Population Growth
The Fibonacci series was discovered by studying population growth
Population growth is also related to the Fibonacci series. It was the question of
how fast rabbits could breed under ideal circumstances that Leonardo Fibonacci originally
investigated in the year 1202. Here was the question he posed:

Suppose a newborn pair of rabbits, one male and one female, is put in the wild. The
rabbits mate at the age of one month and at the end of its second month a female can
produce another pair of rabbits. Suppose that the rabbits never die and that each female
always produces one new pair, with one male and one female, every month from the second
month on. How many pairs will there be in one year? 
The answer is found in series of numbers now known as the Fibonacci
series. Picture that pair A of rabbits gives birth to pairs B, C, D and E.
Each of these in turn begins to give birth to other pairs B1, B2, B3, C1, and C2, who in
turn give birth to B11, etc. At the end of each month, the total population of
rabbits will be a number in the Fibonacci series:
Month 
Rabbits from A: 
from B: 
from C: 
D: 
B1: 
Total 
0 
A 












1 
1 
A 












1 
2 
A 
B 











2 
3 
A 
B 
C 










3 
4 
A 
B 
C 
D 


B1 






5 
5 
A 
B 
C 
D 
E 

B1 
B2 

C1 



8 
6 
A 
B 
C 
D 
E 
F 
B1 
B2 
B3 
C1 
C2 
D1 
B11 
13 
etc. 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
etc. 
The Fibonacci series can be used to predict urban populations
It appears that the Fibonacci series can even be used to predict
populations of major cities, as shown by the relationships of various U.S. urban areas in
1970:
Area 
Census
Rank 
Actual
Population 
Predicted Population 
Method 1 
Method 2 
New York, NE NJ 
1 
16,206,841 


LA Long Beach CA 
2 
8,351,266 
10,016,379 
10,016,379 
Chicago NW IN 
3 
6,714,578 
6,190,462 
5,161,366 
Detroit, MI 
5 
3,970,584 
3,825,916 
4,149,837 
Washington DC 
8 
2,481,459 
2,364,546 
2,453,956 
Houston, TX 
13 
1,677,863 
1,461,370 
1,533,626 
Cincinnati, OH 
21 
1,110,514 
903,176 
1,036,976 
Dayton, OH 
34 
685,942 
558,194 
686,335 
Richmond, VA 
55 
416,563 
344,983 
423,935 
Las Vegas, NV 
89 
236,681 
213,211 
257,450 
New London, CT 
144 
139,121 
131,772 
146,277 
Great Falls, MT 
233 
70,905 
81,439 
85,982 
Method 1 takes the population of the largest city and divides it again
and again by phi. Method 2 takes the population of each successive city and divides
it by phi. 