Rotation indices related to Poncelet’s closure theorem
Waldemar Cieślak; Horst Martini; Witold Mozgawa
Annales UMCS, Mathematica (2015)
- Volume: 68, Issue: 2, page 19-26
- ISSN: 2083-7402
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topWaldemar Cieślak, Horst Martini, and Witold Mozgawa. "Rotation indices related to Poncelet’s closure theorem." Annales UMCS, Mathematica 68.2 (2015): 19-26. <http://eudml.org/doc/269955>.
@article{WaldemarCieślak2015,
abstract = {Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.},
author = {Waldemar Cieślak, Horst Martini, Witold Mozgawa},
journal = {Annales UMCS, Mathematica},
keywords = {Bar billiards; Euler’s triangle formula; Poncelet’s closure theorem; Poncelet’s porism property; bar billiards; Euler's triangle formula; Poncelet's closure theorem; Poncelet's porism property},
language = {eng},
number = {2},
pages = {19-26},
title = {Rotation indices related to Poncelet’s closure theorem},
url = {http://eudml.org/doc/269955},
volume = {68},
year = {2015},
}
TY - JOUR
AU - Waldemar Cieślak
AU - Horst Martini
AU - Witold Mozgawa
TI - Rotation indices related to Poncelet’s closure theorem
JO - Annales UMCS, Mathematica
PY - 2015
VL - 68
IS - 2
SP - 19
EP - 26
AB - Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.
LA - eng
KW - Bar billiards; Euler’s triangle formula; Poncelet’s closure theorem; Poncelet’s porism property; bar billiards; Euler's triangle formula; Poncelet's closure theorem; Poncelet's porism property
UR - http://eudml.org/doc/269955
ER -
References
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- [5] Cieślak, W., The Poncelet annuli, Beitr. Algebra Geom. 55 (2014), 301-309. Zbl1298.53004
- [6] Cieślak, W., Martini, H., Mozgawa, W., On the rotation index of bar billiards and Poncelet’s porism, Bull. Belg. Math. Soc. Simon Stevin 20 (2013), 287-300. Zbl1278.53006
- [7] Lion, G., Variational aspects of Poncelet’s theorem, Geom. Dedicata 52 (1994), 105-118. Zbl0808.51025
- [8] Martini, H., Recent results in elementary geometry, Part II, Symposia Gaussiana, Proc. 2nd Gauss Symposium (Munich, 1993), de Gruyter, Berlin and New York, 1995, 419-443. Zbl0852.51013
- [9] Schwartz, R., The Poncelet grid, Adv. Geom. 7 (2007), 157-175.[WoS] Zbl1123.51027
- [10] Weisstein, E. W., Poncelet’s Porism, http:/mathworld.wolfram.com/Ponceletsporism.html
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