The three points of intersection of the adjacent angle trisectors of any triangle always form an equilateral triangle. Discovered by Frank Morley, it is a celebrated example of a simple, surprising fact hidden in elementary geometry.
Facts
StatementIn any triangle, the points where each pair of adjacent angle trisectors meet form an equilateral triangle, called the Morley triangle. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Principal Result Of
Source MacTutor History of Mathematics, University of St Andrews: Frank Morley
Proved By
Source Morley's Trisector Theorem (Wikipedia)
Sources
1. Morley's Trisector Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, theorem statement sentence
In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle.
lead paragraph, discovery attribution sentence
The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley.
Proved By: Frank Morley, Lead
The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley.
View the Source MacTutor History of Mathematics, University of St Andrews: Frank Morley
MacTutor History of Mathematics, University of St AndrewsPrincipal Result Of: Frank Morley, Biography textQuote, Principal Result Of: Frank Morley, Biography text
He is best known for his theorem about the trisectors of the angles of a triangle.
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