{"id":"https://openalex.org/W3006748907","doi":"https://doi.org/10.1080/00029890.2020.1693228","title":"A Determinant Proof of a Generalized Pythagorean Theorem","display_name":"A Determinant Proof of a Generalized Pythagorean Theorem","publication_year":2020,"publication_date":"2020-02-24","ids":{"openalex":"https://openalex.org/W3006748907","doi":"https://doi.org/10.1080/00029890.2020.1693228","mag":"3006748907"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1693228","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1693228","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/A5079148649","display_name":"Suk-Geun Hwang","orcid":null},"institutions":[{"id":"https://openalex.org/I183533211","display_name":"University of Wisconsin\u2013Whitewater","ror":"https://ror.org/049hrzs50","country_code":"US","type":"education","lineage":["https://openalex.org/I183533211"]},{"id":"https://openalex.org/I31419693","display_name":"Kyungpook National University","ror":"https://ror.org/040c17130","country_code":"KR","type":"education","lineage":["https://openalex.org/I31419693"]}],"countries":["KR","US"],"is_corresponding":false,"raw_author_name":"Suk-Geun Hwang","raw_affiliation_strings":["Department of Mathematics Education, Kyungpook University","Department of Mathematics, University of Wisconsin-Whitewater","Department of Mathematics Education, Kyungpook University, Taegu 702-701, Korea;","Department of Mathematics, University of Wisconsin-Whitewater, Whitewater, WI 53190, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Kyungpook University","institution_ids":["https://openalex.org/I31419693"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Whitewater","institution_ids":["https://openalex.org/I183533211"]},{"raw_affiliation_string":"Department of Mathematics Education, Kyungpook University, Taegu 702-701, Korea;","institution_ids":["https://openalex.org/I31419693"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Whitewater, Whitewater, WI 53190, USA","institution_ids":["https://openalex.org/I183533211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086538085","display_name":"Ki-Bong Nam","orcid":null},"institutions":[{"id":"https://openalex.org/I183533211","display_name":"University of Wisconsin\u2013Whitewater","ror":"https://ror.org/049hrzs50","country_code":"US","type":"education","lineage":["https://openalex.org/I183533211"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ki-Bong Nam","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Whitewater","Department of Mathematics, University of Wisconsin-Whitewater, Whitewater, WI 53190, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Whitewater","institution_ids":["https://openalex.org/I183533211"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Whitewater, Whitewater, WI 53190, USA","institution_ids":["https://openalex.org/I183533211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086538085"],"corresponding_institution_ids":["https://openalex.org/I183533211"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09519369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"127","issue":"3","first_page":"269","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9886999726295471,"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":0.9886999726295471,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.9829445481300354},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.803337037563324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7274361252784729},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.6348391771316528},{"id":"https://openalex.org/keywords/pythagorean-triple","display_name":"Pythagorean triple","score":0.5908663272857666},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5740951299667358},{"id":"https://openalex.org/keywords/proofs-of-fermats-little-theorem","display_name":"Proofs of Fermat's little theorem","score":0.5728830695152283},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.4130297005176544},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39049604535102844},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36488497257232666},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3562178611755371},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.29159337282180786},{"id":"https://openalex.org/keywords/danskins-theorem","display_name":"Danskin's theorem","score":0.24077841639518738},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.07440134882926941},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06263822317123413}],"concepts":[{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.9829445481300354},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.803337037563324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7274361252784729},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6348391771316528},{"id":"https://openalex.org/C80918210","wikidata":"https://www.wikidata.org/wiki/Q208225","display_name":"Pythagorean triple","level":3,"score":0.5908663272857666},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5740951299667358},{"id":"https://openalex.org/C17566778","wikidata":"https://www.wikidata.org/wiki/Q467602","display_name":"Proofs of Fermat's little theorem","level":5,"score":0.5728830695152283},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.4130297005176544},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39049604535102844},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36488497257232666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3562178611755371},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.29159337282180786},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.24077841639518738},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.07440134882926941},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06263822317123413}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2020.1693228","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1693228","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":9,"referenced_works":["https://openalex.org/W1548377147","https://openalex.org/W1655183792","https://openalex.org/W2072715215","https://openalex.org/W2399124633","https://openalex.org/W2413283844","https://openalex.org/W2797281970","https://openalex.org/W4206238846","https://openalex.org/W4241103033","https://openalex.org/W4301476988"],"related_works":["https://openalex.org/W3038906685","https://openalex.org/W2392975301","https://openalex.org/W2259363500","https://openalex.org/W2387543012","https://openalex.org/W2064823537","https://openalex.org/W3209855679","https://openalex.org/W2561763748","https://openalex.org/W275792417","https://openalex.org/W4387891706","https://openalex.org/W4238377583"],"abstract_inverted_index":{"A":[0,58],"generalized":[1,41],"Pythagorean":[2,42],"theorem":[3,43],"is":[4,45,59],"an":[5],"equation":[6],"relating":[7],"the":[8,11,40,49,53,64],"squares":[9],"of":[10,13,15,27,39,52,55],"volumes":[12],"faces":[14],"a":[16,60],"particular":[17],"k-simplex":[18],"in":[19],"n-dimensional":[20],"Euclidean":[21],"space.":[22],"There":[23],"are":[24],"many":[25],"proofs":[26],"this":[28],"theorem.":[29],"This":[30],"note":[31],"presents":[32],"yet":[33],"another":[34],"very":[35],"short":[36],"elementary":[37],"proof":[38],"that":[44],"no":[46],"more":[47],"than":[48],"direct":[50],"expansion":[51],"determinant":[54],"ATA":[56],"where":[57],"matrix":[61],"determined":[62],"by":[63],"simplex.":[65]},"counts_by_year":[],"updated_date":"2026-02-01T03:34:12.195049","created_date":"2025-10-10T00:00:00"}