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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.

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