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Article

MSC: 51-02
Summary:
Článek je věnován zobecněním tzv. věty o motýlovi, půvabného planimetrického tvrzení o tětivách dané kružnice.
References:
[1] Bezverkhnyev, Y.: Haruki’s lemma and a related locus problem. Forum Geom. 8 (2008), 63–72. MR 2429392
[2] Bogomolny, A.: Interactive mathematics miscellany and puzzles: William Wallace proof of the butterfly theorem. [online]. Dostupné z: https://www.cut-the-knot.org/pythagoras/WilliamWallaceButterfly.shtml
[3] Bogomolny, A.: Interactive mathematics miscellany and puzzles: The butterfly theorem. [online]. Dostupné z: https://www.cut-the-knot.org/pythagoras/Butterfly.shtml
[4] Bogomolny, A.: Interactive mathematics miscellany and puzzles: A better butterfly theorem. [online]. Dostupné z: http://www.cut-the-knot.org/pythagoras/BetterButterfly.shtml
[5] Celli, M.: A proof of the butterfly theorem using the similarity factor of the two wings. Forum Geom. 16 (2016), 337–338. MR 3567316
[6] Coxeter, H. S. M., Greitzer, S. L.: Geometry revisited. Mathematical Association of America, Washington, 1967. MR 3155265
[7] Craik, A. D. D., O’Connor, J. J.: Some unknown documents associated with William Wallace (1768–1843). BSHM Bull. 26 (2011), 17–28. DOI 10.1080/17498430.2010.503555 | MR 2787219
[8] Čerin, Z.: A generalization of the butterfly theorem from circles to conics. Math. Commun. 6 (2001), 161–164. MR 1908335
[9] Donaldo, C.: A proof of the butterfly theorem using Ceva’s theorem. Forum Geom. 16 (2016), 185–186. MR 3499737
[10] Klamkin, M. S.: An extension of the butterfly problem. Math. Mag. 38 (1965), 206–208. DOI 10.1080/0025570X.1965.11975634 | MR 1571542
[11] Kung, S.: A butterfly theorem for quadrilaterals. Math. Mag. 78 (2005), 314–316. DOI 10.1080/0025570X.2005.11953348
[12] Prasolov, V. V.: Problems in planimetry. Nauka, Moscow, 1986.
[13] Shklyarsky, O., Chentsov, N. N., Yaglom, I. M.: Selected problems and theorems of elementary mathematics. Moscow, 1952.
[14] Sledge, J.: A generalization of the butterfly theorem. J. Undergraduate Math. 5 (1973), 3–4.
[15] Sliepčević, A.: A new generalization of the butterfly theorem. J. Geom. Graph. 6 (2002), 61–68. MR 1953134
[16] Štěpánová, M.: Věta o motýlech. In: Cesty k matematice III, Hromadová, J., Slavík, A. (eds.), MatfyzPress, Praha, 2018, 103–124.
[17] Trí, Trần Thúc Minh: Mathematics stack exchange: Generalized butterfly theorem. [online]. Dostupné z: https://math.stackexchange.com/questions/2640237/generalized-butterfly-theorem
[18] Volenec, V.: A generalization of the butterfly theorem. Math. Commun. 5 (2000), 157–160. MR 1816270
[19] Volenec, V.: The butterfly theorem for conics. Math. Commun. 7 (2002), 35–38. MR 1932541
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