{"id":"https://openalex.org/W4413213728","doi":"https://doi.org/10.1080/00029890.2025.2529768","title":"How Much String to String a Cardioid?","display_name":"How Much String to String a Cardioid?","publication_year":2025,"publication_date":"2025-08-11","ids":{"openalex":"https://openalex.org/W4413213728","doi":"https://doi.org/10.1080/00029890.2025.2529768"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2025.2529768","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2025.2529768","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/A5016211229","display_name":"David Richeson","orcid":"https://orcid.org/0000-0003-0527-3916"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David Richeson","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0527-3916","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016211229"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30518047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"132","issue":"8","first_page":"807","last_page":"812"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10217","display_name":"Cardiac electrophysiology and arrhythmias","score":0.04050000011920929,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10217","display_name":"Cardiac electrophysiology and arrhythmias","score":0.04050000011920929,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11677","display_name":"Congenital heart defects research","score":0.024800000712275505,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10618","display_name":"Aortic Disease and Treatment Approaches","score":0.02459999918937683,"subfield":{"id":"https://openalex.org/subfields/2740","display_name":"Pulmonary and Respiratory Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.6377301812171936},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.561267614364624},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4644947350025177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3560626208782196}],"concepts":[{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.6377301812171936},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.561267614364624},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4644947350025177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3560626208782196}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2025.2529768","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2025.2529768","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":[{"display_name":"Zero hunger","id":"https://metadata.un.org/sdg/2","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W64729384","https://openalex.org/W259754555","https://openalex.org/W571075951","https://openalex.org/W630310878","https://openalex.org/W2395668405","https://openalex.org/W2796417242","https://openalex.org/W4233277955","https://openalex.org/W4246476882","https://openalex.org/W4252979798","https://openalex.org/W4390771076"],"related_works":["https://openalex.org/W4391375266","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/W2298861036","https://openalex.org/W2057779428"],"abstract_inverted_index":{"A":[0],"residue":[1],"design":[2],"is":[3,84,91],"an":[4],"artistic":[5],"geometric":[6],"construction":[7],"in":[8],"which":[9],"we":[10,23,52],"have":[11],"n":[12,35],"equally-spaced":[13],"points":[14],"on":[15],"a":[16,26,65],"circle":[17],"numbered":[18],"0":[19],"through":[20],"n\u22121,":[21],"and":[22],"join":[24],"with":[25,81],"line":[27,62],"segment":[28],"each":[29],"point":[30],"k":[31],"to":[32,75,86],"ak":[33],"modulo":[34],"for":[36],"some":[37],"fixed":[38],"a\u22652.":[39],"The":[40],"envelopes":[41],"of":[42,57,60,78],"these":[43,61,79],"lines":[44],"are":[45],"epicycloids,":[46],"like":[47],"cardioids.":[48],"In":[49,70],"this":[50],"note,":[51],"prove":[53],"that":[54],"the":[55,58],"sum":[56],"lengths":[59],"segments":[63],"has":[64],"surprisingly":[66],"simple":[67],"closed":[68],"form.":[69],"particular,":[71],"if":[72],"one":[73,77],"wants":[74],"make":[76],"designs":[80],"string,":[82],"it":[83],"easy":[85],"calculate":[87],"how":[88],"much":[89],"string":[90],"required.":[92]},"counts_by_year":[],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}