“A Study on the Relationship and Applications of the Fibonacci Sequence and the Golden Ratio”

Author(s)	Mr. Ajit Prataprao Dhumal
Country	India
Abstract	The Fibonacci sequence and the Golden Ratio represent fundamental mathematical patterns that exhibit a strong quantitative relationship and wide interdisciplinary relevance. This study investigates the mathematical convergence of the ratio of consecutive Fibonacci numbers toward the Golden Ratio (φ ≈ 1.618) and analyses their manifestations across natural, structural, and aesthetic systems. The research employs analytical and literature-based approaches to explore how these patterns describe biological morphogenesis, phyllotactic arrangements, architectural proportions, and artistic compositions. Mathematical modelling illustrates that the Fibonacci progression serves as a numerical approximation of the Golden Ratio, providing a framework for understanding growth efficiency and structural balance in nature and design. The study concludes that the Fibonacci–Golden Ratio relationship exemplifies the deep connection between mathematical theory and real-world phenomena, offering valuable insights into the optimization and harmony observed in both natural and human-created systems.
Keywords	Fibonacci sequence, Golden Ratio, Fibonacci number
Field	Mathematics
Published In	Volume 16, Issue 4, October-December 2025
Published On	2025-10-29
DOI	https://doi.org/10.71097/IJSAT.v16.i4.8931
Short DOI	https://doi.org/g98nc8

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