Turkish Journal of Mathematics
Author ORCID Identifier
ŞÜKRAN SOYLU: 0000-0003-0432-4849
HARUN ÇOLAKOĞLU: 0000-0001-5559-9768
MUSTAFA ÖZDEMİR: 0000-0002-1359-4181
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.
DOI
10.55730/1300-0098.3572
Keywords
Dual numbers, dual vector, dual angle, study map
First Page
29
Last Page
48
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
SOYLU, ŞÜKRAN DUYGU; ÇOLAKOĞLU, HARUN BARIŞ; and ÖZDEMİR, MUSTAFA
(2025)
"Generalization of dual numbers and dual Euclidean 3-Space,"
Turkish Journal of Mathematics: Vol. 49:
No.
1, Article 4.
https://doi.org/10.55730/1300-0098.3572
Available at:
https://journals.tubitak.gov.tr/math/vol49/iss1/4
