Morley triangle
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English[edit]
Etymology[edit]
Named for Anglo-American mathematician Frank Morley.
Noun[edit]
Morley triangle (plural Morley triangles)
- (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.
- 2009, Marcel Berger, Geometry I[1], 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.)
- 2013, Dragoslav S. Mitrinovic, J. Pecaric, V. Volenec, Recent Advances in Geometric Inequalities, 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.
- 2016, Erik Seligman, Math Mutation Classics[2], page 27:
- 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[edit]
- (equilateral triangle formed by intersection points of adjacent trisectors): first Morley triangle, Morley's triangle
Derived terms[edit]
Related terms[edit]
Translations[edit]
triangle formed by intersection points of adjacent trisectors
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