Morley triangle
English
Etymology
Named for Anglo-American mathematician Frank Morley.
Noun
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.
- 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, 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
- (equilateral triangle formed by intersection points of adjacent trisectors): first Morley triangle, Morley's triangle
Derived terms
- second Morley triangle
- third Morley triangle
Related terms
- Morley centre / Morley center
Translations
triangle formed by intersection points of adjacent trisectors
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See also
- Hofstadter point
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