Math + Biography:

The Fibonacci Numbers

 

            Today's Snack: Take a handful of grapes, and count them out in little groups in this sequence: 1, 1, 2, 3, 5 and 8. Now eat them up! Then read about what that sequence means in the story of Fibonacci. Since he was Italian, drink some grape juice in his honor, as grapes are an important product of Italy!

 

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Supplies:

Whole pineapple, pine cone, Shasta daisy if available

World map or globe

Scratch paper and pencil

 

 

A fascinating and important person in math history was known by the name of Fibonacci. His real name was Leonardo of Pisa. He lived in the Italian city of Pisa from 1170 to 1250. He is known as probably the most famous European mathematician of the Middle Ages.

 

 

As a boy, he traveled with his father, who was a merchant, to what we now call Algiers in North Africa. There, he started studying math. At the time, the Arabs were ahead of the Europeans in math. Fibonacci traveled around the Arab world studying with various math experts for many years. Then he returned to Europe and helped popularize their important concepts. (Can you find these places on a world map or globe?)

 

Two of his best accomplishments are: (1) bringing the decimal system of numbers (Hindu-Arabic, which is now 0,1,2,3 etc.) to Europe in place of Roman numerals, which made calculations much easier, and (2) popularizing a unique sequence of numbers which shows a high degree of order in nature and is frequently expressed in everything from architecture to works of art.

 

In Roman numbers, letters represent different quantities. V means 5, X means 10, L means 50, and so on. Fibonacci helped advance mathematics in Europe by bringing the decimal system, based on 10, and the numerical symbols we use today, including zero, which Europe didn't have back then.

 

            The sequence of numbers, now referred to as "Fibonacci Numbers," actually had been discovered centuries earlier, but he explained them for European audiences and helped expand the concept.

 

            The Fibonacci sequence is a series of numbers in which each new number is the sum of the previous two numbers. It starts like this:

 

0, 1, 1, 2, 3, 5, 8, 13, 21 . . .

 

            Take some scratch paper and figure out what the next three numbers are in the sequence. Answers at bottom!

 

            The Fibonacci sequence is interesting to view as a graphic. It has a lot to reveal in the way of showing different relationships between numbers, and proportion between numbers:

 

 

 

            What is really fascinating is how the Fibonacci Numbers are found in nature. It's easiest to trace the sequence in a whole pineapple, a pine cone, and a Shasta daisy (if in bloom outside, or available from a florist). You can examine those things after you look at this link, which shows the sequence as it appears in nature. This shows how Fibonacci was able to see his list of numbers, in order, over and over again in nature:

 

http://britton.disted.camosun.bc.ca/fibslide/jbfibslide.htm

 

           

            See if you recognize any of these references to the Fibonacci Sequence in popular culture:

 

http://en.wikipedia.org/wiki/Fibonacci_numbers_in_popular_culture

 

 

(Answers to next 3 numbers in sequence: 34, 55, 89)