| Title:
|
Lepidoptera mathematica aneb rozličná zobecnění věty o motýlovi (Czech) |
| Title:
|
Lepidoptera Mathematica, or the Varied Generalizations of the Butterfly Theorem (English) |
| Author:
|
Štěpánová, Martina |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
263-281 |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Článek je věnován zobecněním tzv. věty o motýlovi, půvabného planimetrického tvrzení o tětivách dané kružnice. (Czech) |
| MSC:
|
51-02 |
| . |
| Date available:
|
2019-01-29T13:24:31Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147584 |
| . |
| Reference:
|
[1] Bezverkhnyev, Y.: Haruki’s lemma and a related locus problem.. Forum Geom. 8 (2008), 63–72. MR 2429392 |
| Reference:
|
[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 |
| Reference:
|
[3] Bogomolny, A.: Interactive mathematics miscellany and puzzles: The butterfly theorem. [online]. Dostupné z: https://www.cut-the-knot.org/pythagoras/Butterfly.shtml |
| Reference:
|
[4] Bogomolny, A.: Interactive mathematics miscellany and puzzles: A better butterfly theorem. [online]. Dostupné z: http://www.cut-the-knot.org/pythagoras/BetterButterfly.shtml |
| Reference:
|
[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 |
| Reference:
|
[6] Coxeter, H. S. M., Greitzer, S. L.: Geometry revisited.. Mathematical Association of America, Washington, 1967. MR 3155265 |
| Reference:
|
[7] Craik, A. D. D., O’Connor, J. J.: Some unknown documents associated with William Wallace (1768–1843).. BSHM Bull. 26 (2011), 17–28. MR 2787219, 10.1080/17498430.2010.503555 |
| Reference:
|
[8] Čerin, Z.: A generalization of the butterfly theorem from circles to conics.. Math. Commun. 6 (2001), 161–164. MR 1908335 |
| Reference:
|
[9] Donaldo, C.: A proof of the butterfly theorem using Ceva’s theorem.. Forum Geom. 16 (2016), 185–186. MR 3499737 |
| Reference:
|
[10] Klamkin, M. S.: An extension of the butterfly problem.. Math. Mag. 38 (1965), 206–208. MR 1571542, 10.1080/0025570X.1965.11975634 |
| Reference:
|
[11] Kung, S.: A butterfly theorem for quadrilaterals.. Math. Mag. 78 (2005), 314–316. 10.1080/0025570X.2005.11953348 |
| Reference:
|
[12] Prasolov, V. V.: Problems in planimetry.. Nauka, Moscow, 1986. |
| Reference:
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[13] Shklyarsky, O., Chentsov, N. N., Yaglom, I. M.: Selected problems and theorems of elementary mathematics.. Moscow, 1952. |
| Reference:
|
[14] Sledge, J.: A generalization of the butterfly theorem.. J. Undergraduate Math. 5 (1973), 3–4. |
| Reference:
|
[15] Sliepčević, A.: A new generalization of the butterfly theorem.. J. Geom. Graph. 6 (2002), 61–68. MR 1953134 |
| Reference:
|
[16] Štěpánová, M.: Věta o motýlech.. In: Cesty k matematice III, Hromadová, J., Slavík, A. (eds.), MatfyzPress, Praha, 2018, 103–124. |
| Reference:
|
[17] Trí, Trần Thúc Minh: Mathematics stack exchange: Generalized butterfly theorem. [online]. Dostupné z: https://math.stackexchange.com/questions/2640237/generalized-butterfly-theorem |
| Reference:
|
[18] Volenec, V.: A generalization of the butterfly theorem.. Math. Commun. 5 (2000), 157–160. MR 1816270 |
| Reference:
|
[19] Volenec, V.: The butterfly theorem for conics.. Math. Commun. 7 (2002), 35–38. MR 1932541 |
| . |
