"https://www.wikidata.org/wiki/Q2246553","display_name":"Hyperbolic triangle","level":4,"score":0.9139901399612427},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.8581955432891846},{"id":"https://openalex.org/C180110497","wikidata":"https://www.wikidata.org/wiki/Q5474574","display_name":"Foundations of geometry","level":4,"score":0.8396874666213989},{"id":"https://openalex.org/C115094139","wikidata":"https://www.wikidata.org/wiki/Q332430","display_name":"Absolute geometry","level":5,"score":0.836651086807251},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.8030915260314941},{"id":"https://openalex.org/C105653879","wikidata":"https://www.wikidata.org/wiki/Q7100712","display_name":"Ordered geometry","level":5,"score":0.7012034058570862},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.677725076675415},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6454789638519287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5874083638191223},{"id":"https://openalex.org/C39308205","wikidata":"https://www.wikidata.org/wiki/Q7880612","display_name":"Ultraparallel theorem","level":5,"score":0.5718784332275391},{"id":"https://openalex.org/C139966315","wikidata":"https://www.wikidata.org/wiki/Q1003216","display_name":"Hyperbolic angle","level":5,"score":0.570915699005127},{"id":"https://openalex.org/C133347240","wikidata":"https://www.wikidata.org/wiki/Q249148","display_name":"Synthetic geometry","level":4,"score":0.5360397100448608},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.49032333493232727},{"id":"https://openalex.org/C55862258","wikidata":"https://www.wikidata.org/wiki/Q1017238","display_name":"Hyperbolic coordinates","level":5,"score":0.46306246519088745},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.45533081889152527},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.35275596380233765},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.2591210901737213},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.19870495796203613},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.1644485592842102},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.16159498691558838},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.08946189284324646},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.0},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-42101-4_4","doi":"https://doi.org/10.1007/978-3-030-42101-4_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-42101-4_4","pdf_url":null,"source":{"id":"https://openalex.org/S4210218630","display_name":"Undergraduate texts in mathematics","issn_l":"0172-6056","issn":["0172-6056","2197-5604"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Undergraduate Texts in Mathematics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W3022048614"],"related_works":["https://openalex.org/W96513793","https://openalex.org/W1758527124","https://openalex.org/W2804438739","https://openalex.org/W2886080441","https://openalex.org/W171253776","https://openalex.org/W2921910578","https://openalex.org/W7057502567","https://openalex.org/W4252879386","https://openalex.org/W7000650667","https://openalex.org/W2791928621"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2022-05-11T00:00:00"}