Sunday, June 5, 2016

History of Math - Fibonacci

Leonardo Pisano is one of he greatest and most important mathematicians in mathematical history. That name might confuse you since thew title of this post is Fibonacci. You would expect that this post is about Fibonacci. This post is about Fibonacci! His real name is Leonardo of Pisa. The name Fibonacci is short for "Filis Bonacci" which means " son of Bonnaccio" (his father's name was Guglielmo Bonaccio). Fibonacci is pictured below.

Fibonacci had a huge impact on math and changed the course of math history. During the early 1200s, Europeans were still using Roman Numerals. It was Fibonnaci that started to convince Europe that they should use the Arabic symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. He used his book "Liber abbaci (meaning Book of the Abacus or Book of Calculating) to persuade the Europeans to use this system. In the book he explains how to do the 4 basic math operations (add, subtract, multiply, and divide) using his new system. Many of us today would find it comical that professional mathematicians had to learn these basic operations but we have to remember that this was a completely new system. It was like learning another language. You are not going to pick it up with a lot of hard work and studying. 

This new system allowed us to perform these basic operations much easier than using Roman Numerals. It also saved us alot of space because numbers like 1994 are writen as MDCCCCLXXXXIIII in Roman Numerals. If you want to see how difficult it was using Roman Numerals in Math follow this link

When we hear the name Fibonacci, the first thing that comes to mind is the Fibonacci numbers. That would make sense as it is mostly what he is known for (not as many people know he helped move us away from Roman Numerals). In his book "Liber Abbaci" put in the "Rabbit problem" and the solution below.

How Many Pairs of Rabbits Are Created by One Pair in One Year
A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also.

Here is the solution according to Fibonacci: 

Because the above written pair in the first month bore, you will double it; there will be two pairs in one month.
One of these, namely the first, bears in the second month, and thus there are in the second month 3 pairs;
of these in one month two are pregnant and in the third month 2 pairs of rabbits are born, and thus there are 5 pairs in the month;
there will be 144 pairs in this [the tenth] month;
to these are added again the 89 pairs that are born in the eleventh month; there will be 233 pairs in this month.
To these are still added the 144 pairs that are born in the last month; there will be 377 pairs, and this many pairs are produced from the above written pair in the mentioned place at the end of the one year.You can indeed see in the margin how we operated, namely that we added the first number to the second, namely the 1 to the 2, and the second to the third, and the third to the fourth and the fourth to the fifth, and thus one after another until we added the tenth to the eleventh, namely the 144 to the 233, and we had the above written sum of rabbits, namely 377, and thus you can in order find it for an unending number of months.

From this we get the Fibonacci sequence of 1, 1, 2, 3, 5, 8, 13......etc. While Fibonacci studied the Arabic system of numbers, he also studied the arithmetic application of the new numbers from some other local countries. So it is quite possible that he did not invent the problem or the series that is named after him. He was simply the man who showed it to the rest of the world and that is probably why it is named after him.

The concept of the Fibonacci sequence gives us this idea of recursive. For something to be recursive, it means that it has to be based on something previously done. We can see that the Fibonacci numbers are recursive. It takes the 2 previous numbers, adds them together, and that gives you the next number.

As we can see Fibonacci was quite important. He allowed us to move away from Roman Numerals which saved us a lot of time. Imagine some of the crazy calculations we would have had to make if we were still using Roman Numerals. Mathematical proofs would be exponentially longer if they were written using Roman Numerals. Fibonacci was able to show the world the Fibonacci Sequence that also introduced us to the idea of something being recursive. He has had and will continue to have a lasting impact on the world of mathematics


  1. clear: there's a weird font change
    complete: cite your source for the Fibonacci quotes.

    The idea of the what the number system means to mathematics is a big idea and worth some more attention. Proofs would be longer, but that's not really a problem. (Or why is it?) (Content)

    C's: 3/5
    coherent, consolidated, complete +

  2. Thanks for sharing Marty. I actually did not know (or didnt remember) Fibonacci's real name :) I am grateful that we do not explicitly use the Roman numeral system for computations and proofs, you are right, that would be time consuming! The only thing that kind of seems misleading to me is that this post makes me feel like, if I did not have any idea who he was, that the most important work of Fibonacci is the fact that we do not always have to use Roman Numberals.