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Some miscellaneous results of the Fibonacci sequence and the golden ratio | ||
| Caspian Journal of Mathematical Sciences | ||
| دوره 14، شماره 2 - شماره پیاپی 26، مهر 2025، صفحه 394-409 اصل مقاله (723.03 K) | ||
| 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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آمار تعداد مشاهده مقاله: 44 تعداد دریافت فایل اصل مقاله: 15 |
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