A Poncelet Criterion for Special Pairs of Conics in PG(2,pm)PG(2,pm)PG(2,p^m)

Norbert HUNGERBÜHLER; Katharina KUSEJKO

doi:https://doi.org/10.36890/iejg.590595

Makale detayları

A Poncelet Criterion for Special Pairs of Conics in PG(2,pm)PG(2,pm)PG(2,p^m)

Yazarlar:

Norbert HUNGERBÜHLER | Katharina KUSEJKO

Yayıncı:

Kazım İLARSLAN

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Geometry 2020 Vol.13 Issue 1, pp.21-40

Belge Tipi:

Makale

Yayın Tarihi:

1/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000471682

Sıklık:

İki Yıllık

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.590595

Özet:

 


We study Poncelet's Theorem in finite projective planes over the field GF(q), q = pm for p an odd prime and m > 0, for a particular pencil of conics. We investigate whether we can find polygons with n sides which are inscribed in one conic and circumscribed around the other, so-called Poncelet Polygons. By using suitable elements of the dihedral group for these pairs, we prove that the length n of such Poncelet Polygons is independent of the starting point. In this sense Poncelet's Theorem is valid. By using Euler's divisor sum formula for the totient function, we can make a statement about the number of different conic pairs, which carry Poncelet Polygons of length n. Moreover, we will introduce polynomials whose zeros in GF(q) yield information about the relation of a given pair of conics. In particular, we can decide for a given integer n, whether and how we can find Poncelet Polygons

for pairs of conics in the plane PG(2,q). 

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Makale detayları

A Poncelet Criterion for Special Pairs of Conics in PG(2,pm)PG(2,pm)PG(2,p^m)

Yazarlar: Norbert HUNGERBÜHLER | Katharina KUSEJKO

Yayıncı: Kazım İLARSLAN

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Geometry 2020 Vol.13 Issue 1, pp.21-40

Belge Tipi: Makale

Yayın Tarihi: 1/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000471682

Sıklık: İki Yıllık

eISSN: 1307-5624

DOI: https://doi.org/10.36890/iejg.590595

Sayı

Yazarlar:

Norbert HUNGERBÜHLER | Katharina KUSEJKO

Yayıncı:

Kazım İLARSLAN

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Geometry 2020 Vol.13 Issue 1, pp.21-40

Belge Tipi:

Makale

Yayın Tarihi:

1/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000471682

Sıklık:

İki Yıllık

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.590595