{"id":"https://openalex.org/W2073744707","doi":"https://doi.org/10.1007/s10472-014-9436-4","title":"Formalizing complex plane geometry","display_name":"Formalizing complex plane geometry","publication_year":2014,"publication_date":"2014-11-12","ids":{"openalex":"https://openalex.org/W2073744707","doi":"https://doi.org/10.1007/s10472-014-9436-4","mag":"2073744707"},"language":"en","primary_location":{"id":"doi:10.1007/s10472-014-9436-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10472-014-9436-4","pdf_url":null,"source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"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":"Annals of Mathematics and Artificial Intelligence","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/A5103231254","display_name":"Filip Mari\u0107","orcid":"https://orcid.org/0000-0001-7219-6960"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Filip Mari\u0107","raw_affiliation_strings":["Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 1100, Belgrade, Serbia","Faculty of Mathematics, University of Belgrade, Belgrade, Serbia 1100#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 1100, Belgrade, Serbia","institution_ids":["https://openalex.org/I4068193"]},{"raw_affiliation_string":"Faculty of Mathematics, University of Belgrade, Belgrade, Serbia 1100#TAB#","institution_ids":["https://openalex.org/I4068193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054747317","display_name":"Danijela Petrovi\u0107","orcid":"https://orcid.org/0000-0002-6838-1191"},"institutions":[{"id":"https://openalex.org/I4068193","display_name":"University of Belgrade","ror":"https://ror.org/02qsmb048","country_code":"RS","type":"education","lineage":["https://openalex.org/I4068193"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Danijela Petrovi\u0107","raw_affiliation_strings":["Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 1100, Belgrade, Serbia","Faculty of Mathematics, University of Belgrade, Belgrade, Serbia 1100#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 1100, Belgrade, Serbia","institution_ids":["https://openalex.org/I4068193"]},{"raw_affiliation_string":"Faculty of Mathematics, University of Belgrade, Belgrade, Serbia 1100#TAB#","institution_ids":["https://openalex.org/I4068193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.4229,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7543595,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"74","issue":"3-4","first_page":"271","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9940999746322632,"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.9811000227928162,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.7402815818786621},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.6328436136245728},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.585842490196228},{"id":"https://openalex.org/keywords/analytic-geometry","display_name":"Analytic geometry","score":0.563127875328064},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5331487059593201},{"id":"https://openalex.org/keywords/foundations-of-geometry","display_name":"Foundations of geometry","score":0.5325889587402344},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5269749164581299},{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.5247994661331177},{"id":"https://openalex.org/keywords/complex-geometry","display_name":"Complex geometry","score":0.5133106112480164},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.510971188545227},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"Non-Euclidean geometry","score":0.5047043561935425},{"id":"https://openalex.org/keywords/synthetic-geometry","display_name":"Synthetic geometry","score":0.49787378311157227},{"id":"https://openalex.org/keywords/hyperbolic-geometry","display_name":"Hyperbolic geometry","score":0.47100913524627686},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4291483163833618},{"id":"https://openalex.org/keywords/absolute-geometry","display_name":"Absolute geometry","score":0.411128431558609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3710238039493561},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36928242444992065},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.3111880421638489},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2972860336303711},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2565406560897827},{"id":"https://openalex.org/keywords/projective-geometry","display_name":"Projective geometry","score":0.22207754850387573},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1288224160671234}],"concepts":[{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.7402815818786621},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.6328436136245728},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.585842490196228},{"id":"https://openalex.org/C46175816","wikidata":"https://www.wikidata.org/wiki/Q134787","display_name":"Analytic geometry","level":2,"score":0.563127875328064},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5331487059593201},{"id":"https://openalex.org/C180110497","wikidata":"https://www.wikidata.org/wiki/Q5474574","display_name":"Foundations of geometry","level":4,"score":0.5325889587402344},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5269749164581299},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.5247994661331177},{"id":"https://openalex.org/C158843486","wikidata":"https://www.wikidata.org/wiki/Q2137810","display_name":"Complex geometry","level":2,"score":0.5133106112480164},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.510971188545227},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.5047043561935425},{"id":"https://openalex.org/C133347240","wikidata":"https://www.wikidata.org/wiki/Q249148","display_name":"Synthetic geometry","level":4,"score":0.49787378311157227},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.47100913524627686},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4291483163833618},{"id":"https://openalex.org/C115094139","wikidata":"https://www.wikidata.org/wiki/Q332430","display_name":"Absolute geometry","level":5,"score":0.411128431558609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3710238039493561},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36928242444992065},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3111880421638489},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2972860336303711},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2565406560897827},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.22207754850387573},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1288224160671234},{"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/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10472-014-9436-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10472-014-9436-4","pdf_url":null,"source":{"id":"https://openalex.org/S90199469","display_name":"Annals of Mathematics and Artificial Intelligence","issn_l":"1012-2443","issn":["1012-2443","1573-7470"],"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":"Annals of Mathematics and Artificial Intelligence","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W14022547","https://openalex.org/W25515096","https://openalex.org/W86824626","https://openalex.org/W101424827","https://openalex.org/W120661248","https://openalex.org/W1522735064","https://openalex.org/W1528908721","https://openalex.org/W1545409775","https://openalex.org/W1562231403","https://openalex.org/W1572941424","https://openalex.org/W1575011135","https://openalex.org/W1595469144","https://openalex.org/W1606604604","https://openalex.org/W1609259612","https://openalex.org/W1774729455","https://openalex.org/W1789645782","https://openalex.org/W1988136938","https://openalex.org/W2006267566","https://openalex.org/W2007080570","https://openalex.org/W2023933031","https://openalex.org/W2025076058","https://openalex.org/W2067558609","https://openalex.org/W2069766942","https://openalex.org/W2081622012","https://openalex.org/W2091456056","https://openalex.org/W2106192381","https://openalex.org/W2118034154","https://openalex.org/W2139659782","https://openalex.org/W2144907233","https://openalex.org/W2146104088","https://openalex.org/W2185082551","https://openalex.org/W2396167768","https://openalex.org/W2504155696","https://openalex.org/W4250846042","https://openalex.org/W4285719527","https://openalex.org/W4388318445"],"related_works":["https://openalex.org/W1758527124","https://openalex.org/W4252879386","https://openalex.org/W150754550","https://openalex.org/W4236352996","https://openalex.org/W2741154429","https://openalex.org/W1966349650","https://openalex.org/W1907204227","https://openalex.org/W4300904285","https://openalex.org/W1619767803","https://openalex.org/W2973883076"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}