{"id":"https://openalex.org/W2758751785","doi":"https://doi.org/10.1515/forma-2017-0011","title":"Pascal\u2019s Theorem in Real Projective Plane","display_name":"Pascal\u2019s Theorem in Real Projective Plane","publication_year":2017,"publication_date":"2017-07-01","ids":{"openalex":"https://openalex.org/W2758751785","doi":"https://doi.org/10.1515/forma-2017-0011","mag":"2758751785"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2017-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2017-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/25/2/article-p107.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://content.sciendo.com/downloadpdf/journals/forma/25/2/article-p107.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068514239","display_name":"Roland Coghetto","orcid":"https://orcid.org/0000-0002-4901-0766"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roland Coghetto","raw_affiliation_strings":["Rue de la Brasserie 5, 7100 La Louvi\u00e8re , Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rue de la Brasserie 5, 7100 La Louvi\u00e8re , Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5068514239"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8172,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71095553,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"2","first_page":"107","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9958000183105469,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9843000173568726,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/projective-geometry","display_name":"Projective geometry","score":0.7582858800888062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7136390209197998},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6356486082077026},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.5988376140594482},{"id":"https://openalex.org/keywords/pascal","display_name":"Pascal (unit)","score":0.5746498107910156},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.5390687584877014},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4690811038017273},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.4658305048942566},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4345529079437256},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3978465795516968},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3826543092727661},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.15775930881500244},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.15515932440757751},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1216384768486023},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12033802270889282},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.05537307262420654}],"concepts":[{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.7582858800888062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7136390209197998},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6356486082077026},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.5988376140594482},{"id":"https://openalex.org/C75608658","wikidata":"https://www.wikidata.org/wiki/Q44395","display_name":"Pascal (unit)","level":2,"score":0.5746498107910156},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.5390687584877014},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4690811038017273},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.4658305048942566},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4345529079437256},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3978465795516968},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3826543092727661},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.15775930881500244},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.15515932440757751},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1216384768486023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12033802270889282},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.05537307262420654},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/forma-2017-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2017-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/25/2/article-p107.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7ec5c66065d841bf819c5f3a216a20a7","is_oa":false,"landing_page_url":"https://doaj.org/article/7ec5c66065d841bf819c5f3a216a20a7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 25, Iss 2, Pp 107-119 (2017)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/6279","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/6279","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1515/forma-2017-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2017-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/25/2/article-p107.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2758751785.pdf","grobid_xml":"https://content.openalex.org/works/W2758751785.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1601534715","https://openalex.org/W2128085487","https://openalex.org/W2260503838","https://openalex.org/W2403661435","https://openalex.org/W2555605597","https://openalex.org/W2616597022","https://openalex.org/W2810471036"],"related_works":["https://openalex.org/W1984083606","https://openalex.org/W2035170077","https://openalex.org/W1973242087","https://openalex.org/W1968836382","https://openalex.org/W1500174755","https://openalex.org/W2963474355","https://openalex.org/W3022380753","https://openalex.org/W4241309109","https://openalex.org/W1643948452","https://openalex.org/W2336406799"],"abstract_inverted_index":{"Summary":[0],"In":[1],"this":[2],"article":[3],"we":[4,50,97,113],"check,":[5],"with":[6],"the":[7,14,27,52,56,64,87],"Mizar":[8],"system":[9],"[2],":[10],"Pascal\u2019s":[11,21,48,90],"theorem":[12,22,34,91],"in":[13,55,63,120],"real":[15],"projective":[16,19],"plane":[17],"(in":[18],"geometry":[20],"is":[23,35],"also":[24,75],"known":[25],"as":[26],"Hexagrammum":[28],"Mysticum":[29],"Theorem)":[30],"1":[31],".":[32,93],"Pappus\u2019":[33,61],"a":[36,40,95],"special":[37],"case":[38],"of":[39,43,60,89],"degenerate":[41],"conic":[42],"two":[44],"lines.":[45],"For":[46,94],"proving":[47],"theorem,":[49],"use":[51,98,115],"techniques":[53],"developed":[54],"section":[57],"\u201cProjective":[58],"Proofs":[59],"Theorem\u201d":[62],"chapter":[65],"\u201cPappus\u2019":[66],"Theorem:":[67],"Nine":[68],"proofs":[69],"and":[70,101],"three":[71],"variations\u201d":[72],"[11].":[73],"We":[74,110],"follow":[76],"some":[77],"ideas":[78],"from":[79],"Harrison\u2019s":[80],"work.":[81],"With":[82],"HOL":[83],"Light,":[84],"he":[85],"has":[86],"proof":[88],"2":[92],"lemma,":[96],"PROVER9":[99],"3":[100],"OTT2MIZ":[102],"by":[103],"Josef":[104],"Urban":[105],"4":[106],"[12,":[107],"6,":[108],"7].":[109],"note,":[111],"that":[112],"don\u2019t":[114],"Skolem/Herbrand":[116],"functions":[117],"(see":[118],"\u201cSkolemization\u201d":[119],"[1]).":[121]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2017-10-06T00:00:00"}