Open Access
June 2012 Some relations of Poncelet’s porism for two ellipses
Ben T. Nohara, Akio Arimoto
Proc. Japan Acad. Ser. A Math. Sci. 88(6): 85-90 (June 2012). DOI: 10.3792/pjaa.88.85


This paper shows the necessary and sufficient condition for bicentrical polygons which are circumscribed and inscribed by two ellipses using Jacobian elliptic functions. Moreover the formulae for a bicentrical triangle, quadrilateral and pentagon are presented and the fact that these formulae are the necessary and sufficient conditions for bicentrical polygons is presented.


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Ben T. Nohara. Akio Arimoto. "Some relations of Poncelet’s porism for two ellipses." Proc. Japan Acad. Ser. A Math. Sci. 88 (6) 85 - 90, June 2012.


Published: June 2012
First available in Project Euclid: 5 June 2012

zbMATH: 1248.51006
MathSciNet: MR2928896
Digital Object Identifier: 10.3792/pjaa.88.85

Primary: 33E05
Secondary: 51N15

Keywords: bicentrical polygons , elliptic functions , Poncelet’s closure theorem

Rights: Copyright © 2012 The Japan Academy

Vol.88 • No. 6 • June 2012
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