The Minimal Polynomials of 2cos(pi/2k) over the Rationals

DEMİRCİ M., Ikikardes N. Y., Ozgur B., CANGÜL İ. N.

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Halkidiki, Yunanistan, 19 - 25 Eylül 2011, cilt.1389 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 1389
  • Doi Numarası: 10.1063/1.3636731
  • Basıldığı Şehir: Halkidiki
  • Basıldığı Ülke: Yunanistan
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

The number lambda(q) = 2cos pi/q, q is an element of N, q >= 3, appears in the study of Hecke groups which are Fuchsian groups of the first kind, and in the study of regular polyhedra. Here we obtained the minimal polynomial of this number by means of the better known Chebycheff polynomials and the set of roots on the extension Q(lambda(q)). We follow some kind of inductive method on the number q. The minimal polynomial is obtained for even q.