- Feynman point
The Feynman point is the sequence of six 9s which begins at the 762nd decimal place of
π . It is named after physicistRichard Feynman , who once stated during a lecture he would like to memorize the digits of π until that point, so he could recite them and quip "nine nine nine nine nine nine and so on."Arndt, J. and Haenel, C. "Pi — Unleashed". Springer, p. 3, 2001. ISBN 3-540-66572-2.] Wells, D. "The Penguin Dictionary of Curious and Interesting Numbers". Middlesex, England: Penguin Books, p. 51, 1986. ISBN 0-14-026149-4.] The humorous irony of this statement is the suggestion that π is in fact rational, since this is falsely implied by an apparently infinitely recurring sequence of 9s.Full decimal expansion
The full digits of π up to and including the Feynman point are as follows. [ [http://www.joyofpi.com/pi.html The Digits of Pi — First ten thousand] ]
Related statistics
For a randomly chosen real number, the probability of six 9s occurring this early in the decimal representation is only 0.08%.
The next sequence of six consecutive digits is again composed of 9s, starting at position 193,034. The next distinct sequence of six consecutive digits starts with 8 at position 222,299. Of the remaining digits, 0 is the last to first repeat 6 times, starting at position 1,699,927.
The Feynman point is also the first occurrence of four and five consecutive digits. The next appearance of four consecutive digits is of the digit 7 at position 1,589. [See, for example, the online [http://www.angio.net/pi/bigpi.cgi Pi Search] .]
The positions of the first occurrences of strings of 1, 2, ..., 9 consecutive 9s are 5; 44; 762; 762; 762; 762; 1,722,776; 36,356,642; and 564,665,206; respectively OEIS|id=A048940.
References
ee also
*
Piphilology
*Richard Feynman
*Repdigit External links
* [http://mathworld.wolfram.com/FeynmanPoint.html Feynman Point Mathworld Article] — From the
Mathworld project.
* [http://www.angio.net/pi/piquery The Pi-Search Page] — Search the digits of pi.
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