Abstract
In this study, we examined the Oresme sequences defined by Nicole Oresme. We examined the geometric interpretation of Oresme sequences with rational coefficients which are defined by A.F. Horadam as with initial conditions and . We defined the the vector of the Oresme sequence. We calculated the area and volume. We gave the general solution for four squares equation involving Oresme vectors. We calculated the Heron Formula of Oresme sequences. We defined the angle value between these sequences. We also obtained a relationship between the Oresme sequence and the generalized Fibonacci sequence in vector space. We calculated the area and volume of these sequence. We obtained important definitions and theorems for these sequences.
Supporting Institution
Pamukkale University, Bilimsel Araştırma Projeleri Koordinatörlüğü
Project Number
2023FEBE002
Thanks
This work was supported by Scientific Research Projects (BAP) Coordination Unit of Pamukkale University. Project No. 2023FEBE002.
References
- Atanassov K., 2002. New visual perspectives on Fibonacci numbers. World Scientific.
- Cetinberk K., Yuce, S., 2020. On Fibonacci Vectors. Hagia Sophia Journal of Geometry, 2(2), 12-25.
- Cook C. K., 2004. Some sums related to sums of Oresme numbers. In Applications of Fibonacci.
- Halici S., Gur Z., 2023. On Some Derivatives of k- Oresme Polynomials. Bulletin of The International Mathematical Virtual Institute, 13(1), 41-50.
- Halici S., Gur Z., Sayin E., 2022. k- Oresme Polynomials and Their Derivatives, Third International Conference on Mathematics and Its Applications in Science and Engineering, Bucharest, Romania, 4-7 July. Hilton P., Pedersen J., 1994. A note on a geometrical property of Fibonacci numbers, The Fibanacci Quarterly, 32, 386-388.
- Horadam A. F., 1965. Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly 3(3), 161–176.
- Horadam A. F., 1974. Oresme Numbers, The Fibonacci Quarterly 12(3), 267– 271.
- Kızılates C., 2021. New families of Horadam numbers associated with finite operators and their applications. Mathematical Methods in the Applied Sciences, 44(18), 14371-14381.
- Munarini E., 1997. A combinatorial interpretation of the generalized Fibonacci numbers. Advances in Applied Mathematics, 19(3), 306-318.
- Numbers and Their Applications , 87-99.
- Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci.
- Oresme N., 1961. Quaestiones super geometriam Euclidis, ed. by HLL Busard, 2 Vols.
- Salter E., 2005. Fibonacci Vectors. Graduate Theses and Dissertations, University of South Florida, USA.
Abstract
Project Number
2023FEBE002
References
- Atanassov K., 2002. New visual perspectives on Fibonacci numbers. World Scientific.
- Cetinberk K., Yuce, S., 2020. On Fibonacci Vectors. Hagia Sophia Journal of Geometry, 2(2), 12-25.
- Cook C. K., 2004. Some sums related to sums of Oresme numbers. In Applications of Fibonacci.
- Halici S., Gur Z., 2023. On Some Derivatives of k- Oresme Polynomials. Bulletin of The International Mathematical Virtual Institute, 13(1), 41-50.
- Halici S., Gur Z., Sayin E., 2022. k- Oresme Polynomials and Their Derivatives, Third International Conference on Mathematics and Its Applications in Science and Engineering, Bucharest, Romania, 4-7 July. Hilton P., Pedersen J., 1994. A note on a geometrical property of Fibonacci numbers, The Fibanacci Quarterly, 32, 386-388.
- Horadam A. F., 1965. Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly 3(3), 161–176.
- Horadam A. F., 1974. Oresme Numbers, The Fibonacci Quarterly 12(3), 267– 271.
- Kızılates C., 2021. New families of Horadam numbers associated with finite operators and their applications. Mathematical Methods in the Applied Sciences, 44(18), 14371-14381.
- Munarini E., 1997. A combinatorial interpretation of the generalized Fibonacci numbers. Advances in Applied Mathematics, 19(3), 306-318.
- Numbers and Their Applications , 87-99.
- Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci.
- Oresme N., 1961. Quaestiones super geometriam Euclidis, ed. by HLL Busard, 2 Vols.
- Salter E., 2005. Fibonacci Vectors. Graduate Theses and Dissertations, University of South Florida, USA.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Matematik / Mathematics |
| Authors | |
| Project Number | 2023FEBE002 |
| Early Pub Date | August 27, 2024 |
| Publication Date | September 1, 2024 |
| Submission Date | January 17, 2024 |
| Acceptance Date | May 2, 2024 |
| Published in Issue | Year 2024 Volume: 14 Issue: 3 |
