{"id":"https://openalex.org/W2087334641","doi":"https://doi.org/10.1007/s10998-008-8197-5","title":"Circle geometry in affine Cayley-Klein planes","display_name":"Circle geometry in affine Cayley-Klein planes","publication_year":2008,"publication_date":"2008-12-01","ids":{"openalex":"https://openalex.org/W2087334641","doi":"https://doi.org/10.1007/s10998-008-8197-5","mag":"2087334641"},"language":"en","primary_location":{"id":"doi:10.1007/s10998-008-8197-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-008-8197-5","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"},"type":"article","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/A5040806028","display_name":"Horst Martini","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Horst Martini","raw_affiliation_strings":["Faculty of Mathematics, Chemnitz University of Technology, D-09107, Chemnitz, Germany","Chemnitz University of Technology"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Chemnitz University of Technology, D-09107, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"Chemnitz University of Technology","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076284120","display_name":"Margarita Spirova","orcid":null},"institutions":[{"id":"https://openalex.org/I58918642","display_name":"Sofia University \"St. Kliment Ohridski\"","ror":"https://ror.org/02jv3k292","country_code":"BG","type":"education","lineage":["https://openalex.org/I58918642"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Margarita Spirova","raw_affiliation_strings":["Faculty of Mathematics and Informatics, University of Sofia, 5 James Bourchier, 1164, Sofia, Bulgaria","University of Sofia,"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Informatics, University of Sofia, 5 James Bourchier, 1164, Sofia, Bulgaria","institution_ids":["https://openalex.org/I58918642"]},{"raw_affiliation_string":"University of Sofia,","institution_ids":["https://openalex.org/I58918642"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040806028"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.4544,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.64983275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"57","issue":"2","first_page":"197","last_page":"206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9485999941825867,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8749538064002991},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6652355790138245},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6115394234657288},{"id":"https://openalex.org/keywords/affine-plane","display_name":"Affine plane (incidence geometry)","score":0.5475136637687683},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.45703116059303284},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.45692113041877747},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4404579997062683},{"id":"https://openalex.org/keywords/absolute-geometry","display_name":"Absolute geometry","score":0.4376847743988037},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3807263672351837},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33588162064552307},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.1475348174571991}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8749538064002991},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6652355790138245},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6115394234657288},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.5475136637687683},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.45703116059303284},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.45692113041877747},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4404579997062683},{"id":"https://openalex.org/C115094139","wikidata":"https://www.wikidata.org/wiki/Q332430","display_name":"Absolute geometry","level":5,"score":0.4376847743988037},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3807263672351837},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33588162064552307},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.1475348174571991},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/s10998-008-8197-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10998-008-8197-5","pdf_url":null,"source":{"id":"https://openalex.org/S106707257","display_name":"Periodica Mathematica Hungarica","issn_l":"0031-5303","issn":["0031-5303","1588-2829"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Periodica Mathematica Hungarica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W24009375","https://openalex.org/W134819468","https://openalex.org/W152267714","https://openalex.org/W576556701","https://openalex.org/W594120123","https://openalex.org/W608395726","https://openalex.org/W1730540319","https://openalex.org/W1984148040","https://openalex.org/W1987061184","https://openalex.org/W2000823676","https://openalex.org/W2025124865","https://openalex.org/W2026745357","https://openalex.org/W2184663800","https://openalex.org/W2320324859","https://openalex.org/W2323283474","https://openalex.org/W2345278528","https://openalex.org/W2481087612","https://openalex.org/W2656157687","https://openalex.org/W3146907800","https://openalex.org/W4312957690","https://openalex.org/W6637281795","https://openalex.org/W6815092122"],"related_works":["https://openalex.org/W1758527124","https://openalex.org/W2916011546","https://openalex.org/W150754550","https://openalex.org/W2390093603","https://openalex.org/W2073801174","https://openalex.org/W4252879386","https://openalex.org/W4236352996","https://openalex.org/W2026260214","https://openalex.org/W2962983948","https://openalex.org/W976496805"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
