{"id":"https://openalex.org/W2897632525","doi":"https://doi.org/10.1080/00029890.2020.1785253","title":"Chords of an Ellipse, Lucas Polynomials, and Cubic Equations","display_name":"Chords of an Ellipse, Lucas Polynomials, and Cubic Equations","publication_year":2020,"publication_date":"2020-09-13","ids":{"openalex":"https://openalex.org/W2897632525","doi":"https://doi.org/10.1080/00029890.2020.1785253","mag":"2897632525"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1785253","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1785253","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1810.00492","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ben Blum-Smith","orcid":"https://orcid.org/0000-0001-5284-8271"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ben Blum-Smith","raw_affiliation_strings":["NYU Center for Data Science"],"affiliations":[{"raw_affiliation_string":"NYU Center for Data Science","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Japheth Wood","orcid":"https://orcid.org/0000-0002-8575-6901"},"institutions":[{"id":"https://openalex.org/I39661318","display_name":"Bard College","ror":"https://ror.org/04yrgt058","country_code":"US","type":"education","lineage":["https://openalex.org/I39661318"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Japheth Wood","raw_affiliation_strings":["Mathematics Program, Bard College"],"affiliations":[{"raw_affiliation_string":"Mathematics Program, Bard College","institution_ids":["https://openalex.org/I39661318"]}]}],"institutions":[],"countries_distinct_count":1,"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":4,"citation_normalized_percentile":{"value":0.00701061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"127","issue":"8","first_page":"688","last_page":"705"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.7602999806404114,"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"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.7602999806404114,"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/T12504","display_name":"Mathematics and Applications","score":0.06459999829530716,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.04540000110864639,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/fibonacci-number","display_name":"Fibonacci number","score":0.8098000288009644},{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.703000009059906},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.5855000019073486},{"id":"https://openalex.org/keywords/cubic-function","display_name":"Cubic function","score":0.526199996471405},{"id":"https://openalex.org/keywords/lucas-number","display_name":"Lucas number","score":0.4948999881744385},{"id":"https://openalex.org/keywords/fibonacci-polynomials","display_name":"Fibonacci polynomials","score":0.4390000104904175}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.8098000288009644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7569000124931335},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.703000009059906},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5855000019073486},{"id":"https://openalex.org/C65559279","wikidata":"https://www.wikidata.org/wiki/Q16667694","display_name":"Cubic function","level":2,"score":0.526199996471405},{"id":"https://openalex.org/C3634175","wikidata":"https://www.wikidata.org/wiki/Q2503280","display_name":"Lucas number","level":3,"score":0.4948999881744385},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.4390000104904175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3982999920845032},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37139999866485596},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2973000109195709},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27320000529289246},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.2020.1785253","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1785253","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"},{"id":"pmh:oai:arXiv.org:1810.00492","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1810.00492","pdf_url":"https://arxiv.org/pdf/1810.00492","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1810.00492","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1810.00492","pdf_url":"https://arxiv.org/pdf/1810.00492","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W89912732","https://openalex.org/W322461743","https://openalex.org/W1551177513","https://openalex.org/W1927182659","https://openalex.org/W2046407158","https://openalex.org/W2127287214","https://openalex.org/W2134984950","https://openalex.org/W2166623286","https://openalex.org/W2519671284","https://openalex.org/W2914659449","https://openalex.org/W4238728065","https://openalex.org/W4244027607","https://openalex.org/W4247341218","https://openalex.org/W4248388388","https://openalex.org/W4255383357","https://openalex.org/W4298303644","https://openalex.org/W6807104857"],"related_works":[],"abstract_inverted_index":{"A":[0],"beautiful":[1],"theorem":[2,76],"of":[3,18,32,38,59,70,84,90,93,112,130],"Thomas":[4],"Price":[5],"links":[6],"the":[7,11,15,33,53,71,91,104,128,131],"Fibonacci":[8,114],"numbers":[9],"and":[10,42,74,80,116],"Lucas":[12,86,132],"polynomials":[13,87,115],"to":[14,51,61,125],"plane":[16],"geometry":[17],"an":[19,36,82],"ellipse":[20,40],"generalizing":[21],"a":[22,29,43,56,109],"classic":[23],"problem":[24,35],"about":[25],"circles.":[26],"We":[27,96],"give":[28,108],"brief":[30],"history":[31],"circle":[34],"account":[37],"Price\u2019s":[39],"proof":[41,45],"reorganized":[44],"with":[46],"some":[47],"new":[48],"ideas":[49],"designed":[50],"situate":[52],"result":[54],"within":[55],"dense":[57],"web":[58],"connections":[60,100],"classical":[62],"mathematics.":[63],"It":[64],"is":[65],"inspired":[66],"by":[67],"Cardano\u2019s":[68,120],"solution":[69],"cubic":[72],"equation":[73],"Newton\u2019s":[75],"on":[77],"power":[78],"sums":[79],"yields":[81],"interpretation":[83,111],"generalized":[85,113],"in":[88],"terms":[89],"theory":[92],"symmetric":[94],"polynomials.":[95,133],"also":[97],"develop":[98],"additional":[99],"that":[101,119],"surface":[102],"along":[103],"way;":[105],"e.g.,":[106],"we":[107,117],"parallel":[110],"show":[118],"method":[121],"can":[122],"be":[123],"used":[124],"write":[126],"down":[127],"roots":[129]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2018-10-26T00:00:00"}