Feynman point

Feynman point

The Feynman point is the sequence of six 9s which begins at the 762nd decimal place of π. It is named after physicist Richard 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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