If you wanted a random number, historically you could do worse than to pick a sequence from the string of digits in pi. But Purdue University scientists now say other sources might be better.
Physicists including Purdue’s Ephraim Fischbach have completed a study comparing the "randomness" in pi to that produced by 30 software random number generators and one chaos-generating physical machine. After conducting several tests, they have found that while sequences of digits from pi are indeed an acceptable source of randomness – often an important factor in data encryption and in solving certain physics problems – pi’s digit string does not always produce randomness as effectively as manufactured generators do. "We do not believe these results imply anything about a pattern existing in pi’s number set," said Fischbach, who is a professor of physics in Purdue’s College of Science. "However, it may imply that if your livelihood depends on a reliable source of random numbers, as a cryptographer’s might, then some commercially available random number generators might serve you better."
Fischbach conducted the study with Shu-Ju Tu, a former graduate student who has since moved to a postdoctoral fellowship at the University of Texas M.D. Anderson Cancer Center. Their research paper appears in the International Journal of Modern Physics C, vol. 16, no. 2. Pi, the ratio between a circle’s diameter and circumference, has fascinated mathematicians for centuries. A bit larger than the number 3, pi cannot be expressed as a ratio of two whole numbers, and its apparently endless string of digits is sometimes expressed as 3.14159… Modern computers have enabled mathematicians to calculate the value of pi to more than 200 billion digits to the right of the decimal point. But no one has ever found evidence that calculating finer and finer values of pi will ever reveal an end to the string or that there is any regular pattern to be found within it.
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