Geodesic
Rotation indices related to Poncelet’s closure theorem
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 2.

Voir la notice de l'article provenant de la source Library of Science

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 n- gons for any n gt; k. 
@article{AUM_2014_68_2_a6,
     author = {Cie\'slak, Waldemar and Martini, Horst and Mozgawa, Witold},
     title = {Rotation indices related to {Poncelet{\textquoteright}s} closure theorem},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2014_68_2_a6/}
}
TY  - JOUR
AU  - Cieślak, Waldemar
AU  - Martini, Horst
AU  - Mozgawa, Witold
TI  - Rotation indices related to Poncelet’s closure theorem
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2014
VL  - 68
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2014_68_2_a6/
LA  - en
ID  - AUM_2014_68_2_a6
ER  - 
%0 Journal Article
%A Cieślak, Waldemar
%A Martini, Horst
%A Mozgawa, Witold
%T Rotation indices related to Poncelet’s closure theorem
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2014
%V 68
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2014_68_2_a6/
%G en
%F AUM_2014_68_2_a6
Cieślak, Waldemar; Martini, Horst; Mozgawa, Witold. Rotation indices related to Poncelet’s closure theorem. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 68 (2014) no. 2. http://geodesic.mathdoc.fr/item/AUM_2014_68_2_a6/

[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.

[3] Bos, H. J. M., Kers, C., Dort, F., Raven, D. W., Poncelet’s closure theorem, Expo. Math. 5 (1987), 289–364.

[4] Cima, A., Gasull, A., Manosa, V., On Poncelet’s maps, Comput. Math. Appl. 60 (2010), 1457–1464.

[5] Cieslak, W., The Poncelet annuli, Beitr. Algebra Geom. 55 (2014), 301–309.

[6] Cieslak, 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.

[7] Lion, G., Variational aspects of Poncelet’s theorem, Geom. Dedicata 52 (1994), 105– 118.

[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.

[9] Schwartz, R., The Poncelet grid, Adv. Geom. 7 (2007), 157-175.

[10] Weisstein, E. W., Poncelet’s Porism, http:/mathworld. wolfram. com/Ponceletsporism.html