{"id":"https://openalex.org/W2115144499","doi":"https://doi.org/10.1080/10586458.2002.10504466","title":"The Set of Poles of a Two-Sheeted Hyperboloid","display_name":"The Set of Poles of a Two-Sheeted Hyperboloid","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2115144499","doi":"https://doi.org/10.1080/10586458.2002.10504466","mag":"2115144499"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2002.10504466","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2002.10504466","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"],"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/A5071082834","display_name":"Robert Sinclair","orcid":"https://orcid.org/0000-0002-9646-4322"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Robert Sinclair","raw_affiliation_strings":["The University of Melbourne"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5104041709","display_name":"Minoru Tanaka","orcid":null},"institutions":[{"id":"https://openalex.org/I1314466530","display_name":"Tokai University","ror":"https://ror.org/01p7qe739","country_code":"JP","type":"education","lineage":["https://openalex.org/I1314466530"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Minoru Tanaka","raw_affiliation_strings":["Tokai University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokai University","institution_ids":["https://openalex.org/I1314466530"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.20545706,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"1","first_page":"27","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9961000084877014,"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":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperboloid","display_name":"Hyperboloid","score":0.9921540021896362},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7816828489303589},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7521210312843323},{"id":"https://openalex.org/keywords/axis-of-symmetry","display_name":"Axis of symmetry","score":0.5965903997421265},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.45924925804138184},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.455616295337677},{"id":"https://openalex.org/keywords/perpendicular","display_name":"Perpendicular","score":0.4156813621520996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3906744718551636},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.36361071467399597},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3473738729953766},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33931344747543335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06468856334686279}],"concepts":[{"id":"https://openalex.org/C99564226","wikidata":"https://www.wikidata.org/wiki/Q505628","display_name":"Hyperboloid","level":2,"score":0.9921540021896362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7816828489303589},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7521210312843323},{"id":"https://openalex.org/C2993660776","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Axis of symmetry","level":2,"score":0.5965903997421265},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.45924925804138184},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.455616295337677},{"id":"https://openalex.org/C199631012","wikidata":"https://www.wikidata.org/wiki/Q205034","display_name":"Perpendicular","level":2,"score":0.4156813621520996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3906744718551636},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.36361071467399597},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3473738729953766},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33931344747543335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06468856334686279},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10586458.2002.10504466","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2002.10504466","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:CULeuclid:euclid.em/1057860312","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1057860312","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.41999998688697815,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1495768073","https://openalex.org/W1636498747","https://openalex.org/W1664360780","https://openalex.org/W2037876304","https://openalex.org/W2045438304","https://openalex.org/W2057687829","https://openalex.org/W2125924733","https://openalex.org/W2145308838","https://openalex.org/W2160116082","https://openalex.org/W4213186458","https://openalex.org/W4247528458"],"related_works":["https://openalex.org/W2115144499","https://openalex.org/W1969802923","https://openalex.org/W2088001410","https://openalex.org/W1964578222","https://openalex.org/W1537818359","https://openalex.org/W2161491863","https://openalex.org/W2495446501","https://openalex.org/W2001430463","https://openalex.org/W2466365913","https://openalex.org/W2073604728"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"conjectured":[3],"for":[4],"some":[5],"time":[6],"that":[7],"the":[8,30,37],"set":[9],"of":[10,12,33,41],"poles":[11],"a":[13],"rotationally":[14],"symmetric":[15],"two-sheeted":[16],"hyperboloid":[17],"breaks":[18],"into":[19],"two":[20],"disjoint":[21],"sets":[22],"ifsymmetry":[23],"is":[24],"broken":[25],"by":[26],"contraction":[27],"perpendicular":[28],"to":[29],"original":[31],"axis":[32],"symmetry.":[34],"We":[35],"provide":[36],"first":[38],"reliable":[39],"visualizations":[40],"this":[42],"process,":[43],"confirming":[44],"previous":[45],"conjectures":[46],"and":[47],"motivating":[48],"new":[49],"ones.":[50]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}