{"id":"https://openalex.org/W7225592131","doi":"https://doi.org/10.5281/zenodo.24051236","title":"The Triangle-to-Quadratic Method: A Geometric Reconstruction","display_name":"The Triangle-to-Quadratic Method: A Geometric Reconstruction","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225592131","doi":"https://doi.org/10.5281/zenodo.24051236"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24051236","doi":"https://doi.org/10.5281/zenodo.24051236","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24051236","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24051236","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161266850","display_name":"Thomas Sneed II","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sneed II, Thomas","raw_affiliation_strings":["Independent researcher"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161266850"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":1.0,"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":1.0,"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":0.0,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/geometric-reconstruction","display_name":"geometric reconstruction","score":0.6449999809265137},{"id":"https://openalex.org/keywords/quadratic-equations","display_name":"quadratic equations","score":0.902999997138977},{"id":"https://openalex.org/keywords/trigonometric-identities","display_name":"trigonometric identities","score":0.8370000123977661},{"id":"https://openalex.org/keywords/angle-measurement","display_name":"angle measurement","score":0.7649999856948853},{"id":"https://openalex.org/keywords/secondary-school-mathematics","display_name":"high school mathematics","score":0.6100000143051147}],"concepts":[{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.7218000292778015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5914000272750854},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5440999865531921},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.49059998989105225},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.4196999967098236},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3946000039577484},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.349700003862381},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.305400013923645},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29159998893737793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28870001435279846},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.287200003862381},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2639000117778778},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.25940001010894775}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24051236","doi":"https://doi.org/10.5281/zenodo.24051236","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24051236","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24051237","doi":"https://doi.org/10.5281/zenodo.24051237","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24051237","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24051236","doi":"https://doi.org/10.5281/zenodo.24051236","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24051236","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4413182730","https://openalex.org/W2605659466","https://openalex.org/W7218515138","https://openalex.org/W6930994132","https://openalex.org/W3162585376","https://openalex.org/W7034526119","https://openalex.org/W4293569131","https://openalex.org/W2032168977","https://openalex.org/W2796520694","https://openalex.org/W2963996981"],"abstract_inverted_index":{"This":[0],"paper":[1],"documents":[2],"a":[3],"geometric":[4,34],"and":[5,14,41,43,53,84],"algebraic":[6],"method":[7,29],"that":[8],"the":[9],"author":[10],"reports":[11],"independently":[12],"developing":[13],"using":[15],"while":[16],"attending":[17],"Cedar":[18],"Ridge":[19],"High":[20],"School":[21],"in":[22,26,68],"Arkansas,":[23],"before":[24],"graduating":[25],"2009.":[27],"The":[28,63,75],"represents":[30],"triangles":[31],"through":[32],"congruent":[33],"transformations,":[35],"establishes":[36],"relationships":[37,52],"between":[38],"side":[39],"lengths":[40],"area,":[42],"constructs":[44],"quadratic":[45],"equations":[46],"to":[47,59],"recover":[48,60],"unknown":[49],"dimensions.":[50],"Trigonometric":[51],"angle":[54],"identities":[55],"are":[56],"subsequently":[57],"used":[58],"angular":[61],"measurements.":[62],"original":[64],"procedure":[65],"was":[66],"reconstructed":[67],"November":[69],"2026":[70],"after":[71],"approximately":[72],"seventeen":[73],"years.":[74],"work":[76],"is":[77],"presented":[78],"as":[79],"an":[80],"independent":[81],"mathematical":[82,93],"derivation":[83],"educational":[85],"exposition,":[86],"without":[87],"claiming":[88],"priority":[89],"over":[90],"previously":[91],"published":[92],"identities.":[94]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}