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    Öğe
    A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors
    (Amer Inst Mathematical Sciences-Aims, 2023) Babadag, Faik
    This paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented. In addition, a new dual vector called the dual Jacobsthal vector is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of dual space. Finally, this study introduces the dual Jacobsthal and the dual Jacobsthal-Lucas numbers with coefficients of dual numbers. Some fundamental identities are demonstrated, such as the generating function, the Binet formulas, the Cassini's, Catalan's and d'Ocagne identities for these numbers.
  • [ X ]
    Öğe
    A new approach to Leonardo number sequences with the dual vector and dual angle representation
    (Amer Inst Mathematical Sciences-Aims, 2024) Babadag, Faik; Atasoy, Ali
    In this paper, we introduce dual numbers with components including Leonardo number sequences. This novel approach facilitates our understanding of dual numbers and properties of Leonardo sequences. We also investigate fundamental properties and identities associated with Leonardo number sequences, such as Binet's formula and Catalan's, Cassini's and D'ocagne's identities. Furthermore, we also introduce a dual vector with components including Leonardo number sequences and dual angles. This extension not only deepens our understanding of dual numbers, it also highlights the interconnectedness between numerical sequences and geometric concepts. In the future it would be valuable to replicate a similar exploration and development of our findings on dual numbers with Leonardo number sequences.
  • [ X ]
    Öğe
    On hyper-dual vectors and angles with Pell, Pell-Lucas numbers
    (Amer Inst Mathematical Sciences-Aims, 2024) Babadag, Faik; Atasoy, Ali
    In this paper, we introduce two types of hyper-dual numbers with components including Pell and Pell-Lucas numbers. This novel approach facilitates our understanding of hyper-dual numbers and properties of Pell and Pell-Lucas numbers. We also investigate fundamental properties and identities associated with Pell and Pell-Lucas numbers, such as the Binet-like formulas, Vajda-like, Catalan-like, Cassini-like, and d'Ocagne-like identities. Furthermore, we also define hyper-dual vectors by using Pell and Pell-Lucas vectors and discuse hyper-dual angles. This extensionis not only dependent on our understanding of dual numbers, it also highlights the interconnectedness between integer sequences and geometric concepts.
  • Küçük Resim
    Öğe
    A Study on Quaternionic B-2-Slant Helix in Semi-Euclidean 4-Space
    (Rgn Publ, 2016) Babadag, Faik
    In this work, we defined a quaternionic B-2-slant helix in semi-Euclidean space E-2(4). Then we gave Frenet formulae for the quaternionic curve in semi-Euclidean space E-2(4). Also, we investigated some necessary and sufficient conditions for a space curve to be a quaternionic B-2-slant helix according to quaternionic curves in semi-Euclidean space E-2(4).