The Divine Number System: Exploring the Fibonacci Numbers and Sequences

Abstract

The Fibonacci sequence has long been regarded as a divine number system due to its remarkable recurrence in mathematics, nature, art, architecture, and various other disciplines. Elements such as fruits, flowers, leaves, hills, valleys, the Himalayas, rivers, and springs demonstrate a rhythmic balance that makes them aesthetically pleasing. These ideas are of common interest not only for mathematicians but also to biologists, psychologists, architects, artists, musicians, designers, and many other professionals. This research presents an insight into the divine number system through an integrated analytical and exploratory approach to its fundamental patterns, recurrence relations, mathematical structures, identities, properties, and their aesthetic significance. It combines classical recurrence analysis, the golden ratio, Fibonacci ratio, Binet’s formulae, Fibonacci-type sequences, Lucas numbers, Fibonacci matrices, and their generalizations to address the gap via library-based investigations for the broad horizon and area of interest in multidisciplinary research.