BACKGROUND:
Scientists and mathematicians
are always looking for connections in math and science. They collect
and analyze data to see if a pattern emerges. If a mathematical model
of an experiment can be created, it usually reveals that a scientist has
discovered something.
An example of a sequence that
has many natural counterparts is the Fibonacci Sequence. This number
series was named for Leonard Fibonacci (1180-1228). He discovered
a sequence that is based on the idea that each term in it is the sum of
the two preceding numbers. For example, the following is the Fibonacci
Sequence: 1,1,2,3,5,8,13,21,34,55,89,144 which is derived from 1,
1, 2=(1+1), 3=(1+2), 5=(2+3), 8=(3+5), 13=(5+8).
The Fibonacci Sequence was found
to be extremely important in the scientific field of genetics. The
Fibonacci Sequence is found to measure the fraction of a turn between successive
leaves on the stalk of a plant: 1/2 for grasses, 1/3 for sedges, 2/5 for
the apple and cherry, 3/8 for plantain, and 5/13 for the leek. There
are also many other examples from genetics.
PROCEDURE:
- Ask students
what "naturally" means. They may reply "something that grows without
the aid of humans." Then ask if nature designs itself mathematically.
Students should think back on some of the previous years in science and
remember that natural objects usually have a mathematical pattern.
- The worksheet has a
few examples of Fibonacci sequences for the students to work out.
See if the students can make their own. You may also do a search
on the Internet on Fibonacci, and you will be surprised how many links
there are.
- ANSWERS:
- 1,1,2,3,5,8,13,21,34,55,89,144
- 2,4,6,8,10,12,14,16,18,20
- 1,3,5,7,9,11,13,15,17,19
- 1,2,4,7,11,16,22,29,37
(Add 1 to the first number,
add 2 to the second number, add 3 to the third number, etc)
- 1,6,11,16,21,26,31,36,41
- 1,4,9,16,25,36,49,64,81
[Each number is squared (times
by itself)]
- 1,1/2,1/4,1/8,1/16,1/32,1/64,1/128
(Each number is equal to 1/2
o the preceding number)
- 100,95,90,85,80,75,70,65
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