# 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

top- [1] Berger, M., Geometry, I and II, Springer, Berlin, 1987.
- [2] Black, W. L., Howland, H. C., Howland, B., A theorem about zigzags between two circles, Amer. Math. Monthly 81 (1974), 754-757. Zbl0291.50008
- [3] Bos, H. J. M., Kers, C., Dort, F., Raven, D. W., Poncelet’s closure theorem, Expo. Math. 5 (1987), 289-364.[WoS] Zbl0633.51014
- [4] Cima, A., Gasull, A., Manosa, V., On Poncelet’s maps, Comput. Math. Appl. 60 (2010), 1457-1464.[WoS] Zbl1201.51024
- [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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