Published in Scientific Papers. Series E. Land Reclamation, Earth Observation & Surveying, Environmental Engineering, Vol. XIV
Written by Cosmin-Constantin NIÈšU, Anca ROTMAN
Leonardo Fibonacci (c. 1170 - c. 1240-1250), an Italian mathematician often regarded as the most gifted European mathematician of the Middle Ages, played a crucial role in introducing the Hindu–Arabic numeral system to Europe. His seminal work, Liber Abaci (1202), not only promoted this numerical framework but also featured the now-famous Fibonacci sequence - an integer series with deep mathematical properties and widespread applications. This paper explores the mathematical foundations of the Fibonacci sequence, including its recurrence relations, algebraic and matrix representations, and connections to continuous fractions. Furthermore, it examines the relationship between the sequence and the golden ratio (φ), an irrational number often referred to as the "divine proportion". The golden ratio is linked to aesthetically pleasing proportions and appears in various domains such as art, architecture, music, biology, and cosmology. Through historical analysis and illustrative examples, this work highlights the enduring influence of Fibonacci’s legacy and the remarkable intersection between mathematical theory and patterns observed in the natural and cultural world.
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