Generalization of dual numbers and dual Euclidean 3-space

Soylu Ş. D., Çolakoğlu H. B., Özdemir M.

Turkish Journal of Mathematics, vol.49, no.1, pp.29-48, 2025 (SCI-Expanded, Scopus, TRDizin) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.55730/1300-0098.3572
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.29-48
  • Keywords: dual angle, Dual numbers, dual vector, study map
  • Akdeniz University Affiliated: Yes

Abstract

In this study, we consider the generalized dual numbers and determine their algebraic and geometric properties. Then we generalize the well-known D3 module and introduce the generalized dual Euclidean 3-space with its scalar product and norm. After determining the conditions for being a unit generalized dual Euclidean vector, we derive the generalized Euclidean Study map which states that there is a bijective correspondence between directed lines of the space and the elements of the unit generalized dual Euclidean sphere. Finally, we define the dual Euclidean angle between two generalized dual Euclidean vectors.