A new proof of Morley’s theorem. (English) Zbl 1006.51010

Connes, Alain

Les relations entre les mathématiques et la physique théorique. Bures-sur-Yvette: Institut des Hautes Études Scientifiques, 43-46 (1998).

The author gives a conceptual proof of Morley’s famous theorem on angle trisectors of arbitrary triangles in the Euclidean plane. He presents the statement as a group theoretic property of the action of the affine group on the line. This will be valid for any commutative field \(k\) with arbitrary characteristic (though in characteristic 3 the hypothesis of the theorem cannot be satisfied).
For the entire collection see [Zbl 0923.00032].

Reviewer: Horst Martini (Chemnitz)

MSC:

51M04

Elementary problems in Euclidean geometries

Keywords:

Morley’s theorem; angle trisectors; affine group