Trisectors like Bisectors with equilaterals instead of Points

It 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, w...

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Autor principal:	Kuruklis,Spiridon A
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2014
Materias:	Angle trisection Morley’s theorem Morley trisector theorem Morley triangle Morley interior equilateral Morley central equilateral Morley exterior equilateral Pasch’s axiom Morley’s magic Morley’s miracle Morley’s mystery
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462014000200005
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spelling	oai:scielo:S0719-064620140002000052018-10-08Trisectors like Bisectors with equilaterals instead of PointsKuruklis,Spiridon A Angle trisection Morley’s theorem Morley trisector theorem Morley triangle Morley interior equilateral Morley central equilateral Morley exterior equilateral Pasch’s axiom Morley’s magic Morley’s miracle Morley’s mystery It 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.16 n.2 20142014-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462014000200005en10.4067/S0719-06462014000200005
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Angle trisection Morley’s theorem Morley trisector theorem Morley triangle Morley interior equilateral Morley central equilateral Morley exterior equilateral Pasch’s axiom Morley’s magic Morley’s miracle Morley’s mystery
spellingShingle	Angle trisection Morley’s theorem Morley trisector theorem Morley triangle Morley interior equilateral Morley central equilateral Morley exterior equilateral Pasch’s axiom Morley’s magic Morley’s miracle Morley’s mystery Kuruklis,Spiridon A Trisectors like Bisectors with equilaterals instead of Points
description	It 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.
author	Kuruklis,Spiridon A
author_facet	Kuruklis,Spiridon A
author_sort	Kuruklis,Spiridon A
title	Trisectors like Bisectors with equilaterals instead of Points
title_short	Trisectors like Bisectors with equilaterals instead of Points
title_full	Trisectors like Bisectors with equilaterals instead of Points
title_fullStr	Trisectors like Bisectors with equilaterals instead of Points
title_full_unstemmed	Trisectors like Bisectors with equilaterals instead of Points
title_sort	trisectors like bisectors with equilaterals instead of points
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2014
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462014000200005
work_keys_str_mv	AT kuruklisspiridona trisectorslikebisectorswithequilateralsinsteadofpoints
_version_	1714206788874665984

Trisectors like Bisectors with equilaterals instead of Points

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