Dergiler / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 14 Sayı: 3

On Oresme Numbers and Their Geometric Interpretations

Serpil Halıcı(Science Faculty, Depertmant of Mathematics)0000-0002-8071-0437
Sayfa
1291–1300
Yayın Tarihi
2024-09-01
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We obtained important definitions and theorems for these sequences.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, we examined the Oresme sequences defined by Nicole Oresme.
📊
Temel Bulgular & Veri:We examined the geometric interpretation of Oresme sequences with rational coefficients which are defined by A.F.
💡
Sonuç & Katkı:We obtained important definitions and theorems for these sequences.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Reccurences · Fibonnacci generalizations · Oresme numbers

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.

🔖

Bu Makaleye Atıf Yap

Halıcı, S., Sayın, E. (2024). On Oresme Numbers and Their Geometric Interpretations. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 14 Sayı: 3, 1291–1300. https://doi.org/10.21597/jist.1421298

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (14)

  1. Atanassov K., 2002. New visual perspectives on Fibonacci numbers. World Scientific.
  2. Cetinberk K., Yuce, S., 2020. On Fibonacci Vectors. Hagia Sophia Journal of Geometry, 2(2), 12-25.
  3. Cook C. K., 2004. Some sums related to sums of Oresme numbers. In Applications of Fibonacci.
  4. Halici S., Gur Z., 2023. On Some Derivatives of k- Oresme Polynomials. Bulletin of The International Mathematical Virtual Institute, 13(1), 41-50.
  5. 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.
  6. Horadam A. F., 1965. Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly 3(3), 161–176.
  7. Horadam A. F., 1974. Oresme Numbers, The Fibonacci Quarterly 12(3), 267– 271.
  8. 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.
  9. Munarini E., 1997. A combinatorial interpretation of the generalized Fibonacci numbers. Advances in Applied Mathematics, 19(3), 306-318.
  10. Numbers and Their Applications, 87-99.
  11. Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci.
  12. Oresme N., 1961. Quaestiones super geometriam Euclidis, ed. by HLL Busard, 2 Vols.
  13. Salter E., 2005. Fibonacci Vectors. Graduate Theses and Dissertations, University of South Florida, USA.
  14. Numbers and Their Applications, 87-99.