{"id":"https://openalex.org/W2096242358","doi":"https://doi.org/10.20382/jocg.v6i1a12","title":"The Lebesgue universal covering problem","display_name":"The Lebesgue universal covering problem","publication_year":2015,"publication_date":"2015-03-02","ids":{"openalex":"https://openalex.org/W2096242358","doi":"https://doi.org/10.20382/jocg.v6i1a12","mag":"2096242358"},"language":"en","primary_location":{"id":"pmh:oai:journals.carleton.ca/jocg:article/198","is_oa":false,"landing_page_url":"http://jocg.org/index.php/jocg/article/view/198","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol 6, No 1 (2015); 288\u00e2\u0080\u0093299","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://jocg.org/index.php/jocg/article/view/2995","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056752880","display_name":"John C. Baez","orcid":"https://orcid.org/0000-0002-0609-9836"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Baez, John C.","raw_affiliation_strings":["University of California, Riverside"],"affiliations":[{"raw_affiliation_string":"University of California, Riverside","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069466663","display_name":"Karine Bagdasaryan","orcid":null},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bagdasaryan, Karine","raw_affiliation_strings":["University of California, Riverside"],"affiliations":[{"raw_affiliation_string":"University of California, Riverside","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036846951","display_name":"Philip Gibbs","orcid":"https://orcid.org/0000-0002-1806-5537"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gibbs, Philip","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056752880"],"corresponding_institution_ids":["https://openalex.org/I103635307"],"apc_list":null,"apc_paid":null,"fwci":0.5249,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.65856271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9768000245094299,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9768000245094299,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9649999737739563,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9641000032424927,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/mathematics","display_name":"Mathematics","score":0.7247300744056702},{"id":"https://openalex.org/keywords/covering-space","display_name":"Covering space","score":0.6304047703742981},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.616981565952301},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6070598363876343},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5402834415435791},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.466076135635376},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3101864755153656},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2613614797592163}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7247300744056702},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.6304047703742981},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.616981565952301},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6070598363876343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5402834415435791},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.466076135635376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3101864755153656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2613614797592163}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:journals.carleton.ca/jocg:article/198","is_oa":false,"landing_page_url":"http://jocg.org/index.php/jocg/article/view/198","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol 6, No 1 (2015); 288\u00e2\u0080\u0093299","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ojs.library.carleton.ca:article/2995","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/2995","pdf_url":"https://jocg.org/index.php/jocg/article/view/2995","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 6 No. 1 (2015); 288\u2013299","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:c1396b92b50545f888708a2c6b22ddd1","is_oa":true,"landing_page_url":"https://doaj.org/article/c1396b92b50545f888708a2c6b22ddd1","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry, Vol 6, Iss 1 (2015)","raw_type":"article"},{"id":"doi:10.20382/jocg.v6i1a12","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v6i1a12","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/2995","is_oa":true,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/2995","pdf_url":"https://jocg.org/index.php/jocg/article/view/2995","source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry; Vol. 6 No. 1 (2015); 288\u2013299","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2096242358.pdf","grobid_xml":"https://content.openalex.org/works/W2096242358.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2018931513","https://openalex.org/W2058401132","https://openalex.org/W2172249426","https://openalex.org/W2581149919"],"related_works":["https://openalex.org/W2952580304","https://openalex.org/W1998296522","https://openalex.org/W1608618456","https://openalex.org/W2530839785","https://openalex.org/W2938910622","https://openalex.org/W2120029348","https://openalex.org/W2078764535","https://openalex.org/W2963618850","https://openalex.org/W310533995"],"abstract_inverted_index":{"In":[0,92],"1914":[1],"Lebesgue":[2],"defined":[3],"a":[4,9,30,51,103],"'universal":[5],"covering'":[6],"to":[7,70],"be":[8],"convex":[10],"subset":[11,22],"of":[12,20,23,28,74,87,98,117],"the":[13,34,93,96,115,118],"plane":[14],"that":[15,81],"contains":[16],"an":[17,72,85],"isometric":[18],"copy":[19],"any":[21],"diameter":[24],"1.":[25],"His":[26],"challenge":[27],"finding":[29],"universal":[31,53,106,121],"covering":[32,54,107,122],"with":[33,95,108],"least":[35],"possible":[36],"area":[37,73,86,109,116],"has":[38],"been":[39],"addressed":[40],"by":[41,55,123],"various":[42],"mathematicians:":[43],"P\u00e1l,":[44],"Sprague":[45],"and":[46],"Hansen":[47],"have":[48],"each":[49],"created":[50],"smaller":[52,105],"removing":[56],"regions":[57],"from":[58],"those":[59],"known":[60],"before.":[61],"However,":[62],"Hansen's":[63],"last":[64],"reduction":[65],"was":[66],"microsopic:":[67],"he":[68,82],"claimed":[69],"remove":[71],"$6":[75],"\\cdot":[76,90,125],"10^{-18}$,":[77],"but":[78],"we":[79,101],"show":[80],"actually":[83],"removed":[84],"just":[88],"$8":[89],"10^{-21}$.":[91],"following,":[94],"help":[97],"Greg":[99],"Egan,":[100],"find":[102],"new,":[104],"less":[110],"than":[111],"$0.8441153$.":[112],"This":[113],"reduces":[114],"previous":[119],"best":[120],"$2.2":[124],"10^{-5}$.":[126]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}