{"id":"https://openalex.org/W2885333441","doi":"https://doi.org/10.1080/00029890.2018.1467191","title":"Nonuniqueness of Sixpartite Points","display_name":"Nonuniqueness of Sixpartite Points","publication_year":2018,"publication_date":"2018-08-03","ids":{"openalex":"https://openalex.org/W2885333441","doi":"https://doi.org/10.1080/00029890.2018.1467191","mag":"2885333441"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1467191","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1467191","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"The American Mathematical Monthly","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/A5042757907","display_name":"Allan Berele","orcid":null},"institutions":[{"id":"https://openalex.org/I118353179","display_name":"DePaul University","ror":"https://ror.org/04xtx5t16","country_code":"US","type":"education","lineage":["https://openalex.org/I118353179"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Allan Berele","raw_affiliation_strings":["Department of Mathematics, DePaul University, Chicago, IL 60614"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, DePaul University, Chicago, IL 60614","institution_ids":["https://openalex.org/I118353179"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082543996","display_name":"Stefan Catoiu","orcid":"https://orcid.org/0000-0002-5785-0992"},"institutions":[{"id":"https://openalex.org/I118353179","display_name":"DePaul University","ror":"https://ror.org/04xtx5t16","country_code":"US","type":"education","lineage":["https://openalex.org/I118353179"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stefan Catoiu","raw_affiliation_strings":["Department of Mathematics, DePaul University, Chicago, IL 60614"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, DePaul University, Chicago, IL 60614","institution_ids":["https://openalex.org/I118353179"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042757907"],"corresponding_institution_ids":["https://openalex.org/I118353179"],"apc_list":null,"apc_paid":null,"fwci":1.5178,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.81683168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"125","issue":"7","first_page":"638","last_page":"642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9915000200271606,"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":0.9915000200271606,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9901000261306763,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9891999959945679,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.7500299215316772},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.7416277527809143},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7282829880714417},{"id":"https://openalex.org/keywords/perimeter","display_name":"Perimeter","score":0.717800498008728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.640540361404419},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6324016451835632},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5953937768936157},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5620793104171753},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5402318239212036},{"id":"https://openalex.org/keywords/convex-polygon","display_name":"Convex polygon","score":0.47702667117118835},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4532921016216278},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42089036107063293},{"id":"https://openalex.org/keywords/star-shaped-polygon","display_name":"Star-shaped polygon","score":0.41174620389938354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1527111530303955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14062193036079407},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.11056143045425415},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.08010077476501465},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.07510441541671753}],"concepts":[{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.7500299215316772},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.7416277527809143},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7282829880714417},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.717800498008728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.640540361404419},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6324016451835632},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5953937768936157},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5620793104171753},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5402318239212036},{"id":"https://openalex.org/C2780034980","wikidata":"https://www.wikidata.org/wiki/Q3259505","display_name":"Convex polygon","level":3,"score":0.47702667117118835},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4532921016216278},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42089036107063293},{"id":"https://openalex.org/C96366933","wikidata":"https://www.wikidata.org/wiki/Q2122886","display_name":"Star-shaped polygon","level":5,"score":0.41174620389938354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1527111530303955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14062193036079407},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.11056143045425415},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.08010077476501465},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.07510441541671753},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2018.1467191","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1467191","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.46000000834465027,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2055552544","https://openalex.org/W2315722046","https://openalex.org/W2606911552","https://openalex.org/W4210733153","https://openalex.org/W4241014687"],"related_works":["https://openalex.org/W2123516473","https://openalex.org/W2081175594","https://openalex.org/W1585992543","https://openalex.org/W4240339429","https://openalex.org/W1991526295","https://openalex.org/W2375018841","https://openalex.org/W3175422282","https://openalex.org/W4287134842","https://openalex.org/W2511445123","https://openalex.org/W1592173722"],"abstract_inverted_index":{"It":[0],"is":[1,24,32,52,90,102],"known":[2,53],"that":[3,29,54,62],"the":[4,30,37,77],"area":[5,44,92],"of":[6,39,41,74,87],"any":[7,71],"bounded,":[8],"convex":[9,82],"plane":[10,78],"figure":[11],"can":[12],"be":[13],"divided":[14],"into":[15],"equal":[16],"sixths":[17],"by":[18],"three":[19],"concurrent":[20],"lines,":[21],"and":[22,47,95],"it":[23,51],"not":[25,65],"hard":[26],"to":[27],"see":[28],"same":[31],"true":[33],"for":[34,58],"perimeters.":[35],"Calling":[36],"points":[38,46,75,89],"intersection":[40],"such":[42],"lines":[43],"sixpartite":[45,49,93,105],"perimeter":[48,104],"points,":[50],"they":[55,63],"are":[56,64],"unique":[57,66],"triangles.":[59],"We":[60],"prove":[61],"in":[67,76,84,99],"general.":[68],"Moreover,":[69],"given":[70],"finite":[72],"set":[73],"we":[79],"construct":[80],"a":[81,96,103],"polygon":[83,98],"which":[85,100],"each":[86,101],"these":[88],"an":[91],"point,":[94],"second":[97],"point.":[106]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
