For my book I read Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World, by Keith Devlin. The author recounts his journey to Europe and Italy and along the way tells of his discoveries about Fibonacci. The story paints a portrait of a brilliant mathematician whose work not only drastically advanced Mathematics, but drastically advanced civilization. In this post I will talk briefly about the biographical details of Fibonacci’s life, but focus more on his work and some of the more fascinating tidbits I got from text. Fibonacci was born in Pisa, Italy around 1170 as Leonardo Pisano (Leonardo of Pisa). Fibonacci is actually a nickname and the contraction of “filius Bonacci”, meaning “Son of Bonacci”. His father, Bonacci, was merchant, in the trade hub of the western world. Fibonacci then spent several years of his youth in Northern Africa. This is where he learned the invention that would make him renown. After this Fibonacci went back to Italy where he remained for his life. His death is unknown, but it is speculated to have been in the 1240s in Pisa.
The invention that Fibonacci learned in Africa, was a new way to write and calculate numbers. Being the son of a merchant, Fibonacci applied the hindu-arabic system to bookkeeping, showing the practical applications of the new system. He then wrote the book Liber Abaci, a detailed textbook on how to it works, as well as many story problems showing the various applications. This book was hand copied over and over and was used to teach basically all of Europe the system. Before this, merchants were using roman numerals and finger counting methods to keep track of their business. Using the numbers 0-9 and place counting as well as the use of an abacus led to growth of accounting and trading in Europe. This whole topic was very interesting to me as it shows how mathematics drastically changed the world. It really emphasizes to me that at it’s core, mathematics is a tool that we use to advance and grow. Mathematics is such an abstract concept yet it’s applications are so real, it just takes a mind like Fibonacci to realize these applications and the potential it has to change the world. Fibonacci also must have had an incredible work ethic and a very strong feeling about this topic as he put his entire life’s work into it. I will end this blogpost with an example of a problem and solution in Liber Abaci given by the author.
A certain man buys 30 birds which are partridges, pigeons, and sparrows, for 30 denari. A partridge he buys for 3 denari, a pigeon for 2 denari, and 2 sparrows for 1 denaro, namely 1 sparrow for 1/2 denaro. It is sought how many birds he buys of each kind.
You can start by assigning x,y, and z to the number of partridges, pigeons, and sparrows, and you can come up with the equations:
x+y+z=30 (the total number of birds is 30)
3x+2y+1/2z=30 (the price of the birds is 30).
The author notes that two equations with three variables, seems unsolvable at first, but then hints that x,y, and z must be non-zero positive whole numbers. By doubling the second equation you get:
Subtracting the first equation from the second gives us
The trick now is that since 5 divides the first and the third term, it also must divide y. Therefore, y must be 5, 10, 15, … etc. But as x is positive and non zero, y cannot be 10 or larger, thus y is 5. It follows that x=3 and z=22. Tricky!
The hard step for me to understand was deducing that y must be a multiple of 5. Thinking about it though, it makes sense, the first term has to be one of 5, 10, 15, 20, … and the last term must also be 5, 10, 15, 20, 25, 30, … So it makes sense that you must add in multiples of 5 to the first term to get to the third term. I believe this is an example of modular arithmetic!