Friday, May 30, 2014

Weekly 4: History of Fibonacci

For this post, let's explore the history of Fibonacci. Leonardo Pisano (Fibonacci) was born on 1170 to Guglielmo Bonacci, a merchant of some kind. Fibonacci was educated in Bejaia, Algeria in North Africa (where his father worked). Fibonacci actually was enrolled in Bejaia's school of accounting. From all of Fibonacci and his fathers travels, Fibonacci learned the Hindu-Arabic number system, the system we use today. He was one of the first people to introduce the number system to Europe. His book on how to do operations in the new number system was called the Liber abbaci. This book convinced many mathematicians, and others, in Europe to start using the new number system. Actually, much of the book had to do with accounting mathematics: price of goods, how to calculate profit, currency conversion, etc... This number system seems very natural to us. In class it was very difficult to perform operations using roman numerals. I tried to do it and I pretty much was fed up after the first problem. I couldn't imagine doing every day operations in those cruel roman numerals. It's amazing that Fibonacci could even understand more than one number system. But, for me the truly astonishing thing Fibonacci did was to actually recognize that the Hindu-Arabic number system was easier to use. As we have seen, any new number system is hard to get used to, but to recognize one is easier than another seems so difficult. Who knows, maybe our grand children will be learning a different number system than the one we learned (hope not). 

Fibonacci presented many problems in his Liber abbaci, including the one about bunnies we studied in class. Out of this problem came the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc...

As we have seen in our math 495 class, the Fibonacci sequence has a lot to do with the golden ratio. For instance, if you take any two successive numbers in the Fibonacci sequence, the ratio gets closer and closer to the golden ratio. The golden ration also has ties to finance, biology, architecture, and many other areas. There are so many interesting things in nature that deal with the golden ratio, but this post is about Fibonacci. If you wan't to learn more about nature and the golden ration, you should read this article

Fibonacci's book also discussed perfect numbers, rational approximations of square roots of numbers, and sums of arithmetic and geometric series. This may be his most famous book, but another one of his works was Liber quadratorum. Here he discussed number theory including Pythagorean triples, square numbers, and interesting number theory results such as

there is no x, y such that x^2 + y^2 and x^2 - y^2 are both squares.

Since Fibonacci lived before printing, it was difficult to keep some of his original works. Some of his papers were actually lost, including his book on commercial arithmetic Di minor guisa.

Frederick II (the holy roman emperor at the time) actually was aware of Fibonacci because the Emperor's scholars corresponded with him after his return to Pisa in 1200 A.D. One of those scholars, Johannes of Palermo, gave some problems as challenges to Fibonacci. Fibonacci solved three of these problems and gave the solutions in his book Flos which he sent to Frederick II. I never knew mathematicians were so competitive back in the day. I imagine there was trash talking going on all over the intellectual community back then. Actually, when I think about it, we do have math competitions today in colleges and high schools; though I have yet to hear trash talk going on in my math classes. We'll save the trash talk for Richard Sherman

Fibonacci was a very important figure in mathematics and history in general. The Hindu-Arabic number system he brought to Europe was so important in the study of mathematics, science, business, and pretty much any discipline that used numbers (which was like all of them). The Fibonacci sequence is probably the most popular of all sequences because of how much of it is related to science and nature. I hope you enjoyed this non-rigorous post on Fibonacci. I usually like to post proofs and other interesting math theorems, but I'm so thankful for Fibonacci that I thought a brief biography would be nice.


Leonardo Pisano Fibonacci (JOC/EFR, October 1998 School of Mathematics and Statistics, University of      St. Andrews, Scotland)

Nature, The Golden Ration, and Fibonacci too (Copyright © 2011

1 comment:

  1. I'm actually a fan of some good math trash talk.

    Good Fibonacci coverage. Like your point about recognizing the value of one system over another - insightful.

    5C's +