Morley triangle
nounEtymology Named for Anglo-American mathematician Frank Morley.
1
Geometry, Mathematics, Sciences 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.
- 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:
- 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:
1 more example
- 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:
- Synonyms
- equilateral triangle formed by intersection points of adjacent trisectors
- Derived terms
- second Morley triangle, third Morley triangle
- Related terms
- Morley centre, Morley center, Hofstadter point