Morley’s Trisector Theorem

Roland Coghetto

Formalized Mathematics (2015)

  • Volume: 23, Issue: 2, page 75-79
  • ISSN: 1426-2630

Abstract

top
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].

How to cite

top

Roland Coghetto. "Morley’s Trisector Theorem." Formalized Mathematics 23.2 (2015): 75-79. <http://eudml.org/doc/271793>.

@article{RolandCoghetto2015,
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].},
author = {Roland Coghetto},
journal = {Formalized Mathematics},
keywords = {Euclidean geometry; Morley’s trisector theorem; equilateral triangle; Morley's trisector theorem},
language = {eng},
number = {2},
pages = {75-79},
title = {Morley’s Trisector Theorem},
url = {http://eudml.org/doc/271793},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Roland Coghetto
TI - Morley’s Trisector Theorem
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 2
SP - 75
EP - 79
AB - 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].
LA - eng
KW - Euclidean geometry; Morley’s trisector theorem; equilateral triangle; Morley's trisector theorem
UR - http://eudml.org/doc/271793
ER -

References

top
  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  3. [3] Alexander Bogomolny. Morley’s miracle from interactive mathematics miscellany and puzzles. Cut the Knot, 2015. 
  4. [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. 
  5. [5] Czesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005. 
  6. [6] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  7. [7] Roland Coghetto. Some facts about trigonometry and Euclidean geometry. Formalized Mathematics, 22(4):313-319, 2014. doi:10.2478/forma-2014-0031. Zbl1316.51006
  8. [8] Alain Connes. A new proof of Morley’s theorem. Publications Math´ematiques de l’IH ´ES, 88:43-46, 1998. 
  9. [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. Zbl1308.51017
  10. [10] H.S.M. Coxeter and S.L. Greitzer. Geometry Revisited. The Mathematical Association of America (Inc.), 1967. Zbl0166.16402
  11. [11] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  12. [12] Cesare Donolato. A vector-based proof of Morley’s trisector theorem. In Forum Geometricorum, volume 13, pages 233-235, 2013. Zbl1282.51007
  13. [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. Zbl1309.51008
  14. [14] Akihiro Kubo and Yatsuka Nakamura. Angle and triangle in Euclidean topological space. Formalized Mathematics, 11(3):281-287, 2003. 
  15. [15] A. Letac. Solutions (Morley’s triangle). Problem N 490. Sphinx: revue mensuelle des questions r´ecr´eatives, 9, 1939. 
  16. [16] Eli Maor and Eugen Jost. Beautiful geometry. Princeton University Press, 2014. Zbl1323.51001
  17. [17] Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9 (3):455-460, 2001. 
  18. [18] Cletus O. Oakley and Justine C. Baker. The Morley trisector theorem. American Mathematical Monthly, pages 737-745, 1978. Zbl0406.01008
  19. [19] Marco Riccardi. Heron’s formula and Ptolemy’s theorem. Formalized Mathematics, 16 (2):97-101, 2008. doi:10.2478/v10037-008-0014-2. 
  20. [20] Brian Stonebridge. A simple geometric proof of Morley’s trisector theorem. Applied Probability Trust, 2009. 
  21. [21] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990. 
  22. [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  23. [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990. 
  24. [24] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.