{"id":"https://openalex.org/W7225338077","doi":"https://doi.org/10.5281/zenodo.23973494","title":"Pedal triangles, self-adjoint affine maps and a two-thirds similarity","display_name":"Pedal triangles, self-adjoint affine maps and a two-thirds similarity","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225338077","doi":"https://doi.org/10.5281/zenodo.23973494"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23973494","doi":"https://doi.org/10.5281/zenodo.23973494","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23973494","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.23973494","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160898499","display_name":"Hoang Long Nguyen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nguyen, Hoang Long","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160898499"],"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/pedal-triangle","display_name":"pedal triangle","score":0.9769999980926514},{"id":"https://openalex.org/keywords/simson-line","display_name":"Simson line","score":0.8500000238418579},{"id":"https://openalex.org/keywords/circumcircle","display_name":"circumcircle","score":0.6970000267028809},{"id":"https://openalex.org/keywords/triangle-centers","display_name":"triangle centers","score":0.5170000195503235}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7376000285148621},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7218000292778015},{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.6920999884605408},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6287999749183655},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5583000183105469},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5289999842643738},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4943000078201294},{"id":"https://openalex.org/C97787015","wikidata":"https://www.wikidata.org/wiki/Q10615255","display_name":"Incircle and excircles of a triangle","level":2,"score":0.4462999999523163},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33719998598098755},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.275299996137619},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23973494","doi":"https://doi.org/10.5281/zenodo.23973494","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23973494","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.23973495","doi":"https://doi.org/10.5281/zenodo.23973495","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23973495","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.23973494","doi":"https://doi.org/10.5281/zenodo.23973494","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23973494","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1489854032","https://openalex.org/W7098982194","https://openalex.org/W2075701577","https://openalex.org/W3165135777","https://openalex.org/W7100865163","https://openalex.org/W1921609687","https://openalex.org/W6990076753","https://openalex.org/W7225347906","https://openalex.org/W7050366","https://openalex.org/W2050220617"],"abstract_inverted_index":{"The":[0],"affine":[1],"map":[2],"sending":[3],"a":[4,34,40,73,82],"triangle":[5,10,32,74],"ABC":[6,78],"to":[7,18,77],"an":[8],"inscribed":[9],"A1B1C1":[11,28],"is":[12,29,38],"self-adjoint":[13],"exactly":[14],"when":[15,27],"the":[16,19,30,50,54,59,62,69],"perpendiculars":[17],"sides":[20],"at":[21],"A1,":[22],"B1,":[23],"C1":[24],"concur,":[25],"i.e.":[26],"pedal":[31,86],"of":[33,53],"point":[35],"M.":[36],"It":[37],"then":[39],"pure":[41],"strain":[42],"with":[43,79],"principal":[44],"factors":[45],"(\u22121":[46],"\u00b1":[47],"OM/R)/2":[48],"along":[49],"Simson-line":[51],"directions":[52],"points":[55,63],"where":[56],"OM":[57],"meets":[58],"circumcircle.":[60],"Consequently,":[61],"dividing":[64],"AA1,":[65],"BB1,":[66],"CC1":[67],"in":[68],"ratio":[70,80],"2:1":[71],"form":[72],"inversely":[75],"similar":[76],"OM/(3R),":[81],"property":[83],"that":[84],"characterizes":[85],"triangles.":[87]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}