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)
