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Trisectors like Bisectors with equilaterals instead of Points

dc.creatorKuruklis, Spiridon A.
dc.date2014-06-01
dc.identifierhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/1278
dc.identifier10.4067/S0719-06462014000200005
dc.descriptionIt is established that among all Morley triangles of △ABC the only equilaterals are the ones determined by the intersections of the proximal to each side of △ABC trisectors of either interior, or exterior, or one interior and two exterior angles. It is showed that these are in fact equilaterals, with uniform proofs. It is then observed that the intersections of the interior trisectors with the sides of the interior Morley equilateral form three equilaterals. These along with Pasch’s axiom are utilized in showing that Morley’s theorem does not hold if the trisectors of one exterior and two interior angles are used in its statement.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttps://revistas.ufro.cl/ojs/index.php/cubo/article/view/1278/1130
dc.sourceCUBO, A Mathematical Journal; Vol. 16 No. 2 (2014): CUBO, A Mathematical Journal; 71–110en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 16 Núm. 2 (2014): CUBO, A Mathematical Journal; 71–110es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectAngle trisectionen-US
dc.subjectMorley’s theoremen-US
dc.subjectMorley trisector theoremen-US
dc.subjectMorley triangleen-US
dc.subjectMorley interior equilateralen-US
dc.subjectMorley central equilateralen-US
dc.subjectMorley exterior equilateralen-US
dc.subjectPasch’s axiomen-US
dc.subjectMorley’s magicen-US
dc.subjectMorley’s miracleen-US
dc.subjectMorley’s mysteryen-US
dc.titleTrisectors like Bisectors with equilaterals instead of Pointsen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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