Read aloud Generations of mathematicians have broken their teeth on the question: Do all digits and number sequences occur equally often in the decimal places of the circle number Pi or are certain numbers preferred? David Bailey of the Lawrence Berkeley National Laboratory, along with his colleague Richard Crandall, has now found an infinite number of numbers that are random and resemble Pi in a certain sense. The two mathematicians present their work in a pre-publication. The bad news: For Pi itself, the evidence of randomness is still missing. But the numbers found by Bailey and Crandall have in common with Pi that one can compute any decimal place of these numbers with a calculation rule, without knowing the decimal places before it. The calculation rule for Pi Bailey had found himself in 1996 with two Canadian colleagues. The existence of such a calculation procedure had previously been considered impossible.

Last year, Bailey and Crandall had discovered that this computational rule produced a certain kind of sequence of numbers that? as an unproven hypothesis from chaos theory claims? uniformly distributed between 0 and 1 (wissenschaft.de reported about it). The exciting thing about this discovery was that if this hypothesis from chaos theory is really correct, then it automatically proves the randomness of Pi.

The circle number Pi, which indicates the ratio of the circumference of a circle to its diameter, has been known for at least 4, 000 years. From a biblical passage in the First Book of Kings (7, 23), probably from the year 950 BC. For Pi, the value is 3. Archimedes (287-212 BC) gave Pi a value between 3.1408 and 3.1428. Today Pi is known to a few hundred billion decimal places. The first 10, 000 digits can be found here. A chronology for calculating Pi can be found here.

If you want to know how many decimal places of Pi the number sequence of his birthday appears, click here. display

Axel Tilleman

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