Applied Science - Science and Math (6B) Pre Lab
 OBJECTIVES: Exploring how mathematical sequences are found in nature. Investigating the Fibonacci Sequence. VOCABULARY: mathematicians sequence series MATERIALS:  worksheet Students determine Fibonacci sequences.
 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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