The Symmetry of the Markets—Beautiful By Any Name (Part 2)

01/29/2008 12:00 am EST


Timothy Morge


The Fibonacci number series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. actually first appeared, under the name matrameru (mountain of cadence), in the work of the Sanskrit grammarian Pingala (Chandah-shastra, 'The Art of Prosody', 450 or 200 BC). Prosody was important in ancient Indian ritual because of an emphasis on the purity of utterance. Later, Leonardo of Pisa used this same series of numbers in his biological treatise 'Liber Abaci'. He considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that:

  1. In the first month there is just one newly-born pair,
  2. New-born pairs become fertile from their second month on,
  3. Each month every fertile pair begets a new pair, and
  4. The rabbits never die.

It was Johannes Kepler that later observed that the ratio of consecutive Fibonacci numbers converges. He wrote that "as 5 is to 8 so is 8 to 13, practically, and as 8 is to 13, so is 13 to 21 almost", and concluded that the limit approaches the golden ratio 1.618 or d [pronounced 'Fee']. But where did the Golden Ratio come from and how is it related to these other mathematical numbers traders commonly call 'Fib numbers'?

More tomorrow in Part 3.

By Timothy Morge email

Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers" 1986. ISSN 0047-6269], "The So-called Fibonacci numbers in ancient and medieval India." Sigler, Laurence E. (trans.) (2002). Fibonacci's Liber Abaci. Springer-Verlag. ISBN 0-387-95419-8.

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