{"id":"https://openalex.org/W2958114780","doi":"https://doi.org/10.1080/00029890.2019.1606578","title":"Arctangent Formulas and Pi","display_name":"Arctangent Formulas and Pi","publication_year":2019,"publication_date":"2019-07-09","ids":{"openalex":"https://openalex.org/W2958114780","doi":"https://doi.org/10.1080/00029890.2019.1606578","mag":"2958114780"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2019.1606578","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1606578","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/A5011239817","display_name":"Marc Chamberland","orcid":null},"institutions":[{"id":"https://openalex.org/I173288447","display_name":"Grinnell College","ror":"https://ror.org/04tmmky42","country_code":"US","type":"education","lineage":["https://openalex.org/I173288447"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marc Chamberland","raw_affiliation_strings":[",","Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112","institution_ids":["https://openalex.org/I173288447"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040674695","display_name":"Eugene A. Herman","orcid":null},"institutions":[{"id":"https://openalex.org/I173288447","display_name":"Grinnell College","ror":"https://ror.org/04tmmky42","country_code":"US","type":"education","lineage":["https://openalex.org/I173288447"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eugene A. Herman","raw_affiliation_strings":[",","Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Grinnell College, Grinnell, IA 50112","institution_ids":["https://openalex.org/I173288447"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011239817"],"corresponding_institution_ids":["https://openalex.org/I173288447"],"apc_list":null,"apc_paid":null,"fwci":0.3799,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57108661,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"126","issue":"7","first_page":"646","last_page":"650"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9927999973297119,"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":0.9927999973297119,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9358000159263611,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/pi","display_name":"Pi","score":0.7345917224884033},{"id":"https://openalex.org/keywords/inverse-trigonometric-functions","display_name":"Inverse trigonometric functions","score":0.6450506448745728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4205273389816284},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3406876027584076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2853480577468872},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1821398138999939}],"concepts":[{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.7345917224884033},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.6450506448745728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4205273389816284},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3406876027584076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2853480577468872},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1821398138999939}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2019.1606578","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2019.1606578","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1993439210","https://openalex.org/W2087815995","https://openalex.org/W4206508069","https://openalex.org/W4252109616"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W3155892526","https://openalex.org/W2298861036","https://openalex.org/W3148032049"],"abstract_inverted_index":{"Using":[0],"both":[1],"geometrical":[2],"and":[3,13],"analytical":[4],"approaches,":[5],"new":[6],"multivariable":[7],"formulas":[8],"connecting":[9],"the":[10,14],"arctangent":[11],"function":[12],"number":[15],"\u03c0":[16],"are":[17],"produced.":[18]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-02-01T03:34:12.195049","created_date":"2025-10-10T00:00:00"}