Displaying similar documents to “Rotation indices related to Poncelet’s closure theorem”

Rotation indices related to Poncelet’s closure theorem

Waldemar Cieślak, Horst Martini, Witold Mozgawa (2015)

Annales UMCS, Mathematica

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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 ngons for any n > k.

Circuminscribed polygons in a plane annulus

Waldemar Cieślak, Elżbieta Szczygielska (2008)

Annales UMCS, Mathematica

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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.

Integral formula for secantoptics and its application

Witold Mozgawa, Magdalena Skrzypiec (2012)

Annales UMCS, Mathematica

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Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieślak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results. ...

A Construction of a Skewaffine Structure in Laguerre Geometry

Andrzej Matraś (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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J. Andre constructed a skewaffine structure as a group space of a normally transitive group. In this paper his construction is used to describe the structure of the set of circles not passing through a point of a Laguerre plane. Sufficient conditions to ensure that this structure is a skewaffine plane are given.

Integral formula for secantoptics and its application

Witold Mozgawa, Magdalena Skrzypiec (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieslak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results. ...