Fibonacci!

FIBONACCI

Fibonacci was a merchant in the late thirteenth century who made very valuable contributions to mathematics. In his book, Liber Abaci (published in 1306) he proposed the use of arabic numerals, which are still the numbers we use today. One of his other contributions was the famous Rabbit Problem.

Imagine a male and a female rabbit in a closed environment. Furthermore, assume that a pair of rabbits can mate after only one month. Additionally, the offspring will always be one male and one female. If rabbits never die, how many rabbits will there be after a year?

The answer leads to "Fibonacci's Sequence", one of the most prolific occurences in nature. The total number of rabbits, cummulatively, is:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...
This is a very interesting pattern, despite the elegance of its simplicity. Each number is the sum of the previous two numbers. The ratio of two consecutive numbers is .618, known as phi, or Ø. This number appears repeatedly in nature, including: trees, leaves, pinecones, pineapples, sunflowers, rivers, DNA, architecture, music, petals of flowers, and a wide variety of other places.

The above image accurately demonstrates the Golden Rectangle, a collection of rectangles with sides whose lengths are numbers from Fibonacci's Sequence. This Golden Rectangle has been the blueprint for famous buildings and pieces of art. It is often accepted as the "most appealing rectangle". Even the Chamber Nautilus subscribes to the proportions prescribed by this rectangle. Check out this website, a wonderful exploration of Fibonacci and his work.

Fibonacci