fibonacci sequence science why its in nature

Fibonacci starts by declaring, “The nine Indian figures are: 9, 8, 7, 6, 5, 4, 3, 2, 1.

One essential element of the Liber Abaci was that it proposed the Hindu-Arabic numerical system to the West. Many people view the Liber Abaci as Fibonacci’s magnum opus because of the inclusion of not only pure mathematical elements such as the Hindu-Arabic system but also because of the introduction of applied mathematical elements such as cost and profit, barter, partnership, investment, allegation, and mensuration – the measuring of geometric magnitudes (Swetz, 2007). The book, much like Euclid’s Elements, became an object of fascination and was widely reproduced and disseminated in Europe after Fibonacci finished writing it (Waerden & Baitak, 2019). The Liber abaci further incorporates the preceding discoveries of Pythagoras, Euclid, and Diophantus, including algorithmic methods acquired from Arab sources. The number zero, originally serving as a place holder, would later serve as the foundation for the decimal system. In addition to the Fibonacci numbers, it also included the number Zephirum, which translates to zero (Ballieu, 2009). During this time, Fibonacci travelled around the Mediterranean to gain expertise in ancient counting systems, with a focus on the Hindu-Arabic system which would later serve as the basis of his book, Liber Abaci ( The Book of Calculations). Fibonacci taught mathematics in Bugia, where his father, who was a trader, held a diplomatic post (Gies, 2020). The Fibonacci numbers are generally acknowledged to originate from Italian mathematician Leonardo Pisano, also known as Fibonacci. This paper intends to highlight and elaborate on the origin and occurrences of the Fibonacci sequence and Fibonacci numbers, as well as the importance of the golden ratio not only in nature but also in scientific fields such as engineering. This problem is more famously termed as “the problem of division of a line segment in extreme and mean ratio” (Benavoli et al., 2019). The Golden Ratio is believed to have come from Euclid, particularly from his famous book Elements, where he tried to solve a problem concerning the division of a line segment into two unequal parts and noted the size ratio of the resultant parts. The term ‘Golden Ratio’ is often used interchangeably with the term ‘Golden Section,’ although some scholars have designated the term ‘Golden Section’ to be the reciprocal of the Golden Ratio.

The Golden Ratio is a concept that bears a strong connection to the Fibonacci Sequence. The Fibonacci sequence can be written as. Where Fn represents the nth Fibonacci number. The Fibonacci sequence, and the associated Fibonacci numbers, are defined by the following equation:į n = F n-1 + F n-2 for all n ≥ 3 where F 1 = 1 F 2 = 1 One source of natural patterns is the Fibonacci sequence and the associated Fibonacci numbers. The Fibonacci sequence has proven to be ubiquitous, not only in the natural world but also in some structures within the human body like the cochlea (Pietsch et al., 2017). Throughout history, human beings have engrossed themselves with the unabating search for patterns in the physical world.

Fibonacci sequence science why its in nature