MathNovatory/Pure Maths/Fibonacci Numbers/History

A Short History of Fibonacci Numbers

The Fibonacci numbers first appeared, under the name mātrāmeru (mountain of cadence), in the work of the Sanskrit grammarian Pingala (Chandah-shāstra, the Art of Prosody, 450 or 200 BC). Prosody was important in ancient Indian ritual because of an emphasis on the purity of utterance. The Indian mathematician Virahanka (6th century AD) showed how the Fibonacci sequence arose in the analysis of meters with long and short syllables. Subsequently, the Jain philosopher Hemachandra (c.1150) composed a well-known text on these. A commentary on Virahanka's work by Gopāla in the 12th century also revisits the problem in some detail. (Wikipedia)

The book on arithmetic, the Liber Abaci (1202), by Leonardo Pisano (also known as Fibonacci) contained a puzzle for the breeding of rabbits. He considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that :

  • in the first month there is just one newly-born pair
  • new-born pairs become fertile from their second month on
  • each month every fertile pair begets a new pair
  • the rabbits never die
  • This problem is often poorly resolved by getting off to a bad start in the first month, ending the month with 2 pairs instead of only 1. The answer seems to be 233 pairs at the end of 12 months and not 377 pairs. We have found no indication that Pisano was aware of the Indian work previously accomplished.

    San Jose
    The Fibonacci Association, incorporated in 1963, focuses on Fibonacci numbers and related mathematics, emphasizing new results, research proposals, challenging problems, and new proofs of old ideas. It is located in San Jose State University, San Jose, California. Principal publications include the Fibonacci Quarterly and A Primer For The Fibonacci Numbers, in which we find the rabbit problem, uniquely quantitative use of Fibonacci numbers (only positive values) and indiscriminately equal importance attached to the Lucas numbers.

    On a site called, launched in 2007, the qualitative structure of the Fibonacci series is exposed in all its splendor, leading to a new form of "Fibonacci division" which has been programmed into a Fibonacci divisor. Will the international attention on the Fibonacci series be gradually shifting to Montreal?