{"id":"https://openalex.org/W1449190760","doi":"https://doi.org/10.1007/978-3-642-25070-5_7","title":"Some Lemmas to Hopefully Enable Search Methods to Find Short and Human Readable Proofs for Incidence Theorems of Projective Geometry","display_name":"Some Lemmas to Hopefully Enable Search Methods to Find Short and Human Readable Proofs for Incidence Theorems of Projective Geometry","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1449190760","doi":"https://doi.org/10.1007/978-3-642-25070-5_7","mag":"1449190760"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-25070-5_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-25070-5_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5004426485","display_name":"Dominique Michelucci","orcid":"https://orcid.org/0000-0002-1256-9080"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210136953","display_name":"Laboratoire d\u2019\u00c9lectronique, Informatique et Image","ror":"https://ror.org/04gnd7c94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I190752583","https://openalex.org/I190861549","https://openalex.org/I4210118524","https://openalex.org/I4210134562","https://openalex.org/I4210136953","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Dominique Michelucci","raw_affiliation_strings":["LE2I, UMR CNRS 5158, 9 av Alain Savary, BP 47870, 21078, Dijon cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LE2I, UMR CNRS 5158, 9 av Alain Savary, BP 47870, 21078, Dijon cedex, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210136953"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004426485"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210136953"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0320781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"118","last_page":"131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9857000112533569,"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/T10533","display_name":"Teaching and Learning Programming","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/1706","display_name":"Computer Science Applications"},"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/mathematical-proof","display_name":"Mathematical proof","score":0.891143798828125},{"id":"https://openalex.org/keywords/projective-geometry","display_name":"Projective geometry","score":0.7957555055618286},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.7054165601730347},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.6478904485702515},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.6003457903862},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.5598569512367249},{"id":"https://openalex.org/keywords/ordered-geometry","display_name":"Ordered geometry","score":0.513305127620697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47655633091926575},{"id":"https://openalex.org/keywords/projective-differential-geometry","display_name":"Projective differential geometry","score":0.45146799087524414},{"id":"https://openalex.org/keywords/projective-space","display_name":"Projective space","score":0.416044145822525},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4141632914543152},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40315189957618713},{"id":"https://openalex.org/keywords/collineation","display_name":"Collineation","score":0.3821178078651428},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31374043226242065},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.3084125518798828},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2842060923576355},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.052434682846069336}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.891143798828125},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.7957555055618286},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.7054165601730347},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.6478904485702515},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.6003457903862},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.5598569512367249},{"id":"https://openalex.org/C105653879","wikidata":"https://www.wikidata.org/wiki/Q7100712","display_name":"Ordered geometry","level":5,"score":0.513305127620697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47655633091926575},{"id":"https://openalex.org/C176021007","wikidata":"https://www.wikidata.org/wiki/Q7249466","display_name":"Projective differential geometry","level":5,"score":0.45146799087524414},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.416044145822525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4141632914543152},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40315189957618713},{"id":"https://openalex.org/C163434512","wikidata":"https://www.wikidata.org/wiki/Q390741","display_name":"Collineation","level":4,"score":0.3821178078651428},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31374043226242065},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3084125518798828},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2842060923576355},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.052434682846069336},{"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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-25070-5_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-25070-5_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W109897293","https://openalex.org/W161392887","https://openalex.org/W950940858","https://openalex.org/W1577444404","https://openalex.org/W1604826792","https://openalex.org/W1996050741","https://openalex.org/W2022751246","https://openalex.org/W2084471906","https://openalex.org/W2106099245","https://openalex.org/W2110205709","https://openalex.org/W2120243289","https://openalex.org/W2502358513","https://openalex.org/W2621442514","https://openalex.org/W2762770850","https://openalex.org/W2895354161","https://openalex.org/W3146474094","https://openalex.org/W3158633990","https://openalex.org/W4299626558"],"related_works":["https://openalex.org/W2048786085","https://openalex.org/W2015576813","https://openalex.org/W2087796241","https://openalex.org/W2012112611","https://openalex.org/W2373502407","https://openalex.org/W1994973484","https://openalex.org/W2004296393","https://openalex.org/W4252107605","https://openalex.org/W2805722871","https://openalex.org/W1964535876"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}