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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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1898-9934
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Volume 23, Issue 2 (Jun 2015)

Issues

Morley’s Trisector Theorem

Roland Coghetto
  • Rue de la Brasserie 5 7100 La Louvière, Belgium
Published Online: 2015-08-13 | DOI: https://doi.org/10.1515/forma-2015-0007

Abstract

Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].

MSC: 51M04; 03B35

Keywords: Euclidean geometry; Morley’s trisector theorem; equilateral triangle

MML: identifier: EUCLID11; version: 8.1.045.32.1237

References

  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Google Scholar

  • [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Google Scholar

  • [3] Alexander Bogomolny. Morley’s miracle from interactive mathematics miscellany and puzzles. Cut the Knot, 2015.Google Scholar

  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Google Scholar

  • [5] Czesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.Google Scholar

  • [6] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Google Scholar

  • [7] Roland Coghetto. Some facts about trigonometry and Euclidean geometry. Formalized Mathematics, 22(4):313-319, 2014. doi:10.2478/forma-2014-0031.CrossrefGoogle Scholar

  • [8] Alain Connes. A new proof of Morley’s theorem. Publications Math´ematiques de l’IH ´ES, 88:43-46, 1998.Google Scholar

  • [9] John Conway. On Morley’s trisector theorem. The Mathematical Intelligencer, 36(3):3, 2014. ISSN 0343-6993. doi:10.1007/s00283-014-9463-3.Web of ScienceCrossrefGoogle Scholar

  • [10] H.S.M. Coxeter and S.L. Greitzer. Geometry Revisited. The Mathematical Association of America (Inc.), 1967.Google Scholar

  • [11] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Google Scholar

  • [12] Cesare Donolato. A vector-based proof of Morley’s trisector theorem. In Forum Geometricorum, volume 13, pages 233-235, 2013.Google Scholar

  • [13] O.A.S. Karamzadeh. Is John Conway’s proof of Morley’s theorem the simplest and free of A Deus Ex Machina ? The Mathematical Intelligencer, 36(3):4-7, 2014. ISSN 0343-6993. doi:10.1007/s00283-014-9481-1.CrossrefWeb of ScienceGoogle Scholar

  • [14] Akihiro Kubo and Yatsuka Nakamura. Angle and triangle in Euclidean topological space. Formalized Mathematics, 11(3):281-287, 2003.Google Scholar

  • [15] A. Letac. Solutions (Morley’s triangle). Problem N 490. Sphinx: revue mensuelle des questions r´ecr´eatives, 9, 1939.Google Scholar

  • [16] Eli Maor and Eugen Jost. Beautiful geometry. Princeton University Press, 2014.Google Scholar

  • [17] Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9 (3):455-460, 2001.Google Scholar

  • [18] Cletus O. Oakley and Justine C. Baker. The Morley trisector theorem. American Mathematical Monthly, pages 737-745, 1978.Google Scholar

  • [19] Marco Riccardi. Heron’s formula and Ptolemy’s theorem. Formalized Mathematics, 16 (2):97-101, 2008. doi:10.2478/v10037-008-0014-2.CrossrefGoogle Scholar

  • [20] Brian Stonebridge. A simple geometric proof of Morley’s trisector theorem. Applied Probability Trust, 2009.Google Scholar

  • [21] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Google Scholar

  • [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Google Scholar

  • [24] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.Google Scholar

About the article

Received: 2015-03-26

Published Online: 2015-08-13

Published in Print: 2015-06-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2015-0007.

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© by Roland Coghetto. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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