Dissertation/Thesis Abstract

Extensions of Morley's theorem
by Gordon, Richard Harvey, M.A., San Jose State University, 1970, 122; 1489311
Abstract (Summary)

A review of the literature since 1899, when Morley offered his original hypothesis, is presented. 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 the n-sectors. An important by-product of the author's investigation of the p-sided polygon confirms the uniqueness of the equilateral triangle of Morley's theorem. The author concludes with a discussion of the associated isogonal attributes and thoughts for further study.

Indexing (document details)
Advisor: Smart, James R.
Commitee: Braun, Alfred S.
School: San Jose State University
Department: Mathematics
School Location: United States -- California
Source: MAI 49/04M, Masters Abstracts International
Subjects: Mathematics, Theoretical Mathematics
Keywords: Apollonius, Hessian, Isogonal, N-sectors, Quadrilateral, Trisectors
Publication Number: 1489311
ISBN: 978-1-124-50299-1
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