Department of Mathematics
Server

Morley's Theoremm: In any triangle, adjacent trisectors meet at the vertices of an equilateral triangle. This theorem of the Euclidean plane was discovered by Frank Morley in 1896. The earliest geometric proof of this was due to T. Naraniengar (1909) and was popularized by H. S. M. Coxeter (in "Geometry, Revisited"). Since then there are many elegant geometric proofs of this theorem (most notably by John Conway in 1995, see [3]). Here we present a recent algebraic proof of this theorem due to 1982 Field Medalist Alain Connes.

References:

1. Frank Morley, Extensions of Clifford's chain theorem, Amer. J. Math. 51 (1929), p. 469.
2. T. Naraniengar, Mathematical Questions and Their Solutions from the Educational Times 15, 47, 1909
3. John Conway
4. Connes, Alain, A new proof of Morley's theorem. Les relations entre les mathématiques et la physique théorique, 43-46, Inst. Hautes Études Sci., Bures-sur-Yvette, 1998.