Yazar "Atasoy, Ali" seçeneğine göre listele

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  • Küçük Resim
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    A new approach to curve couples with Bishop frame
    (Ankara Univ, Fac Sci, 2024) Babadağ, Faik; Atasoy, Ali
    . This paper presents a detailed study of a new generation of the Bishop frame with components including three orthogonal unit vectors, which are tangent vector, normal vector and binormal vector. It is a frame field described on a curve in Euclidean space, which is an alternative to the Frenet frame. It is useful for curves for which the second derivative is not available. Moreover, the conditions which the Bishop frame of one curve coincides with the Bishop frame of another curve are defined. It would be valuable to replicate similar approaches in the Bishop frame of one curve coincides with the Bishop frame of another curve.
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    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.
  • Küçük Resim
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    A New Polar Representation for Split and Dual Split Quaternions
    (Springer Basel Ag, 2017) Atasoy, Ali; Ata, Erhan; Yayli, Yusuf; Kemer, Yasemin
    We present a new different polar representation of split and dual split quaternions inspired by the Cayley-Dickson representation. In this new polar form representation, a split quaternion is represented by a pair of complex numbers, and a dual split quaternion is represented by a pair of dual complex numbers as in the Cayley-Dickson form. Here, in a split quaternion these two complex numbers are a complex modulus and a complex argument while in a dual split quaternion two dual complex numbers are a dual complex modulus and a dual complex argument. The modulus and argument are calculated from an arbitrary split quaternion in Cayley-Dickson form. Also, the dual modulus and dual argument are calculated from an arbitrary dual split quaternion in Cayley-Dickson form. By the help of polar representation for a dual split quaternion, we show that a Lorentzian screw operator can be written as product of two Lorentzian screw operators. One of these operators is in the two-dimensional space produced by 1 and i vectors. The other is in the three-dimensional space generated by 1, j and k vectors. Thus, an operator in a four-dimensional space is expressed by means of two operators in two and three-dimensional spaces. Here, vector 1 is in the intersection of these spaces.
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    Öğe
    Obtaining triplet from quaternions
    (Ramazan Yaman, 2021) Atasoy, Ali; Yayli, Yusuf
    In this study, we obtain triplets from quaternions. First, we obtain triplets from real quaternions. Then, as an application of this, we obtain dual triplets from the dual quaternions. Quaternions, in many areas, it allows ease in calculations and geometric representation. Quaternions are four dimensions. The triplets are in three dimensions. When we express quaternions with triplets, our study is conducted even easier. Quaternions are very important in the display of rotational movements. Dual quaternions are important in the expression of screw movements. Reducing movements from four dimensions to three dimensions makes our study easier. This simplicity is achieved by obtaining triplets from quaternions.
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    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.
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    Öğe
    Some Methods of Mathematical Calculation of Ali Kuscu in 15th Century
    (Istanbul Univ Press, Istanbul Univ Rectorate, 2020) Atasoy, Ali
    The contributions of Ali Kuscu (1403-1474) to science can be regarded as of great significance within the field of scientific studies. There is not much detailed research on the technical examination of these contributions. However, it is highly significant that his works in the field of mathematics and astronomy have remained in use for centuries as the main source in the world of science. He calculated the surface area of the moon with values very close to those measured by today's technology under the conditions of the 15th century, the century in which he lived. NASA also appreciated these works, and centuries later, a part of the month was named after Ali Kuscu. Ali Kuscu, who conducted important studies in the field of social sciences, is a versatile scientist in addition to his scientific achievements in astronomy and mathematics. He was not only content with the knowledge he gained in Samarkand, but he also improved himself in Tabriz. He became a respected scientist for centuries by developing himself in science and social fields during the period when transportation, communication and obtaining available information were very difficult. The conqueror of Istanbul won the appreciation of Fatih Sultan Mehmet, the sultan of the Ottoman Empire. He managed the madrasahs in Istanbul and gave lectures. Many scientists of the period took mathematics and astronomy lessons from Ali Kuscu. In this study, some mathematical methods used by Ali Kuscu in scientific calculations are examined. For this purpose, the study attempts to explain the effects of mathematical methods used in the world of science with the help of translations of some of Ali Kuscu's works.