A Comprehensive Survey on the Fibonacci Sequence and Its Applications

Anshika Rani, Braham Pal Singh

Abstract: The Fibonacci sequence is a fundamental mathematical pattern in which each term is the sum of the two preceding numbers. This paper examines its key mathematical properties, its close relationship with the golden ratio and its relationships with Pascal?s triangle. It explores the occurrence of Fibonacci patterns in nature, including plants, flowers, and spiral structures. The study also highlights its applications in art, architecture, and the human body. In addition, the paper discusses its role in computer science, particularly in algorithms and data structures, and reviews modern research, emphasizing its wide relevance across science, mathematics, and technology.

Keywords: Fibonacci sequence, Golden Ratio (φ), Recurrence relation, Pascal?s triangle, Applications in nature and Computer algorithm