{"id":"https://openalex.org/W2152290369","doi":"https://doi.org/10.1145/1377676.1377709","title":"Extremal problems on triangle areas in two and three dimensions","display_name":"Extremal problems on triangle areas in two and three dimensions","publication_year":2008,"publication_date":"2008-06-09","ids":{"openalex":"https://openalex.org/W2152290369","doi":"https://doi.org/10.1145/1377676.1377709","mag":"2152290369"},"language":"en","primary_location":{"id":"doi:10.1145/1377676.1377709","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377676.1377709","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fourth annual symposium on Computational geometry","raw_type":"proceedings-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/A5091313409","display_name":"Adrian Dumitrescu","orcid":"https://orcid.org/0000-0002-1118-0321"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Adrian Dumitrescu","raw_affiliation_strings":["University of Wisconsin, Miolwaukee, WI, USA"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin, Miolwaukee, WI, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["Tel Aviv University, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Csaba D. T\u00f3th","raw_affiliation_strings":["University of Calgary, Calgary, AB, Canada"],"affiliations":[{"raw_affiliation_string":"University of Calgary, Calgary, AB, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5091313409"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4876,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.87635904,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"208","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991000294685364,"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":0.9991000294685364,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6407877802848816},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6330924034118652},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5813928842544556},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.567861020565033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.512948215007782},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4813481271266937},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.33532941341400146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28328293561935425},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.1286049485206604},{"id":"https://openalex.org/keywords/paleontology","display_name":"Paleontology","score":0.0767260491847992}],"concepts":[{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6407877802848816},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6330924034118652},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5813928842544556},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.567861020565033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.512948215007782},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4813481271266937},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33532941341400146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28328293561935425},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.1286049485206604},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0767260491847992},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1377676.1377709","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1377676.1377709","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fourth annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.146.2090","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.146.2090","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~michas/a-sub.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.216.7950","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.216.7950","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwm.edu/faculty/ad/area.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.248.6951","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.6951","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0710.4109v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W13988344","https://openalex.org/W116433216","https://openalex.org/W116441594","https://openalex.org/W170892534","https://openalex.org/W564800084","https://openalex.org/W1444168583","https://openalex.org/W1494417595","https://openalex.org/W1539895965","https://openalex.org/W1551919361","https://openalex.org/W1561602969","https://openalex.org/W1721100836","https://openalex.org/W1863703112","https://openalex.org/W1967421215","https://openalex.org/W1988090433","https://openalex.org/W1994720529","https://openalex.org/W2002417698","https://openalex.org/W2009870896","https://openalex.org/W2018858611","https://openalex.org/W2028747718","https://openalex.org/W2035884884","https://openalex.org/W2039157981","https://openalex.org/W2047819748","https://openalex.org/W2066782398","https://openalex.org/W2072637582","https://openalex.org/W2074709558","https://openalex.org/W2083644514","https://openalex.org/W2094422067","https://openalex.org/W2101764588","https://openalex.org/W2112998433","https://openalex.org/W2155681397","https://openalex.org/W2163913133","https://openalex.org/W2166961358","https://openalex.org/W2167816765","https://openalex.org/W2168138462","https://openalex.org/W2168747680","https://openalex.org/W2170459217","https://openalex.org/W2183676805","https://openalex.org/W2319149236","https://openalex.org/W2481227236","https://openalex.org/W2622381546","https://openalex.org/W2775046532","https://openalex.org/W2912202394","https://openalex.org/W2949342774","https://openalex.org/W2963234396","https://openalex.org/W3159952184","https://openalex.org/W4210453869","https://openalex.org/W6600579306","https://openalex.org/W6603147192"],"related_works":["https://openalex.org/W1919101720","https://openalex.org/W4390822878","https://openalex.org/W96888382","https://openalex.org/W2041308758","https://openalex.org/W3198856780","https://openalex.org/W2371953206","https://openalex.org/W597159773","https://openalex.org/W2361023359","https://openalex.org/W2349543044","https://openalex.org/W3007915326"],"abstract_inverted_index":{"The":[0],"study":[1],"of":[2,13,34,36,56],"extremal":[3],"problems":[4],"on":[5,28],"triangle":[6],"areas":[7,58],"was":[8],"initiated":[9],"in":[10,19,47,51],"a":[11],"series":[12],"papers":[14],"by":[15,43,60],"Erd\u00f6s":[16],"and":[17,50,53],"Purdy":[18],"the":[20,32,37,48,54,61],"early":[21],"1970s.":[22],"Here":[23],"we":[24],"present":[25],"new":[26],"results":[27],"such":[29],"problems,":[30],"concerning":[31],"number":[33,55],"triangles":[35],"same":[38],"area":[39],"that":[40],"are":[41],"spanned":[42],"finite":[44],"point":[45],"sets":[46],"plane":[49],"3-space,":[52],"distinct":[57],"determined":[59],"triangles.":[62]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}