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EXTREMAL PERIMETERS OF QUADRANGLES IN THE PONCELET PORISM

Part of: General convexity Classical differential geometry Real and complex geometry Analytic and descriptive geometry

Published online by Cambridge University Press:  13 February 2015

WALDEMAR CIEŚLAK  and
WITOLD MOZGAWA
WALDEMAR CIEŚLAK
Affiliation:
Politechnika Lubelska, Katedra Matematyki Stosowanej, ul. Nadbystrzycka 40, 20-618 Lublin, Poland email izacieslak@wp.pl
WITOLD MOZGAWA*
Affiliation:
Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland email mozgawa@poczta.umcs.lublin.pl
*
✉mozgawa@poczta.umcs.lublin.pl
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Abstract

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Extremal problems for quadrangles circuminscribed in a circular annulus with the Poncelet porism property are considered. Quadrangles with the maximal and the minimal perimeters are determined. Two conjectures end the paper.

Keywords

Poncelet porismPoncelet’s closure theoremextremal quadrangles

MSC classification

Primary: 51M04: Elementary problems in Euclidean geometries
Secondary: 51N20: Euclidean analytic geometry 52A10: Convex sets in $2$ dimensions (including convex curves) 53A04: Curves in Euclidean space
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 3 , June 2015 , pp. 487 - 501
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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