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Ramezani, Sayyed Mehrab, Kamandar, Mahdi, Delbaznasab, ‎Ali, Ilkhanizadeh Manesh, Asma. (1404). Some miscellaneous results of the Fibonacci sequence and the golden ratio. پژوهشنامه مدیریت اجرایی, (), -. doi: 10.22080/cjms.2025.29210.1759
Sayyed Mehrab Ramezani; Mahdi Kamandar; ‎Ali Delbaznasab; Asma Ilkhanizadeh Manesh. "Some miscellaneous results of the Fibonacci sequence and the golden ratio". پژوهشنامه مدیریت اجرایی, , , 1404, -. doi: 10.22080/cjms.2025.29210.1759
Ramezani, Sayyed Mehrab, Kamandar, Mahdi, Delbaznasab, ‎Ali, Ilkhanizadeh Manesh, Asma. (1404). 'Some miscellaneous results of the Fibonacci sequence and the golden ratio', پژوهشنامه مدیریت اجرایی, (), pp. -. doi: 10.22080/cjms.2025.29210.1759
Ramezani, Sayyed Mehrab, Kamandar, Mahdi, Delbaznasab, ‎Ali, Ilkhanizadeh Manesh, Asma. Some miscellaneous results of the Fibonacci sequence and the golden ratio. پژوهشنامه مدیریت اجرایی, 1404; (): -. doi: 10.22080/cjms.2025.29210.1759

Some miscellaneous results of the Fibonacci sequence and the golden ratio

Caspian Journal of Mathematical Sciences
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 مهر 1404
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2025.29210.1759
نویسندگان
Sayyed Mehrab Ramezani* 1؛ Mahdi Kamandar2؛ ‎Ali Delbaznasab3؛ Asma Ilkhanizadeh Manesh4
1‎Faculty of Technology and Mining, ‎Yasouj University
2‎‎Department of Applied Mathematics‎, ‎Faculty of Mathematics and Computer‎, ‎Shahid Bahonar University of Kerman, Kerman‎, ‎Iran.
3Farhangian University, Yasouj‎, ‎Iran
4‎‎Department of Mathematics‎, ‎Vali-e-Asr University of Rafsanjan, Rafsanjan‎, ‎Iran
تاریخ دریافت: 20 اردیبهشت 1404،  تاریخ بازنگری: 04 مرداد 1404،  تاریخ پذیرش: 26 مرداد 1404 
چکیده
The Fibonacci sequence and the golden ratio
for centuries due to their deep mathematical properties and diverse applications in theoretical and applied fields. This paper explores the mathematical relationships between these two concepts and their practical uses in different fields. We construct a power series using Fibonacci numbers and demonstrate that the radius of convergence of this series is equal to the golden ratio. Furthermore, we investigate the conditions under which three Fibonacci numbers can form a triangle and analyze the properties of such triangles. We also introduce the concept of pseudo-right-angled triangles and provide a characterization of these figures. Finally, we analyze and decompose the polynomial \( x^n - F_n x - F_{n-1} = 0 \), a relation in which the golden ratio emerges as a root.
کلیدواژه‌ها
Fibonacci Sequence؛ Golden Ratio؛ Pseudo-Right-Angled
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