A Trigonometrical Approach to Morley's Observation

Abstract: Simple trigonometrical arguments verify that in a triangle the trisectors, proximal to sides respectively, meet at the vertices of an equilateral triangle by showing that the length of each side is 8R times the sines of the angles between the sides of the triangle and the trisectors that d...

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Autores principales:	Gasteratos,Ioannis, Kuruklis,Spiridon, Kuruklis,Thedore
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2017
Materias:	Angle trisection;, proximal trisector triangle trisectors Morley's theorem Morley triangle Morley's magic Morley's miracle Morley's mystery
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200073
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spelling	oai:scielo:S0719-064620170002000732018-04-25A Trigonometrical Approach to Morley's ObservationGasteratos,IoannisKuruklis,SpiridonKuruklis,Thedore Angle trisection;, proximal trisector triangle trisectors Morley's theorem Morley triangle Morley's magic Morley's miracle Morley's mystery Abstract: Simple trigonometrical arguments verify that in a triangle the trisectors, proximal to sides respectively, meet at the vertices of an equilateral triangle by showing that the length of each side is 8R times the sines of the angles between the sides of the triangle and the trisectors that determine it, where R is the radius of the circumcircle of the triangle. The 27 meeting points of the trisectors, proximal to a side, determine 18 such equilaterals, which in pairs share a vertex having two collinear sides and the third parallel. Hence these points are located 6 by 6 on three triples of parallel lines.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.19 n.2 20172017-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200073en10.4067/S0719-06462017000200073
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Angle trisection;, proximal trisector triangle trisectors Morley's theorem Morley triangle Morley's magic Morley's miracle Morley's mystery
spellingShingle	Angle trisection;, proximal trisector triangle trisectors Morley's theorem Morley triangle Morley's magic Morley's miracle Morley's mystery Gasteratos,Ioannis Kuruklis,Spiridon Kuruklis,Thedore A Trigonometrical Approach to Morley's Observation
description	Abstract: Simple trigonometrical arguments verify that in a triangle the trisectors, proximal to sides respectively, meet at the vertices of an equilateral triangle by showing that the length of each side is 8R times the sines of the angles between the sides of the triangle and the trisectors that determine it, where R is the radius of the circumcircle of the triangle. The 27 meeting points of the trisectors, proximal to a side, determine 18 such equilaterals, which in pairs share a vertex having two collinear sides and the third parallel. Hence these points are located 6 by 6 on three triples of parallel lines.
author	Gasteratos,Ioannis Kuruklis,Spiridon Kuruklis,Thedore
author_facet	Gasteratos,Ioannis Kuruklis,Spiridon Kuruklis,Thedore
author_sort	Gasteratos,Ioannis
title	A Trigonometrical Approach to Morley's Observation
title_short	A Trigonometrical Approach to Morley's Observation
title_full	A Trigonometrical Approach to Morley's Observation
title_fullStr	A Trigonometrical Approach to Morley's Observation
title_full_unstemmed	A Trigonometrical Approach to Morley's Observation
title_sort	trigonometrical approach to morley's observation
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2017
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462017000200073
work_keys_str_mv	AT gasteratosioannis atrigonometricalapproachtomorleysobservation AT kuruklisspiridon atrigonometricalapproachtomorleysobservation AT kuruklisthedore atrigonometricalapproachtomorleysobservation AT gasteratosioannis trigonometricalapproachtomorleysobservation AT kuruklisspiridon trigonometricalapproachtomorleysobservation AT kuruklisthedore trigonometricalapproachtomorleysobservation
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A Trigonometrical Approach to Morley's Observation

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