Dictionary

Morley triangle en · NOUN

Etymology

Named for Anglo-American mathematician Frank Morley.

Meanings

1. 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.
   • 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! 2016, Erik Seligman, Math Mutation Classics, page 27:
   • 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. 2013, Dragoslav S. Mitrinovic, J. Pecaric, V. Volenec, Recent Advances in Geometric Inequalities, page 276:
   • 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.) 2009, Marcel Berger, Geometry I, page 276:

Forms

Deriveds

second Morley triangle · third Morley triangle

Relateds

Morley center · Hofstadter point · Morley centre

Synonyms

equilateral triangle formed by intersection points of adjacent trisectors (first Morley triangle, Morley's triangle)

Translations (4)

it triangolo di Morley (triangle formed by intersection points of adjacent trisectors) · de Morley-Dreieck (triangle formed by intersection points of adjacent trisectors) · fr triangle de Morley (triangle formed by intersection points of adjacent trisectors) · it primo triangolo di Morley (triangle formed by intersection points of adjacent trisectors)

wikipedia: Frank Morley