- Tytuł:
- On rational radii coin representations of the wheel graph
- Autorzy:
-
Agnarsson, Geir
Dunham, Jill - Powiązania:
- https://bibliotekanauki.pl/articles/729067.pdf
- Data publikacji:
- 2013
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
planar graph
coin graph
flower
polynomial ring
Galois theory - Opis:
- A flower is a coin graph representation of the wheel graph. A petal of a flower is an outer coin connected to the center coin. The results of this paper are twofold. First we derive a parametrization of all the rational (and hence integer) radii coins of the 3-petal flower, also known as Apollonian circles or Soddy circles. Secondly we consider a general n-petal flower and show there is a unique irreducible polynomial Pₙ in n variables over the rationals ℚ, the affine variety of which contains the cosinus of the internal angles formed by the center coin and two consecutive petals of the flower. In that process we also derive a recursion that these irreducible polynomials satisfy.
- Źródło:
-
Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 2; 167-199
1509-9415 - Pojawia się w:
- Discussiones Mathematicae - General Algebra and Applications
- Dostawca treści:
- Biblioteka Nauki
Artykuł