{"id":"https://openalex.org/W2472636575","doi":"https://doi.org/10.1080/10586458.2016.1270858","title":"Differential Equations and Exact Solutions in the Moving Sofa Problem","display_name":"Differential Equations and Exact Solutions in the Moving Sofa Problem","publication_year":2017,"publication_date":"2017-01-19","ids":{"openalex":"https://openalex.org/W2472636575","doi":"https://doi.org/10.1080/10586458.2016.1270858","mag":"2472636575"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2016.1270858","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1270858","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Differential_Equations_and_Exact_Solutions_in_the_Moving_Sofa_Problem/4567987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057565945","display_name":"Dan Romik","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dan Romik","raw_affiliation_strings":["Department of Mathematics, University of California Davis, Davis, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California Davis, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057565945"],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":null,"apc_paid":null,"fwci":0.1848,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.54273829,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"27","issue":"3","first_page":"316","last_page":"330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987999796867371,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.830471396446228},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6183288097381592},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5102114677429199},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4797757565975189},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4586181640625},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4269440174102783},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.421131432056427},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.41768988966941833},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38017719984054565},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1715776026248932},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08220607042312622},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07854723930358887}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.830471396446228},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6183288097381592},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5102114677429199},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4797757565975189},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4586181640625},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4269440174102783},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.421131432056427},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.41768988966941833},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38017719984054565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1715776026248932},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08220607042312622},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07854723930358887},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/10586458.2016.1270858","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1270858","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt6sf4g2nd","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/6sf4g2nd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/4567987","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Differential_Equations_and_Exact_Solutions_in_the_Moving_Sofa_Problem/4567987","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:qt6sf4g2nd","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/6sf4g2nd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Romik, Dan. (2016). Differential equations and exact solutions in the moving sofa problem. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/6sf4g2nd","raw_type":"article"},{"id":"doi:10.6084/m9.figshare.4567987.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.4567987.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/4567987","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Differential_Equations_and_Exact_Solutions_in_the_Moving_Sofa_Problem/4567987","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[{"score":0.7599999904632568,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W629196792","https://openalex.org/W1572708899","https://openalex.org/W1996256003","https://openalex.org/W2024307683","https://openalex.org/W2073809747","https://openalex.org/W2329421836","https://openalex.org/W2472636575","https://openalex.org/W4241654653","https://openalex.org/W4295634057"],"related_works":["https://openalex.org/W4206327962","https://openalex.org/W2010009304","https://openalex.org/W2385263368","https://openalex.org/W1996851061","https://openalex.org/W3021694725","https://openalex.org/W2347422947","https://openalex.org/W2061292372","https://openalex.org/W2025195393","https://openalex.org/W2940695648","https://openalex.org/W2048650277"],"abstract_inverted_index":{"The":[0],"moving":[1,83],"sofa":[2,84],"problem,":[3,85],"posed":[4],"by":[5,42,50,93],"Moser":[6],"in":[7,24,44,97,128],"1966,":[8],"asks":[9],"for":[10],"the":[11,60,81,89,99,113,117,152],"planar":[12],"shape":[13,40,72,100,124],"of":[14,27,54,88],"maximal":[15],"area":[16,140],"that":[17,73],"can":[18,125],"move":[19],"around":[20],"a":[21,25,38,52,70,77,86,108,135],"right-angled":[22],"corner":[23],"hallway":[26],"unit":[28],"width":[29],"and":[30,95,115,131,147,160],"is":[31,101,134,141],"conjectured":[32],"to":[33,68,80,103,106,112,116,143,151],"have":[34],"as":[35,76],"its":[36,132],"solution":[37,79],"complicated":[39],"derived":[41],"Gerver":[43],"1992.":[45],"We":[46,63],"extend":[47],"Gerver's":[48,120],"techniques":[49],"deriving":[51],"family":[53],"six":[55],"differential":[56],"equations":[57,154],"arising":[58],"from":[59],"area-maximization":[61],"property.":[62],"then":[64],"use":[65],"this":[66],"result":[67],"derive":[69],"new":[71,123],"we":[74],"propose":[75],"possible":[78],"ambidextrous":[82],"variant":[87],"problem":[90],"previously":[91],"studied":[92],"Conway":[94],"others":[96],"which":[98],"required":[102],"be":[104,126],"able":[105],"negotiate":[107],"right-angle":[109],"turn":[110],"both":[111],"left":[114],"right.":[118],"Unlike":[119],"construction,":[121],"our":[122],"expressed":[127],"closed":[129],"form,":[130],"boundary":[133],"piecewise":[136],"algebraic":[137],"curve.":[138],"Its":[139],"equal":[142],",":[144],"where":[145],"X":[146],"Y":[148],"are":[149],"solutions":[150],"cubic":[153],"x2(x":[155],"+":[156,162],"3)":[157,163],"=":[158,164],"8":[159],"x(4x2":[161],"1,":[165],"respectively.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}