{"id":"https://openalex.org/W3008041887","doi":"https://doi.org/10.1007/978-3-030-41258-6_20","title":"The Fermat-Torricelli Problem of Triangles on the Sphere with Euclidean Metric: A Symbolic Solution with Maple","display_name":"The Fermat-Torricelli Problem of Triangles on the Sphere with Euclidean Metric: A Symbolic Solution with Maple","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3008041887","doi":"https://doi.org/10.1007/978-3-030-41258-6_20","mag":"3008041887"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-41258-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-41258-6_20","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5085583877","display_name":"Xiaofeng Guo","orcid":"https://orcid.org/0000-0003-3129-493X"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]},{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaofeng Guo","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai, 200444, China","School of Mathematical Sciences, East China Normal University, Shanghai, 200062, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai, 200444, China","institution_ids":["https://openalex.org/I113940042"]},{"raw_affiliation_string":"School of Mathematical Sciences, East China Normal University, Shanghai, 200062, China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066842145","display_name":"Tuo Leng","orcid":"https://orcid.org/0000-0002-2921-3291"},"institutions":[{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tuo Leng","raw_affiliation_strings":["School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China","institution_ids":["https://openalex.org/I141962983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058328411","display_name":"Zhenbing Zeng","orcid":"https://orcid.org/0000-0002-9728-1114"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenbing Zeng","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai, 200444, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai, 200444, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085583877"],"corresponding_institution_ids":["https://openalex.org/I113940042","https://openalex.org/I66867065"],"apc_list":null,"apc_paid":null,"fwci":0.6029,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63934756,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"263","last_page":"278"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12504","display_name":"Mathematics and Applications","score":0.9979000091552734,"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":0.9975000023841858,"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/maple","display_name":"Maple","score":0.8449077606201172},{"id":"https://openalex.org/keywords/fermats-last-theorem","display_name":"Fermat's Last Theorem","score":0.7336375117301941},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6895617246627808},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6120386123657227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6010322570800781},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5539261698722839},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5380048751831055},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4604405164718628},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45265406370162964},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4242591857910156},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.42140695452690125},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3466564416885376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23308342695236206},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20554214715957642},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19666385650634766},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.06438407301902771}],"concepts":[{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.8449077606201172},{"id":"https://openalex.org/C87670640","wikidata":"https://www.wikidata.org/wiki/Q132469","display_name":"Fermat's Last Theorem","level":2,"score":0.7336375117301941},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6895617246627808},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6120386123657227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6010322570800781},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5539261698722839},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5380048751831055},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4604405164718628},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45265406370162964},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4242591857910156},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.42140695452690125},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3466564416885376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23308342695236206},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20554214715957642},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19666385650634766},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.06438407301902771},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-41258-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-41258-6_20","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W91999360","https://openalex.org/W629560095","https://openalex.org/W1498665408","https://openalex.org/W1599026900","https://openalex.org/W1981613180","https://openalex.org/W1986242184","https://openalex.org/W1990495928","https://openalex.org/W1993741266","https://openalex.org/W2001343527","https://openalex.org/W2019162816","https://openalex.org/W2024833542","https://openalex.org/W2029397348","https://openalex.org/W2031552116","https://openalex.org/W2057280743","https://openalex.org/W2080132708","https://openalex.org/W2086709935","https://openalex.org/W2144770505","https://openalex.org/W2154514904","https://openalex.org/W2511952958","https://openalex.org/W2531059567","https://openalex.org/W2797354117","https://openalex.org/W4237842662","https://openalex.org/W6600820135"],"related_works":["https://openalex.org/W3008027610","https://openalex.org/W2619973341","https://openalex.org/W4300811723","https://openalex.org/W2210259036","https://openalex.org/W2187413387","https://openalex.org/W2886642959","https://openalex.org/W851952888","https://openalex.org/W2140907685","https://openalex.org/W4210971937","https://openalex.org/W4386225212"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}