The Fibonacci sequence was discovered by studying population growth.
Population growth is also related to the Fibonacci series. In 1202, Leonardo Fibonacci investigated the question of how fast rabbits could breed under ideal circumstances. Here is the question that 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. 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. Pair A of rabbits gives birth to pairs B, C, D and E. Each of these new pairs in turn gives 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|
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:
|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|
|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.
In biology, once an egg is fertilized, it divides and multiplies in count until it reaches a point at which the ratio of the succeeding number of cells to the previous number of cells is phi (1.618 …).