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"Fibonacci at Random," by Ivars Peterson. Science News, 12 June 1999, pages 376-377.
Mathematicians have known for centuries that the ratios of successive terms in the Fibonacci sequence approach the so-called Golden Ratio 1.6180339887... Now, computer scientist Divakar Viswanath has taken a fresh look at Fibonacci numbers and has discovered a new constant.
Viswanath added randomness to the Fibonacci sequence. One version is as follows: at each step of the sequence, flip a coin. If it comes up heads, add the two previous numbers in the sequence to produce the next term. If it is tails, subtract the last term from the previous term. Vismanath found that if he considered the absolute values of the resulting terms in the sequence, the nth term is approximately equal to the number 1.13198824... to the nth power.
It is not obvious that this should happen, Viswanath claims, and a rigorous proof of the result was difficult. But upon its completion, Viswanath gave mathematics a new constant.
--- Benjamin Stein
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