Download fibonacci numbers

FIBONACCI NUMBERS
Names _________________________
Period _____
The first fifteen Fibonacci numbers are:
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610
1. What sort of number is every third term?
2. Choose any three consecutive Fibonacci numbers. Multiply the first by the
third. Square the second. Repeat this for other groups of three. Write
what you notice?
3. Choose any four consecutive Fibonacci numbers. Multiply the first by the
fourth. Multiply the second by the third. Repeat for other groups of four.
Write what you notice.
4. If T1 = the first term, T2 = the second term, T3 = the third term and so on:
a)
b)
c)
d)
Find the sum of the first four terms. Compare the total with T6.
Add the first five terms. Compare the total with T7.
Add the first six terms. Compare the total with T8.
Without adding, find the sum of the first 12 terms.
5. Find the next ten terms in the sequence:
Fibonacci Rabbits
Fibonacci described his numbers using a rabbit breeding analogy. After 2 months, a pair of rabbits will breed
and create a new pair of rabbits, and they will continue to create one new pair each month after that. So start
with couple A in the first month. After month 2 they are old enough to breed. They will create a new pair in
month 3 (call the new pair couple B). In month 4, A will create another pair (couple C), but B is not old enough
yet. In month 5, A creates again (couple D), and B is finally old enough to create too (couple E), but C is not old
enough yet. Complete the table to calculate and prove the total number of pairs of rabbits after 8 months.
Month
1
2
3
4
5
6
7
8
Reproducing Pairs
Young Pairs
A
A
B
B C
C D E
A
A
A B
Total Pairs
What does this have to do with the Golden Ratio?
This sequence of numbers was first discovered by a man named Leonardo Fibonacci, and hence is known
as Fibonacci’s Sequence. The relationship of this sequence to the Golden Ratio lies not in the actual
numbers of the sequence, but in the ratio of the consecutive numbers. Let’s look at some of these ratios:
2/1=
8/5=
34/21=
3/2=
13/8=
55/34=
5/3=
21/13=
89/55=
What do you notice?
What do you think will happen if we continue to look at the ratios as the numbers in the sequence get
larger and larger?
How Golden are You?
Measure (in centimeters) and record the following for each member of your group:
Name
A
Fingertip to Elbow
Who is the most Golden of your group?
B
Wrist to Elbow
Ratio
A/B