On Poncelet’s porism

Waldemar Cieślak, Elżbieta Szczygielska

Abstract


We consider circular annuli with Poncelet’s porism property. We prove two identities which imply Chapple’s, Steiner’s and other formulas. All porisms can be expressed in the form in which elliptic functions are not used.

Keywords


Porism; annulus; bicentric polygon

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References


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

Cieślak, W., Szczygielska, E., Circuminscribed polygons in a plane annulus, Ann. Univ. Mariae Curie-Skłodowska Sect. A 62 (2008), 49-53.

Kerawala, S. M., Poncelet porism in two circles, Bull. Calcutta Math. Soc. 39 (1947), 85-105.

Weisstein, E. W., Poncelet’s Porism, From Math World - A Wolfram Web Resource. http://mathworld.wolfram.com/PonceletsPorism.html




DOI: http://dx.doi.org/10.17951/a.2010.54.2.21-28
Data publikacji: 2016-07-29 10:39:54
Data złożenia artykułu: 2016-07-28 21:58:59

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Copyright (c) 2010 Waldemar Cieślak, Elżbieta Szczygielska