By: Vino Raditio Wibowo, Alvi Khairin Nisa, Muhammad Aditya Ferdito, and Safiratul Hasanah
(Student Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Andalas University)
LEONARDO PISANO also known as Fibonacci is one of the most talented mathematicians of the Middle Ages. He was born in Pisa (now Italy) around 1170. His name at birth was Leonardo, but because he was7 the son of Guglielmo Bonacci, so he was often called Leonardo Fibonacci.
Fibonacci followed his father who held a diplomatic post in North Africa. His father’s job was to represent the merchants of the Republic of Pisa who were trading in Bugia, now called Bejaia.
In North Africa, he was educated by customs and moors.
The trip with his father provided Fibonacci an advantage in learning the mathematical systems of each country he visited.
He enabled him to get to know different cultures and numerical systems.
Fibonacci learned an Arabic system of numbers that he would eventually develop into a Fibonacci sequence.
Fibonacci returned to Pisa around 1200. In Pisa, he began to write notes that were then made into books. The notes Fibonacci wrote played a key role in developing ancient mathematical skills as well as having a significant impact on himself.
At the time, there was no printing, so Fibonacci wrote the book in person. The first book to come out is Liber Abaci. The book Liber Abaci opens to European knowledge of the current use of numbers.
The book Liber Abaci includes the introduction of the Hindu-Arabic numerical system on page 2 which opens with the phrase “These are the nine addresses of the Indians 9, 8, 7, 6, 5, 4, 3, 2, 1. And so, with these nine copies, and with the symbol 0, which is called zephyr in Arabic, whatever number you please can be written, as is below us.”
Fibonacci applies this Hindu-Arabic numeration to count the profit margin, the barter, the change of money, the conversion of weight and size, partnership, and interest.
Apart from Hindu-Arabic numerals, it also contains a Roman writing number with a new system, an algorithm for doing arithmetic with Hindu-Arabic numerals, some counting tables and multiplication tables on page 6, and the rabbit problem of loading the delete known today as the Fibonacci sequence starting at the bottom of page 283 and also on page 240.
The rabbit problem begins with the Fibonacci question, “Beginning with a pair of rabbits (one male and one female), how many pairs of rabbits will be born in a year if each month each male and female gives birth to a new pair of rabbits after just one month?”
And then answered in the book’s Fibonacci answer,” In the first month there is only one pair, in the second month there is one adult pair and one baby set, in the third month there will be two adult pairs and one baby set, and then there will be two pairs of adults and one set of babies, and then there will be two pairs of adults and one set of babies, and so on.”
So Fibonacci’s questions and answers come from a number called the Fibonacci sequence of 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 500, and so on. From the sequence comes the conclusion that a Fibonacci pattern is a sequence of numbers with the next number value derived from adding both previous numbers in a row and then can be described in the formula: = +
Another Fibonacci book is Practica Geometriae which appeared in the 1220s. If translated, the book has the meaning of the practice of geometry. Geometry opened with a letter dedicated to Domenico Ispano, an important figure in Frederick II’s palace.
The contents of the book are a collection of geometry problems, which are organized into eight chapters on the theorems based on Euclid and the Euclid divisions.
The other two books published after geometry are Flosi and Liber Quadratorum. Flosi and Liber Quadratorum occurred in 1225.
Fibonacci in Flosi’s book provides an accurate approach to the roots of: In the book Liber Quadratorum, there is a theory of numbers.
Fibonacci in the book Liber Quadratorum deals with the resolving of rational numbers of various equations involving squared.
A. FIBONACCI CONTRIBUTIONS
Leonardo Fibonacci’s contributions are not limited to mathematics alone, he also contributes significantly to other fields of science.
1). Fibonacci’s contributions to the world of mathematics.
Through his book Liber Abaci, he introduced the use of Arabic numerals and the Hindu-Arabic local decimal system to Europe. Furthermore, Fibonacci’s key inventions include Fibonacci numbers and the Fibonacci sequence.
Fibonacci numbers are numbers obtained by adding up the previous two numbers. That means, 0+1=1, then 1+1=2, 1+2=3, 2+3=5, etc.
Whereas the Fibonacci sequence is a number pattern that lists Fibonacci numbers such as 0, 1, 1, 2, 3, 5, 8, 13, and 21 in a specific sequence.
Fibonacci numbers are also related to the golden ratio. The golden ratio is the relationship between two adjacent numbers in the Fibonacci sequence.
Source: Golden Ratio (https://www.bluebeaconcreative.com/wpcontent/uploads/2022/11/1651459167210.jpeg)
2). Fibonacci’s contributions to the music world.
The Fibonacci Sequence holds significance within Western harmony and musical scales, influencing various elements:
a). An octave on the piano comprises 13 notes, with eight being white keys and five black keys.
b). A scale consists of eight notes, where the third and fifth notes establish a fundamental chord.
c). Within a scale, the dominant note, which is the fifth note, coincides with the eighth note among the 13 notes in an octave.
Source: Piano used Fibonacci sequence (https://www.classicfm.com/discovermusic/fibonacci-sequence-in-music/)
d). The ratio of eight divided by 13 approximates the Golden Ratio as 0.61538…
e). These numerical elements 3, 5, 8, 13 are part of the recognizable pattern found within the Fibonacci Sequence.
f). Such famous musicians as Beethoven and Mozart often use the Fibonacci pattern in their music. This number pattern can be seen in the tempo (speed) and rhythm of a song arranged by the Fibonacci sequence.
3). Fibonacci’s contributions to nature.
This pattern is also seen in the structure of living things, such as flowers, coconut shells, and snails.
Source: Fibonacci sequence seen in the flower (https://clevelanddesign.com/insights/the-nature-of-design-the-fibonacci-sequence-and-the-golden-ratio/)
Fibonacci numbers are also used to make glass houses, crop seed patterns, and textiles.
4). Fibonacci’s contributions to the Fibonacci art world also influence art.
In the art world, the Fibonacci sequence relating to golden ratios is used to guide layout, to set picture composition, to manage typography, design, etc. Over time, art using Fibonacci sequence became more beautiful.
Source: The Mona Lisa used Fibonacci sequence (https://img.bndlyr.com/ns1votvt5w/_assets/n4spfxv4ku0nib2y4u4hqu.jpg?fit=fill&w=920)
B. FIBONACCI ACHIEVEMENT
The city of Pisa (technically a republic at that time) honored Fibonacci and granted him a salary in 1240 for his help in advising Pisa and its citizens on accounting issues (Deb Russel, 2019).
REFERENCE
Bryan, M. (2023, December 30). Fibonacci Facts. Retrieved January 1, 2024, from Facts.net: https://facts.net/fibonacci-facts/
Gies, F. C. (2023, December 22). Fibonacci. Retrieved December 30, 2023, from Britannica: https://www.britannica.com/biography/Fibonacci
Huffman, C. J. (2017). Mathematical Treasure: Fibonacci’s Liber Abaci. . Retrieved December 3, 2023, from Mathematical Association of America: https://maa.org/press/periodicals/convergence/mathematical-treasure-fibonacci-s-liber-abaci
Hughes, B. (2008). Fibonacci’s De practica geometrie. New York: Springer.
Norval, E. (2020, January 16). The Golden Ratio And Fibonacci Sequence In Art. Retrieved December 30, 2023, from https://www.compulsivecontents.com/detail-event/the-golden-ratio-and-fibonacci-sequence-in-art/
O’Connor, J.J and E.F Robertson. (1998). Leonardo Pisano Fibonacci. Retrieved December 4, 2023, from MacTutor: https://mathshistory.st-andrews.ac.uk/Biographies/Fibonacci/
Rizzi, S. (2022, May 20). What is the Fibonacci Sequence – and why is it the secret to musical greatness? Retrieved December 30, 2023, from Classic Fm: https://www.classicfm.com/discover-music/fibonacci-sequence-in-music/
Sigler, L. (2002). Fibonacci’s Liber Abaci (A Translation into Modern English of Leonardo Pisano’s Book of Calculation). New York: Springer.
