8:23 AM
specific-question Since it was bumped, it is an opportunity to retag the question correctly: Can Morley's theorem be generalized? I have added mg.metric-geometry. (The question had no top-level tag.) I was not sure whether to add triangles or not. This theorem is about triangles - OTOH the OP maybe hopes for generalization for simplices or some other objects.
22
Morley's theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle. In a talk some years ago, David Rusin made the provocative claim that Morley's theorem is a rare example of a striking theorem that defies generalization. ...
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. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley. It has various generalizations; in particular, if all of the trisectors are intersected, one obtains four other equilateral triangles.
== Proofs ==
There are many proofs of Morley's theorem, some of which are very technical.
Several early proofs were based on delicate trigonometric...
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12:27 PM
I have noticed a post which was bumped by changing Lebesque to Lebesgue: data.stackexchange.com/mathoverflow/query/1070272/…
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