{"id":"https://openalex.org/W2044933319","doi":"https://doi.org/10.1007/s00454-003-0819-2","title":"The Thirteen Spheres: A New Proof","display_name":"The Thirteen Spheres: A New Proof","publication_year":2004,"publication_date":"2004-03-01","ids":{"openalex":"https://openalex.org/W2044933319","doi":"https://doi.org/10.1007/s00454-003-0819-2","mag":"2044933319"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-003-0819-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-0819-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-0819-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-0819-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053103458","display_name":"Kurt M. Anstreicher","orcid":"https://orcid.org/0000-0002-6306-9940"},"institutions":[{"id":"https://openalex.org/I4210155590","display_name":"Management Sciences (United States)","ror":"https://ror.org/05shz5j84","country_code":"US","type":"company","lineage":["https://openalex.org/I4210155590"]},{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kurt M. Anstreicher","raw_affiliation_strings":["Department of Management Sciences,\nUniversity of Iowa,\nIowa City, IA 52242\n , USA","Department of Management Sciences, University of Iowa, Iowa City, IA 52242 , USA"],"affiliations":[{"raw_affiliation_string":"Department of Management Sciences,\nUniversity of Iowa,\nIowa City, IA 52242\n , USA","institution_ids":["https://openalex.org/I126307644","https://openalex.org/I4210155590"]},{"raw_affiliation_string":"Department of Management Sciences, University of Iowa, Iowa City, IA 52242 , USA","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053103458"],"corresponding_institution_ids":["https://openalex.org/I126307644","https://openalex.org/I4210155590"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.7929,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.90052568,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"4","first_page":"613","last_page":"625"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9990000128746033,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9929999709129333,"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/spheres","display_name":"SPHERES","score":0.8761862516403198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6805675029754639},{"id":"https://openalex.org/keywords/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.6268296241760254},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5890657305717468},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.5676075220108032},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5485150218009949},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5009145736694336},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3110834062099457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19579041004180908},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18722668290138245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1316140592098236}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.8761862516403198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6805675029754639},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.6268296241760254},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5890657305717468},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.5676075220108032},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5485150218009949},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5009145736694336},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3110834062099457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19579041004180908},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18722668290138245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1316140592098236},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-003-0819-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-0819-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-0819-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.15.3846","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.3846","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.biz.uiowa.edu/faculty/anstreicher/thirteen.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.572.8318","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.572.8318","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2002/10/554.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-003-0819-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-003-0819-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-003-0819-2.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete and Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2044933319.pdf","grobid_xml":"https://content.openalex.org/works/W2044933319.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W13495895","https://openalex.org/W182666922","https://openalex.org/W600114403","https://openalex.org/W1488862788","https://openalex.org/W1560249236","https://openalex.org/W1987132854","https://openalex.org/W1995507179","https://openalex.org/W1995990042","https://openalex.org/W2054085030","https://openalex.org/W2054912417","https://openalex.org/W2068028167","https://openalex.org/W2079565519","https://openalex.org/W2120062331","https://openalex.org/W2476986258","https://openalex.org/W2584020404","https://openalex.org/W2797523816","https://openalex.org/W2973658695","https://openalex.org/W3016843226","https://openalex.org/W4247949814","https://openalex.org/W4255317205","https://openalex.org/W4290824462","https://openalex.org/W4292408570","https://openalex.org/W6732536474"],"related_works":["https://openalex.org/W2359979928","https://openalex.org/W2368353614","https://openalex.org/W2390369954","https://openalex.org/W1529719486","https://openalex.org/W4232052003","https://openalex.org/W2005766378","https://openalex.org/W2040752023","https://openalex.org/W2045139282","https://openalex.org/W1971745998","https://openalex.org/W2035779693"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
