Morley triangle

English right|thumb|A Morley triangle (purple) Morley's trisector theorem Etymology Named for Anglo-American mathematician Frank Morley. Noun en geometry Any of a number of triangles described in Morley's trisector theorem, especially the equilateral triangle formed from the points of intersection of adjacent angle trisectors of a given triangle. en 2009 Marcel Berger Geometry I 276 https://books.google.com.au/books?id=Se1HAAAAQBAJ&pg=PA276&dq=%22Morley+triangle%22%7C%22Morley+triangles%22&hl=en&sa=X&ved=0ahUKEwi7ocz0mejNAhWEJpQKHb7ZAloQ6AEIhgEwEQ#v=onepage&q=%22Morley%20triangle%22%7C%22Morley%20triangles%22&f=false Show that the sides of the Morley triangle of T (cf. 10.3.10) lie on three of those lines (notice that each vertex of the Morley triangle is the center of a cardioid lying inside T and tangent to all its sides, one of them twice.) en 2013 Dragoslav S. Mitrinovic; J. Pecaric; V. Volenec Recent Advances in Geometric Inequalities https://books.google.com.au/books?id=cEvqCAAAQBAJ&pg=PA276&dq=%22Morley+triangle%22%7C%22Morley+triangles%22&hl=en&sa=X&ved=0ahUKEwi7ocz0mejNAhWEJpQKHb7ZAloQ6AEIfjAQ#v=onepage&q=%22Morley%20triangle%22%7C%22Morley%20triangles%22&f=false 276 The length of a side of the Morley triangle of a given triangle T is less than one third the length of the smallest side of T.Remark. The Morley triangle of T is the equilateral triangle formed by the intersection in pairs of the angle trisectors of T. en 2016 Erik Seligman Math Mutation Classics 27 https://books.google.com.au/books?id=KC0WDAAAQBAJ&pg=PA27&dq=%22Morley+triangle%22%7C%22Morley+triangles%22&hl=en&sa=X&ved=0ahUKEwi7ocz0mejNAhWEJpQKHb7ZAloQ6AEIJjAA#v=onepage&q=%22Morley%20triangle%22%7C%22Morley%20triangles%22&f=false There are a total of 18 Morley triangles that can be constructed. One amusing article I spotted on the web was from a math enthusiast who wrote a computer program trying to illustrate the central Morley triangle we started with, but due to a bug actually trisected the exterior angles in come cases... and was surprised to produce equilateral Morley triangles anyway! Synonyms equilateral triangle formed by intersection points of adjacent trisectors en first Morley triangle, en Morley's triangle Derived terms en second Morley triangle en third Morley triangle Related terms en Morley centre / en Morley center Translations triangle formed by intersection points of adjacent trisectors French: fr triangle de Morley m German: de Morley-Dreieck n Italian: it primo triangolo di Morley m, it triangolo di Morley m See also en Hofstadter point en eponyms