{"id":"https://openalex.org/W7225634744","doi":"https://doi.org/10.36347/sjpms.2026.v13i10.001","title":"Exact Doubling of Circles, Squares, and Regular Triangles Using Only Straightedge and Compass in Euclidean Geometry","display_name":"Exact Doubling of Circles, Squares, and Regular Triangles Using Only Straightedge and Compass in Euclidean Geometry","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225634744","doi":"https://doi.org/10.36347/sjpms.2026.v13i10.001"},"language":"en","primary_location":{"id":"doi:10.36347/sjpms.2026.v13i10.001","doi":"https://doi.org/10.36347/sjpms.2026.v13i10.001","is_oa":true,"landing_page_url":"https://doi.org/10.36347/sjpms.2026.v13i10.001","pdf_url":"https://saspublishers.com/article/25091/download/","source":{"id":"https://openalex.org/S4210194730","display_name":"Scholars Journal of Physics Mathematics and Statistics","issn_l":"2393-8056","issn":["2393-8056","2393-8064"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scholars Journal of Physics, Mathematics and Statistics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://saspublishers.com/article/25091/download/","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102561501","display_name":"Tran Dinh Son","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tran Dinh Son","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5102561501"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"10","first_page":"322","last_page":"330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9970999956130981,"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":0.9970999956130981,"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/T12170","display_name":"History and Theory of Mathematics","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/squaring-the-circle","display_name":"squaring the circle","score":0.8050000071525574},{"id":"https://openalex.org/keywords/straightedge-and-compass-constructions","display_name":"compass and straightedge construction","score":0.765999972820282},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.7799999713897705},{"id":"https://openalex.org/keywords/geometric-construction","display_name":"geometric construction","score":0.7080000042915344},{"id":"https://openalex.org/keywords/equilateral-triangle","display_name":"equilateral triangle","score":0.5009999871253967}],"concepts":[{"id":"https://openalex.org/C2778361833","wikidata":"https://www.wikidata.org/wiki/Q34735","display_name":"Compass","level":2,"score":0.9038000106811523},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.684499979019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6453999876976013},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5604000091552734},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4207000136375427},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.39329999685287476},{"id":"https://openalex.org/C98653994","wikidata":"https://www.wikidata.org/wiki/Q875937","display_name":"Isosceles triangle","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.337799996137619},{"id":"https://openalex.org/C98371066","wikidata":"https://www.wikidata.org/wiki/Q230848","display_name":"Euclidean algorithm","level":2,"score":0.31459999084472656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3061999976634979},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30239999294281006},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C25653684","wikidata":"https://www.wikidata.org/wiki/Q207648","display_name":"Solid geometry","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2612000107765198},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25850000977516174},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25220000743865967},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.36347/sjpms.2026.v13i10.001","doi":"https://doi.org/10.36347/sjpms.2026.v13i10.001","is_oa":true,"landing_page_url":"https://doi.org/10.36347/sjpms.2026.v13i10.001","pdf_url":"https://saspublishers.com/article/25091/download/","source":{"id":"https://openalex.org/S4210194730","display_name":"Scholars Journal of Physics Mathematics and Statistics","issn_l":"2393-8056","issn":["2393-8056","2393-8064"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scholars Journal of Physics, Mathematics and Statistics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.36347/sjpms.2026.v13i10.001","doi":"https://doi.org/10.36347/sjpms.2026.v13i10.001","is_oa":true,"landing_page_url":"https://doi.org/10.36347/sjpms.2026.v13i10.001","pdf_url":"https://saspublishers.com/article/25091/download/","source":{"id":"https://openalex.org/S4210194730","display_name":"Scholars Journal of Physics Mathematics and Statistics","issn_l":"2393-8056","issn":["2393-8056","2393-8064"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scholars Journal of Physics, Mathematics and Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225634744.pdf","grobid_xml":"https://content.openalex.org/works/W7225634744.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2006895952","https://openalex.org/W4211209398","https://openalex.org/W4387175818","https://openalex.org/W4391889139","https://openalex.org/W4408532601","https://openalex.org/W4416573307"],"related_works":["https://openalex.org/W4408532601","https://openalex.org/W4411515908","https://openalex.org/W4407585626","https://openalex.org/W4396808339","https://openalex.org/W7171985932","https://openalex.org/W7201885875","https://openalex.org/W4412646727","https://openalex.org/W4404250596","https://openalex.org/W4401870088","https://openalex.org/W4412646827"],"abstract_inverted_index":{"This":[0,70,132],"research":[1,71,133],"focuses":[2],"on":[3],"finding":[4],"an":[5],"exact":[6],"solution":[7],"to":[8,73,142],"the":[9,35,66,80,94,110,127,144],"problems":[10],"of":[11,82,96,112,129],"\u201cdoubling":[12,19],"a":[13,16,20,25,28,42,61,75,83,89,97,104,113,122,136],"circle\u201d,":[14],"\"doubling":[15],"square\"":[17],"and":[18,27,51,103,124],"regular":[21,105,115],"triangle\u201d,":[22],"using":[23],"only":[24,121],"straightedge":[26,123],"compass":[29,125],"in":[30,49,139],"Euclidean":[31,130],"geometry.":[32,131],"In":[33],"2025,":[34],"ancient":[36],"Greek":[37,68],"problem":[38,56],"known":[39],"as":[40,47,60],"\"Doubling":[41],"Cube\"":[43],"was":[44],"solved":[45],"exactly,":[46],"documented":[48],"https://doi.org/10.14445/22315373/IJMTT-V69I8P506":[50],"https://doi.org/10.36347/sjpms.2025.v12i02.001,":[52],"[3].":[53],"The":[54],"current":[55],"can":[57],"be":[58],"viewed":[59],"derivative":[62],"issue":[63],"stemming":[64],"from":[65],"aforementioned":[67],"challenge.":[69],"aims":[72],"determine":[74],"circle":[76,85],"that":[77,91,107],"possesses":[78,92,108],"double":[79,93,109],"area":[81,87,95,101,111,118],"given":[84,98,114],"with":[86,100,117],"\u03c0r\u00b2,":[88],"square":[90,99],"a\u00b2,":[102],"triangle":[106,116],"A,":[119],"utilizing":[120],"within":[126],"framework":[128],"article":[134],"uses":[135],"distinct":[137],"approach":[138],"Geometric":[140],"Construction":[141],"solving":[143],"problems.":[145]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
