Leonardo Fibonacci, or more famously known as “Fibonacci”, was an Italian mathematician from the middle ages born in the late twelfth century in Pisa. Little is known to the world about his personal life, however, his works and discoveries regarding the field of math have most definitely left a significant impact on the history of numbers.
Fibonacci is best known for his book: “Liber Abaci” which brought about a huge change amongst the European mathematics system. After studying the different numerical systems and methods of calculation from various countries such as Egypt, Syria, Greece, Sicily, and Provence, he introduced the Hindu-Arabic numeral system via his book to the western mathematicians. This included various notations, the principle of place values, and the use of numerals in arithmetical operations. Although it initially did not receive much appreciation due to the Crusades (religious wars initiated by the Latin Church against Islam), people eventually changed their myopic views and the Hindu-Arabic numeral system prevailed the Roman numeral system. The concept was applied to areas such as profit margins, barters, money changing, conversion of weights and measures, partnerships, and interests.
His other book called “Practica Geometriae” also helped many artisans as it instructed its readers on how to compute with Pisan units of measure, find square and cube roots, determine dimensions of both rectilinear and curved surfaces and solids, work with tables for indirect measurement, and perhaps fire the imagination of builders with analyses of pentagons and decagons. And “Liber Quadratorum”
established the Fibonacci’s identity or Brahmagupta’s identity (an Indian mathematician who earlier came to the same conclusion) i.e the product of two sums of two squares is itself a sum of two squares e.g. (1^2 + 4^2) (2^2 + 7^2) = 26^2 + 15^2 = 30^2 + 1^2
Another one of his great contributions to mathematics was the “Fibonacci Sequence”. The number sequence was derived from a question from Liber Abaci - “A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?”. This gave rise to the first recursive number sequence (the relation between successive
terms can be displayed by a formula) known to Europe - Fn = Fn-1 + Fn-2 i.e a term is equal to the sum of the two previous terms. This discovery proved to have many interesting mathematical properties.
The Fibonacci numbers are omnipresent; they are found all around nature: many species of flowering plants have their numbers of petals in the Fibonacci Sequence; the spiral arrangements of pineapples, and those of pinecones, also in the seeds of sunflower heads. It can even be found in shells, flowers, animal horns, human bodies, storm systems and even complete galaxies. The real-life application of this sequence in the today’s world is found in stock market analysis to estimate the action that the price of a particular stock will take, based on certain ratios found within the sequence and in computer programming to design recursive algorithms.
The ratio between two consecutive terms of the sequence is approximately equal to the Golden Ratio φ (phi) which is an irrational number. This ratio was used by many architects and artists when considering proportionality as they proved to be aesthetically pleasing.
Although these properties of the sequence were not discovered by Fibonacci himself, he did provide everyone with a base for endless exploration.
By Aashi Mehta
Bibliography:
https://www.storyofmathematics.com/medieval_fibonacci.html
https://www.britannica.com/biography/Fibonacci
https://www.maa.org/press/periodicals/convergence/mathematical-treasure-fibonacci-s-practica-
geometriae
https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1043&context=ucareresearch
https://www.webopedia.com/TERM/F/Fibonacci_numbers.html
