Circuminscribed polygons in a plane annulus
Waldemar Cieślak; Elżbieta Szczygielska
Annales UMCS, Mathematica (2008)
- Volume: 62, Issue: 1, page 49-53
- ISSN: 2083-7402
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topWaldemar Cieślak, and Elżbieta Szczygielska. "Circuminscribed polygons in a plane annulus." Annales UMCS, Mathematica 62.1 (2008): 49-53. <http://eudml.org/doc/268216>.
@article{WaldemarCieślak2008,
abstract = {Each oval and a natural number n ≥ 3 generate an annulus which possesses the Poncelet's porism property. A necessary and sufficient condition of existence of circuminscribed n-gons in an annulus is given.},
author = {Waldemar Cieślak, Elżbieta Szczygielska},
journal = {Annales UMCS, Mathematica},
keywords = {Poncelet's porism; isoptics; parallel curves},
language = {eng},
number = {1},
pages = {49-53},
title = {Circuminscribed polygons in a plane annulus},
url = {http://eudml.org/doc/268216},
volume = {62},
year = {2008},
}
TY - JOUR
AU - Waldemar Cieślak
AU - Elżbieta Szczygielska
TI - Circuminscribed polygons in a plane annulus
JO - Annales UMCS, Mathematica
PY - 2008
VL - 62
IS - 1
SP - 49
EP - 53
AB - Each oval and a natural number n ≥ 3 generate an annulus which possesses the Poncelet's porism property. A necessary and sufficient condition of existence of circuminscribed n-gons in an annulus is given.
LA - eng
KW - Poncelet's porism; isoptics; parallel curves
UR - http://eudml.org/doc/268216
ER -
References
top- Berger, M., Geometry I, Springer-Verlag, New York, 1994.
- Bos, H. J. M., Kers, C., Oort, F. and Raven, D. W., Poncelet's closure theorem, Exposition. Math. 5 (1987), 289-364. Zbl0633.51014
- Cieślak, W., Miernowski, A. and Mozgawa, W., Isoptics of a closed strictly convex curve, Global differential geometry and global analysis (Berlin, 1990), Lecture Notes in Math., 1481, Springer, Berlin, 1991, 28-35. Zbl0739.53001
- Laugwitz, D., Differential and Riemannian Geometry, Academic Press, New York-London, 1965. Zbl0139.38903
- Mozgawa, W., Bar billiards and Poncelet's porism, to appear.[WoS] Zbl1165.53303
- Santalo, L., Integral geometry and geometric probability, Encyclopedia of Mathematics and Its Applications, Vol. 1, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976.
- Weisstein, E. W., Poncelet's Porism, From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/ponceletsPorism.html
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