6.AM. MORLEY'S THEOREM
This also has an extensive history and I give only a few items.
T. Delahaye and H. Lez. Problem no. 1655 (Morley's triangle). Mathesis (3) 8 (1908) 138 139. ??NYS.
E. J. Ebden, proposer; M. Satyanarayana, solver. Problem no. 16381 (Morley's theorem). The Educational Times (NS) 61 (1 Feb 1908) 81 & (1 Jul 1908) 307 308 = Math. Quest. and Solutions from "The Educational Times" (NS) 15 (1909) 23. Asks for various related triangles formed using interior and exterior trisectors to be shown equilateral. Solution is essentially trigonometric. No mention of Morley.
Frank Morley. On the intersections of the trisectors of the angles of a triangle. (From a letter directed to Prof. T. Hayashi.) J. Math. Assoc. of Japan for Secondary Education 6 (Dec 1924) 260 262. (= CM 3:10 (Dec 1977) 273 275.
Frank Morley. Letter to Gino Loria. 22 Aug 1934. Reproduced in: Gino Loria; Triangles équilatéraux dérivés d'un triangle quelconque. MG 23 (No. 256) (Oct 1939) 364 372. Morley says he discovered the theorem in c1904 and cites the letter to Hayashi. Loria mentions other early work and gives several generalizations.
H. F. Baker. Note 1476: A theorem due to Professor F. Morley. MG 24 (No. 261) (Oct 1940) 284 286. Easy proof and reference to other proofs. He cites a related result of Steiner.
Anonymous [R. P.] Morley's trisector theorem. Eureka 16 (Oct 1953) 6-7. Short proof, working backward from the equilateral triangle.
Dan Pedoe. Notes on Morley's proof of his theorem on angle trisectors. CM 3:10 (Dec 1977) 276 279. "... very tentative ... first steps towards the elucidation of his work."
C. O. Oakley & Charles W. Trigg. A list of references to the Morley theorem. CM 3:10 (Dec 1977) 281 290 & 4 (1978) 132. 169 items.
André Viricel (with Jacques Bouteloup). Le Théorème de Morley. L'Association pour le Développement de la Culture Scientifique, Amiens, 1993. [This publisher or this book was apparently taken over by Blanchard as Blanchard was selling copies with his label pasted over the previous publisher's name in Dec 1994.] A substantial book (180pp) on all aspects of the theorem. The bibliography is extremely cryptic, but says it is abridged from Mathesis (1949) 175 ??NYS. The most recent item cited is 1970.
Dostları ilə paylaş: |