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Extensions Of Morley's Theorem, Richard Harvey Gordon

Master's Theses

A review of the literature since 1899 when Morley offered his original hypothesis. Various authors have given proofs of the theorem, shown the existence of 27 such triangles, and established relationships to other mathematical concepts: isogonal conjugates, Lemoine point, Hessian points and axis, circles of Apollonius, Brianchon hexagons. The author explores the various intersections of the n-sectors of the angles of a general triangle, showing, incidentally, the uniqueness of the Morley equilateral triangle. Turning to the quadrilateral, the intersections of the tri-sectors of: the angles of a parallelogram, rectangle, trapezoid, and kite-shaped quadrilateral are examined, as well as those of …