Meaning of Morley triangle | Babel Free

Definitions

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.

Equivalents

Examples

“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.)”

“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.”

“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!”

CEFR level