"Fibonacci at Random," by Ivars Peterson. Science News, 12 June 1999,pages 376-377.
Mathematicians have known for centuries that the ratios of successiveterms in the Fibonacci sequence approach the so-called Golden Ratio1.6180339887... Now, computer scientist Divakar Viswanath has taken afresh look at Fibonacci numbers and has discovered a new constant.
Viswanath added randomness to the Fibonacci sequence. One versionis as follows: at each step of the sequence, flip a coin. If itcomes up heads, add the two previous numbers in the sequence to producethe next term. If it is tails, subtract the last term from theprevious term. Vismanath found that if he considered the absolutevalues of the resulting terms in the sequence, the nth term isapproximately equal to the number 1.13198824... to the nth power.
It is not obvious that this should happen, Viswanath claims, and arigorous proof of the result was difficult. But upon its completion,Viswanath gave mathematics a new constant.
--- Benjamin Stein